The leafage of a chordal graph

The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n - lg n - (1/2) lg lg n + O(1). The proper leafage l*(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and lower bounds on l*(G). Leafage equals proper leafage on claw-free chordal graphs. We use asteroidal sets and structural properties of chordal graphs.Comment: 19 pages, 3 figure

Quantum MHV diagrams

Over the past two years, the use of on-shell techniques has deepened our understanding of the S-matrix of gauge theories and led to the calculation of many new scattering amplitudes. In these notes we review a particular on-shell method developed recently, the quantum MHV diagrams, and discuss applications to one-loop amplitudes. Furthermore, we briefly discuss the application of D-dimensional generalised unitarity to the calculation of scattering amplitudes in non-supersymmetric Yang-Mills

An Economic Theory of the Glass Ceiling

The glass ceiling is one of the most controversial and emotive aspects of employment in organisations. This paper provides a model of the glass ceiling that exhibits the following features that are frequently thought to characterise the problem: (i) there is a lower number of female employees in higher positions, (ii) women have to work harder than men to obtain equivalent jobs, (iii) women are then paid less than men when promoted, and (iv) some organisations are more female friendly than others. These features emerge as an equilibrium phenomenon, when identical firms compete in "Bertrand-like" fashion. Furthermore, they also occur even when offering women the same contract as men in higher positions would be sufficient to ensure that women in those positions would always prefer permanent career over non-market alternatives.Glass Ceiling, Promotions, Career Options

An Economic Theory of Glass Ceiling

In the 'glass ceiling' debate there appear to be two strongly held and opposing interpretations of the evidence, one suggesting it is really the result of gender differences and the other that there is discrimination by gender. This paper provides an economic theory of the glass ceiling and one of the main insights of our analysis is that in some real sense these two interpretations are not in conflict with each other. The glass ceiling emerges as an equilibrium phenomenon when firms compete à la Bertrand even though employers know that offering women the same contract as men would be sufficient to erase all differences among promoted workers. The model also provides new insights into anti-discrimination policy measures. (Updated from working paper 07/183)glass ceilings, promotions, career options

A lens-coupled scintillation counter in cryogenic environment

In this work we present an elegant solution for a scintillation counter to be integrated into a cryogenic system. Its distinguishing feature is the absence of a continuous light guide coupling the scintillation and the photodetector parts, operating at cryogenic and room temperatures respectively. The prototype detector consists of a plastic scintillator with glued-in wavelength-shifting fiber located inside a cryostat, a Geiger-mode Avalanche Photodiode (G-APD) outside the cryostat, and a lens system guiding the scintillation light re-emitted by the fiber to the G-APD through optical windows in the cryostat shields. With a 0.8mm diameter multiclad fiber and a 1mm active area G-APD the coupling efficiency of the "lens light guide" is about 50%. A reliable performance of the detector down to 3K is demonstrated.Comment: 14 pages, 11 figure

Time to Dropout From College: A Hazard Model with Endogenous Waiting

Using data from the 1979 National Longitudinal Survey of Youth (NLSY79), we investigate the college attendance, dropout, and graduate behavior of high school graduates. Bivariate duration models, which allow the unobserved determinants of spell durations to be correlated across spells, are developed and used to study the impact of the waiting time from high school graduation until college enrollment on college dropout and graduation rates. We find that delaying college entry after graduating high school significantly increases the chances of college dropout and reduces the probability of attaining a four-year degree. Among those who first enroll in four-year institutions, delaying college entry by one year after high school graduation reduces the probability of graduating with a four- year degree by up to 32 percent in models that account for the endogeneity of delaying enrollment. There is also empirical evidence that the negative impact of delayed enrollment on graduation probabilities varies by Armed Forces Qualifying Test (AFQT) score with the largest estimated impact of delaying occurring for those with low AFQT scores.

The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [2] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $\Gamma$ in a Hilbert space $H$. We prove the existence and uniqueness of a strong solution of this problem when $\Gamma$ is a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when $\Gamma=K_\alpha$, where $K_\alpha={f\in L^2 (0,1)|f\geq -\alpha},\alpha\geq0$