Combinatorics of simple marked mesh patterns in 132-avoiding permutations

We present some combinatorial interpretations for coefficients appearing in series partitioning the permutations avoiding 132 along marked mesh patterns. We identify for patterns in which only one parameter is non zero the combinatorial family in bijection with 132-avoiding permutations and also preserving the statistic counted by the marked mesh pattern.Comment: 11 pages, 6 figures, submitted at FPSAC 201

Lamb Shift in Light Muonic Atoms - Revisited

In connection with recent and proposed experiments, and new theoretical results, my previous calculations of the Lamb shift in muonic hydrogen will be reviewed and compared with other work. In addition, numerical results for muonic deuterium and helium will be presented. Some previously neglected (but very small) effects are included.Comment: 41 pages. This paper has appeared in Annals of Physics, vol. 327, pp 733-763 (2012). The present version has corrected several misprints, and updated some references to take into account new result

Deformed diagonal harmonic polynomials for complex reflection groups

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded W-module, to the undeformed version.Comment: 11 pages, 1 figur

Lamb Shift in Muonic Hydrogen

The Lamb shift in muonic hydrogen continues to be a subject of experimental and theoretical investigation. Here my older work on the subject is updated to provide a complementary calculation of the energies of the 2p-2s transitions in muonic hydrogen.Comment: 15 pages, no figures. 2 small misprints corrected. Published in Phys. Rev.

Geometrically enhanced closed-loop multi-turn sensor devices that enable reliable magnetic domain wall motion

We experimentally realize a sophisticated structure geometry for reliable magnetic domain wall-based multi-turn-counting sensor devices, which we term closed-loop devices that can sense millions of turns. The concept relies on the reliable propagation of domain walls through a cross-shaped intersection of magnetic conduits, to allow the intertwining of loops of the sensor device. As a key step to reach the necessary reliability of the operation, we develop a combination of tilted wires called the syphon structure at the entrances of the cross. We measure the control and reliability of the domain wall propagation individually for cross-shaped intersections, the syphon geometries and finally combinations of the two for various field configurations (strengths and angles). The various measured syphon geometries yield a dependence of the domain wall propagation on the shape that we explain by the effectively acting transverse and longitudinal external applied magnetic fields. The combination of both elements yields a behaviour that cannot be explained by a simple superposition of the individual different maximum field operation values. We identify as an additional process the nucleation of domain walls in the cross, which then allows us to fully gauge the operational parameters. Finally, we demonstrate that by tuning the central dimensions of the cross and choosing the optimum angle for the syphon structure reliable sensor operation is achieved, which paves the way for disruptive multi-turn sensor devices

MEDIUM TO LONG TERM IMPACTS ON FORMER PARTICIPANTS OF THE SHOULDER TO SHOULDER GLOBAL BRIGADES TO ECUADOR

Medium to Long Term Impacts on Former Participants of the Shoulder to Shoulder Global Brigades to Ecuador. International service learning and voluntourism programs in global health evoke benefits for both community and the intervener. While it is clear that the Shoulder to Shoulder Global program at the University of Kentucky provides a service to an economically resource poor community in Santo Domingo, Ecuador, what is unclear is the impact these interprofessional experiences have on the participants that travel with the four times a year health brigades. This study proposes to answer the question of what are the educational, personal and professional impacts that brigade participants experience. Alumni of the Shoulder to Shoulder Global health brigades from 2007 – 2017 were sent a twenty-three question survey to better understand the impact of this program. Seventy-five responses to the quantitative and qualitative questions were received and a chi square analysis was performed of subgroups within the seventy-five respondents. The findings indicate that this program has positively impacted participants in all three areas, with strong evidence to show that the impacts are related to the initial and intermediate outcomes, with more data needed to better assess the long-term program outcomes

On the combinatorics of quadrant marked mesh patterns in 132-avoiding permutations

International audienceThe study of quadrant marked mesh patterns in 132-avoiding permutations was initiated by Kitaev, Remmel and Tiefenbruck. We refine several results of Kitaev, Remmel and Tiefenbruck by giving new combinatorial interpretations for the coefficients that appear in the generating functions for the distribution of quadrant marked mesh patterns in 132-avoiding permutations. In particular , we study quadrant marked mesh patterns where we specify conditions on exactly one of the four possible quadrants in a quadrant marked mesh pattern. We show that for the first two quadrants, certain of these coefficients are counted by elements of Catalan's triangle and give a new combinatorial interpretation of these coefficients for quadrant four. We also give a new bijection between 132-avoiding permutations and non-decreasing parking functions