Bounds on the diameter of Cayley graphs of the symmetric group

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.Comment: 17 pages, 6 table

Skill Variety, Innovation and New Business Formation

__Abstract__ We extend Lazear’s theory of skills variety and entrepreneurship in three directions. First, we provide a theoretical framework linking new business creation with an entrepreneur’s skill variety. Second, in this model we allow for both generalists and specialists to possess skill variety. Third, we test our model empirically using data from Germany and the Netherlands. Individuals with more varied work experience seems indeed more likely to successfully start up a new business and being a generalist does not seem to be important in this regard. Finally, we find that innovation positively moderates the relationship between having varied experiences, and being successful in starting up a new business. Our conclusion is that entrepreneurs with more varied work experience are more likely to introduce innovations that have not only technical, but also commercial value. Our findings support the notion that entrepreneurship can be learned

Simultaneous neutron reflectometry and infrared reflection absorption spectroscopy (IRRAS) study of mixed monolayer reactions at the air–water interface

The simultaneous application of neutron reflectometry (NR) and infrared reflection absorption spectroscopy (IRRAS) to the study of the oxidation kinetics of organic monolayers at the air–water interface is described for the first time. This advance was possible thanks to the development of a new sample environment that includes a gas-delivery system and is compatible with in situ application of the two techniques within the constraints of short-term neutron beam-line access. We studied the oxidation of monolayers of the mono-molecular film palmitoleic acid and of a binary mixture of oleic (OA) and stearic (SA) acids by gas-phase ozone. We contrast the two highly complementary techniques and demonstrate that IRRAS provides key additional insight into the alignment of surfactant molecules at the air–water interface. We highlight the potential of the more economical and widely available IRRAS technique to complement NR studies. We also found an apparent increase of the NR signal upon oxidation of a mixed SA/OA monolayer, as well as evidence of slow intensity fluctuations of the SA- generated IRRAS signal. We demonstrate how simultaneous NR-IRRAS substantially enhances future studies of increasingly complex surfactant mixtures and their atmospheric surface reactions

Towards c=0 Flows

We discuss some implications of the gravitational dressing of the renormalization group for conformal field theories perturbed by relevant operators. The renormalization group flows are defined with respect to the dilatation operator associated with the $J_0^{(0)}$ mode of the $SL(2,R)$ affine algebra. We discuss the possibility of passing under the $c=25$ barrier along renormalization group flows in some models.Comment: LaTex file, 11 pages, QMW Preprint, QMW 94-2

Learning curve analysis of thoracic endovascular aortic repair in relation to credentialing guidelines

ObjectiveRecently, practice guideline documents have recommended the completion of different levels of interventional experience and 5 or 10 thoracic endovascular aortic cases prior to surgeon credentialing. This study’s purpose was to determine whether these requirements are valid by reviewing three surgeons’ learning curves with thoracic aortic endovascular repairs.MethodsBetween 1998 and 2006, 67 patients underwent emergent or elective endovascular repair of thoracic aortic pathologies by one of three vascular surgeons with extensive experience with catheter manipulation and abdominal aortic endografts. Following standard retrospective review, each surgeon’s learning curve was analyzed using the cumulative sum failure method with a target success rate of 95% derived from the literature. The main outcome variable was primary technical success.ResultsThese 67 patients presented with several pathologies including elective (n = 31) and ruptured (n = 11) thoracic aortic aneurysms, acute dissections or aortic ulcers (n = 10), and acute blunt thoracic aortic trauma (n = 15). The mean age was 65 (range: 20 to 90) and the early (30 day) mortality rate was 19.4% in urgent cases (n = 36) and 0% in elective cases (n = 31). Paraplegia occurred in two patients (3%). Primary technical success was achieved in 62 cases (92.5%) and did not differ between surgeons (92.6%, 91.3%, 94.1%, respectively; P = .9). Each surgeon’s cases were plotted sequentially and the resulting learning curves were similar. Although acceptable outcomes were obtained throughout the study period, improved results, compared with the target success rate, were not achieved until each surgeon treated 5 to 10 patients.ConclusionThis study supports the case volume requirements of the Society for Vascular Surgery credentialing guidelines, which also requires extensive catheter and guidewire experience. With this background in catheter manipulation and endovascular abdominal aortic repair, surgeons can achieve optimal outcomes with thoracic aortic lesions following 5 to 10 cases

On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data

Consider an inviscid Burgers equation whose initial data is a Levy a-stable process Z with a > 1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller than 1/a, as soon as a is close to 1. This gives a negative answer to a conjecture of Janicki and Woyczynski. Along the way, we contradict a recent conjecture of Z. Shi about the lower tails of integrated stable processes

Background Symmetries In Orbifolds With Discrete Wilson Lines

Target space symmetries are studied for orbifold compactified string theories containing Wilson line background fields. The symmetries determined are for those moduli which contribute to the string loop threshold corrections of the gauge coupling constants. The groups found are subgroups of the modular group $PSL(2, Z)$ and depend on the choice of discrete Wilson lines and the shape of the underlying six-dimensional lattice.Comment: 31 pages, QMW--TH--94/0

Structural investigation of sulfobetaines and phospholipid monolayers at the air-water interface

Mixtures of sulfobetaine based lipids with phosphocholine phospholipids are of interest in order to study the interactions between zwitterionic surfactants and the phospholipids present in cell membranes. In this study we have investigated the structure of mixed monolayers of sulfobetaines and phosphocholine phospholipids. The sulfobetaine used has a single 18-carbon tail, and is referred to as SB3-18, and the phospholipid used is DMPC. Surface pressure-area isotherms of the samples were used to determine whether any phase transitions were present during the compression of the monolayers. Neutron and X-ray reflectometry were then used to investigate the structure of these monolayers perpendicular to the interface. We found that the average headgroup and tail layer thickness was reasonably consistent across all mixtures, with a variation of less than 3 Å reported in the total thickness of the monolayers at each surface pressure. However, by selective deuteration of the two components of the monolayers, it was found that the two components have different tail layer thicknesses. For the mixture with equal compositions of DMPC and SB3-18 or with a higher composition of DMPC the tail tilts were found to be constant, resulting in a greater tail layer thickness for SB3-18 due to its longer tail. For the mixture higher in SB3-18 this was not the case, the tail tilt angle for the two components was found to be different and DMPC was found to have a greater tail layer thickness than SB3-18 as a result.</p

Statistical pairwise interaction model of stock market

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.Comment: 11 pages, 8 figure

Moments of the Virtual Photon Structure Function

The photon structure function is a useful testing ground for QCD. It is perturbatively computable apart from a contribution from what is usually called the hadronic component of the photon. There have been many proposals for this nonperturbative part of the real photon structure function. By studying moments of the virtual photon structure function, we explore the extent to which these proposed nonperturbative contributions can be identified experimentally.Comment: LaTeX, 16 pages + 14 compressed and uuencoded postscript figures, UMN-TH-1111/9