Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles

Given an rc-graph $R$ of permutation $w$ and an rc-graph $Y$ of permutation $v$, we provide an insertion algorithm, which defines an rc-graph $R\leftarrow Y$ in the case when $v$ is a shuffle with the descent at $r$ and $w$ has no descents greater than $r$ or in the case when $v$ is a shuffle, whose shape is a hook. This algorithm gives a combinatorial rule for computing the generalized Littlewood-Richardson coefficients $c^{u}_{wv}$ in the two cases mentioned above.Comment: 22 page

Using Biofeedback in HIV+ Patients

Background - The prevalence of HIV in Washington, DC is estimated to be at least 3%, triple what the World Health Organization defines as an epidemic. Even at that conservative estimate, the number of people living with HIV in the District of Columbia is the highest in the nation. Individuals living with HIV face stigma, anxiety, stress and depression, among a host of other physical and mental effects. Stress has a significant impact on the immune system and a biofeedback program can be of benefit to patients undergoing any stress. Biofeedback is a technique that trains people to improve their health by controlling certain bodily processes that normally happen involuntarily, such as heart rate, blood pressure, muscle tension, and skin temperature, usually with deep breathing and relaxation techniques. Objective – The objective of this project is to work with a small group of HIV+ patients to examine the effects of biofeedback on stress and anxiety levels and heart rate variability, as well as to equip them with a new tool to cope with stress. Additionally, this project serves as a small pilot program to determine how best to implement a similar program on a larger scale. Methods – For this project, I worked with 3 HIV+ patients at Bread for the City under the supervision of Dr. Randi Abramson (Medical Director of Bread for the City). Five 30-minute biofeedback sessions were conducted with each patient using the HeartMath iPad application. Additionally, two surveys (the Perceived Stress Scale and the PROMIS-29) were administered at the first and last session to assess emotional parameters such as stress, depression, and pain. One patient did not complete the final session or survey. Results – While some survey parameters remained unchanged or worsened, some parameters improved after the program. Additionally, all patients provided anecdotal evidence of the benefits they received from the program. Lastly, much was learned about how to implement a program like this on a larger scale, as well as in populations that may be marginalized, oppressed, or disadvantaged. Conclusions – Important takeaways from this project are the implications of a large-scale program of this nature. Many challenges were revealed throughout the study, especially as it pertains to implementing a program like this in marginalized or oppressed populations. However, biofeedback is a simple technique that can be easily incorporated into a patient’s treatment regimen and can have significant benefits for interested patients

The Spectrum of Topologically Massive Quantum Electrodynamics

We discuss the possibility for the spectrum of topologically massive quantum electrodynamics with spinor matter fields to contain unexpected and unusual stable particle excitations for certain values of the topological photon mass. The new field theoretical phenomena arising from this novel spectral structure are briefly discussed.Comment: 14 pages, plain TeX; PUPT-1364, UBCTP 92-03

Investigations of Pairing in Anyon Systems

We investigate pairing instabilities in the Fermi-liquid-like state of a single species of anyons. We describe the anyons as Fermions interacting with a Chern-Simons gauge field and consider the weak coupling limit where their statistics approaches that of Fermions. We show that, within the conventional BCS approach, due to induced repulsive Coulomb and current-current interactions, the attractive Aharonov-Bohm interaction is not sufficient to generate a gap in the Fermion spectrum.Comment: (11 pages, 2 Figures not included