Reconfiguring Independent Sets in Claw-Free Graphs

We present a polynomial-time algorithm that, given two independent sets in a claw-free graph $G$, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex $v$ from the current independent set $S$ and to add a new vertex $w$ (not in $S$) such that the result is again an independent set. We also consider the more restricted model where $v$ and $w$ have to be adjacent

Potential for measurement of the tensor magnetic polarizability of the deuteron in storage ring experiments

General formulas describing deuteron spin dynamics in storage rings with allowance for the tensor electric and magnetic polarizabilities are derived. It is found that an initially tensor-polarized deuteron beam can acquire a final horizontal vector polarization of the order of 1%. This effect allows one to measure the tensor magnetic polarizability of the deuteron in storage ring experiments. We also confirm an existence of the effect found by Baryshevsky and Gurinovich, hep-ph/0506135 and Baryshevsky, hep-ph/0510158; hep-ph/0603191 that the tensor magnetic polarizability of the deuteron causes the spin rotation with two frequencies and experiences beating for polarized deuteron beams in storage rings.Comment: Corrected text, 8 page

Independent Set Reconfiguration in Cographs

We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both of size at least $k$, is it possible to transform $I$ into $J$ by adding and removing vertices one-by-one, while maintaining an independent set of size at least $k$ throughout? This problem is known to be PSPACE-hard in general. For the case that $G$ is a cograph (i.e. $P_4$-free graph) on $n$ vertices, we show that it can be solved in time $O(n^2)$, and that the length of a shortest reconfiguration sequence from $I$ to $J$ is bounded by $4n-2k$, if such a sequence exists. More generally, we show that if $X$ is a graph class for which (i) TAR-Reachability can be solved efficiently, (ii) maximum independent sets can be computed efficiently, and which satisfies a certain additional property, then the problem can be solved efficiently for any graph that can be obtained from a collection of graphs in $X$ using disjoint union and complete join operations. Chordal graphs are given as an example of such a class $X$

Feedback Systems for Linear Colliders

Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at high bandwidth and fast response. To correct for the motion of individual bunches within a train, both feedforward and feedback systems are planned. SLC experience has shown that feedback systems are an invaluable operational tool for decoupling systems, allowing precision tuning, and providing pulse-to-pulse diagnostics. Feedback systems for the NLC will incorporate the key SLC features and the benefits of advancing technologies.Comment: Invited talk presented at IEEE Particle Accelerator Conference (PAC99

School-based curriculum development in Scotland: Curriculum policy and enactment

Recent worldwide trends in curriculum policy have re-emphasised the role of teachers in school-based curriculum development. Scotland’s Curriculum for Excellence is typical of these trends, stressing that teachers are agents of change. This paper draws upon empirical data to explore school-based curriculum development in response to Curriculum for Excellence. We focus on two case studies – secondary schools within a single Scottish local education authority. In the paper we argue that the nature and extent of innovation in schools is dependent upon teachers being able to make sense of often complex and confusing curriculum policy, including the articulation of a clear vision about what such policy means for education within each school

Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

A very thin havar film vacuum window for heavy ions to perform radiobiology studies at the BNL Tandem

Heavy ion beams from the BNL Tandem Van de Graaff accelerators will be made available for radiobiology studies on cell cultures. Beam energy losses need to be minimized both in the vacuum window and in the air in order to achieve the ranges required for the cells to be studied. This is particularly challenging for ions heavier than iron. The design is presented of a 0.4-inch diameter Havar film window that will satisfy these requirements. Films as thin as 80 microinches were successfully pressure tested. The final thickness to be used may be slightly larger to help in achieving pin hole free windows. We discuss design considerations and present pressure and vacuum test results as well as tests with heavy ion beams

Consumer credit in comparative perspective

We review the literature in sociology and related fields on the fast global growth of consumer credit and debt and the possible explanations for this expansion. We describe the ways people interact with the strongly segmented consumer credit system around the world—more specifically, the way they access credit and the way they are held accountable for their debt. We then report on research on two areas in which consumer credit is consequential: its effects on social relations and on physical and mental health. Throughout the article, we point out national variations and discuss explanations for these differences. We conclude with a brief discussion of the future tasks and challenges of comparative research on consumer credit.Accepted manuscrip

Beam-energy and laser beam-profile monitor at the BNL LINAC

We are developing a non-interceptive beam profile and energy monitor for H{sup -} beams in the high energy beam transport (HEBT) line at the Brookhaven National Lab linac. Electrons that are removed from the beam ions either by laser photodetachment or stripping by background gas are deflected into a Faraday cup. The beam profile is measured by stepping a narrow laser beam across the ion beam and measuring the electron charge vs. transverse laser position. There is a grid in front of the collector that can be biased up to 125kV. The beam energy spectrum is determined by measuring the electron charge vs. grid voltage. Beam electrons have the same velocity as the beam and so have an energy of 1/1836 of the beam protons. A 200MeV H{sup -} beam yields 109keV electrons. Energy measurements can be made with either laser-stripped or gas-stripped electrons