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

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

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

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

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

Androgen receptor complexes probe DNA for recognition sequences by short random interactions

Owing to the tremendous progress in microscopic imaging of fluorescently labeled proteins in living cells, the insight into the highly dynamic behavior of transcription factors has rapidly increased over the past decade. However, a consistent quantitative scheme of their action is still lacking. Using the androgen receptor (AR) as a model system, we combined three different fluorescence microscopy assays: single-molecule microscopy, photobleaching and correlation spectroscopy, to provide a quantitative model of the action of this transcription factor. This approach enabled us to distinguish two types of AR-DNA binding: very brief interactions, in the order of a few hundred milliseconds, and hormone-induced longer-lasting interactions, with a characteristic binding time of several seconds. In addition, freely mobile ARs were slowed down in the presence of hormone, suggesting the formation of large AR-co-regulator complexes in the nucleoplasm upon hormone activation. Our data suggest a model in which mobile hormone-induced complexes of transcription factors and co-regulators probe DNA by briefly binding at random sites, only forming relatively stable transcription initiation complexes when bound to specific recognition sequences

On the relation of Thomas rotation and angular velocity of reference frames

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in \cite{rindler}, is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper \cite{herrera}, however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of \cite{rindler} is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of \cite{rindler}. Along the way we also establish some general properties of {\it rotating reference frames}, which may be of independent interest.Comment: 14 pages, 2 figure

Spin structure of the nucleon: QCD evolution, lattice results and models

The question how the spin of the nucleon is distributed among its quark and gluon constituents is still a subject of intense investigations. Lattice QCD has progressed to provide information about spin fractions and orbital angular momentum contributions for up- and down-quarks in the proton, at a typical scale \mu^2~4 GeV^2. On the other hand, chiral quark models have traditionally been used for orientation at low momentum scales. In the comparison of such model calculations with experiment or lattice QCD, fixing the model scale and the treatment of scale evolution are essential. In this paper, we present a refined model calculation and a QCD evolution of lattice results up to next-to-next-to-leading order. We compare this approach with the Myhrer-Thomas scenario for resolving the proton spin puzzle.Comment: 11 pages, 6 figures, equation (9) has been corrected leading to a revised figure 1b. Revision matches published versio