Towards nonlinear quantum Fokker-Planck equations

It is demonstrated how the equilibrium semiclassical approach of Coffey et al. can be improved to describe more correctly the evolution. As a result a new semiclassical Klein-Kramers equation for the Wigner function is derived, which remains quantum for a free quantum Brownian particle as well. It is transformed to a semiclassical Smoluchowski equation, which leads to our semiclassical generalization of the classical Einstein law of Brownian motion derived before. A possibility is discussed how to extend these semiclassical equations to nonlinear quantum Fokker-Planck equations based on the Fisher information

Regularization of the Hamiltonian constraint and the closure of the constraint algebra

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.Comment: 23 pages, epsfig.st

Graphical Evolution of Spin Network States

The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.Comment: 24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections in the final formula in the main body of the paper and in the formula for the Tetrahedral net in the Appendi

A Comparison of the Ovulation Method With the CUE Ovulation Predictor in Determining the Fertile Period

The purpose of this study was to compare the CUE Ovulation Predictor with the ovulation method in determining the fertile period. Eleven regularly ovulating women measured their salivary and vaginal electrical resistance (ER) with the CUE, observed their cervical-vaginal mucus, and measured their urine for a luteinizing hormone (LH) surge on a daily basis. Data from 21 menstrual cycles showed no statistical difference (T= 0.33, p= 0.63) between the CUE fertile period, which ranged from 5 to 10 days (mean = 6.7 days, SD = 1.6), and the fertile period of the ovulation method, which ranged from 4 to 9 days (mean = 6.5 days, SD = 2.0). The CUE has potential as an adjunctive device in the learning and use of natural family planning methods

Brownian markets

Financial market dynamics is rigorously studied via the exact generalized Langevin equation. Assuming market Brownian self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior with a long-time tail, similar to empirical observations. Individual stocks are also described via the generalized Langevin equation. They are classified by their relation to the market memory as heavy, neutral and light stocks, possessing different kinds of autocorrelation functions

Standardization of electroencephalography for multi-site, multi-platform and multi-investigator studies: Insights from the canadian biomarker integration network in depression

Subsequent to global initiatives in mapping the human brain and investigations of neurobiological markers for brain disorders, the number of multi-site studies involving the collection and sharing of large volumes of brain data, including electroencephalography (EEG), has been increasing. Among the complexities of conducting multi-site studies and increasing the shelf life of biological data beyond the original study are timely standardization and documentation of relevant study parameters. We presentthe insights gained and guidelines established within the EEG working group of the Canadian Biomarker Integration Network in Depression (CAN-BIND). CAN-BIND is a multi-site, multi-investigator, and multiproject network supported by the Ontario Brain Institute with access to Brain-CODE, an informatics platform that hosts a multitude of biological data across a growing list of brain pathologies. We describe our approaches and insights on documenting and standardizing parameters across the study design, data collection, monitoring, analysis, integration, knowledge-translation, and data archiving phases of CAN-BIND projects. We introduce a custom-built EEG toolbox to track data preprocessing with open-access for the scientific community. We also evaluate the impact of variation in equipment setup on the accuracy of acquired data. Collectively, this work is intended to inspire establishing comprehensive and standardized guidelines for multi-site studies