Path-integral approach to mutual information calculation for nonlinear communication channel with small second dispersion at large signal-to-noise power ratio

We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and in the leading order in the parameter signal-to-noise ratio (SNR). Further, we find the explicit expression for the mutual information in case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal.Comment: 42 pages, 5 figure

An Innovative Mixed Methods Approach to Studying the Online Health Information Seeking Experiences of Adults With Chronic Health Conditions

This article presents an innovative sequential mixed methods approach to researching the experiences of U.K. adults with chronic health conditions seeking health information online. The use of multiple methods integrated within a single study ensured that the focus of the research was emergent and relevant and ultimately provided a more complete picture of the experience of online health information seeking through joint discussion. This was achieved by communicating both breadth and depth of data relating to the phenomenon. Findings indicate that if the study had used a single research method in isolation, something would have been lost or misunderstood regarding the phenomenon, thus demonstrating the value of each stage within the research design and of the integration of these findings. © The Author(s) 2012

Elementary amenable subgroups of R. Thompson's group F

The subgroup structure of Thompson's group F is not yet fully understood. The group F is a subgroup of the group PL(I) of orientation preserving, piecewise linear self homeomorphisms of the unit interval and this larger group thus also has a poorly understood subgroup structure. It is reasonable to guess that F is the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we explore the complexity of the elementary amenable subgroups of F in an attempt to understand the boundary between the elementary amenable subgroups and the non-elementary amenable. We construct an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.Comment: 20 page

Homotopy bases and finite derivation type for Schutzenberger groups of monoids

Given a finitely presented monoid and a homotopy base for the monoid, and given an arbitrary Schutzenberger group of the monoid, the main result of this paper gives a homotopy base, and presentation, for the Schutzenberger group. In the case that the R-class R' of the Schutzenberger group G(H) has only finitely many H-classes, and there is an element s of the multiplicative right pointwise stabilizer of H, such that under the left action of the monoid on its R-classes the intersection of the orbit of the R-class of s with the inverse orbit of R' is finite, then finiteness of the presentation and of the homotopy base is preserved.Comment: 24 page