Cutting A Pie Is Not A Piece Of Cake

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and better for at least one)? David Gale first asked this question for pies. We provide complete answers for both cakes and pies. The answers depend on the number of players (two versus three or more players) and whether the players' preferences satisfy certain continuity assumptions. We also give some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. We suggest possible applications and conclude with two open questions

Fast switching current detection at low critical currents

A pulse-and-hold technique is used to measure the switching of small critical current Josephson junctions. This technique allows one to achieve a good binary detection and therefore measure switching probabilities. The technique overcomes limitations on simple square pulses and allows for the measurement of junctions with critical currents of the order of 10nA with bias pulses of the order of 100ns. A correlation analysis of the switching events is performed to show how the switching probability depends on the wait time between repeated bias pulses.Comment: Changed abstract Added reference 1

Error bounds on block Gauss Seidel solutions of coupled\ud multiphysics problems

Mathematical models in many fields often consist of coupled sub–models, each of which describe a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub–models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss–Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss–Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non–linear coupled fluid–temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss–Seidel iteration.\ud \ud Copyright c 2000 John Wiley & Sons, Ltd

Singular order parameter interaction at nematic quantum critical point in two dimensional electron systems

We analyze the infrared behavior of effective N-point interactions between order parameter fluctuations for nematic and other quantum critical electron systems with a scalar order parameter in two dimensions. The interactions exhibit a singular momentum and energy dependence and thus cannot be represented by local vertices. They diverge for all N greater or equal 4 in a collinear static limit, where energy variables scale to zero faster than momenta, and momenta become increasingly collinear. The degree of divergence is not reduced by any cancellations and renders all N-point interactions marginal. A truncation of the order parameter action at quartic or any other finite order is therefore not justified. The same conclusion can be drawn for the effective action describing fermions coupled to a U(1) gauge field in two dimensions.Comment: 18 pages, 1 figur

Research needs for Chagas disease prevention.

We present an overview of the two main strategies for the primary (vector control) and secondary (patient care) prevention of Chagas disease (CD). We identify major advances, knowledge gaps, and key research needs in both areas. Improved specific chemotherapy, including more practical formulations (e.g., paediatric) or combinations of existing drugs, and a better understanding of pathogenesis, including the relative weights of parasite and host genetic makeup, are clearly needed. Regarding CD vectors, we find that only about 10-20% of published papers on triatomines deal directly with disease control. We pinpoint the pitfalls of the current consensus on triatomine systematics, particularly within the Triatomini, and suggest how some straightforward sampling and analytical strategies would improve research on vector ecology, naturally leading to sounder control-surveillance schemes. We conclude that sustained research on CD prevention is still crucial. In the past, it provided not only the know-how, but also the critical mass of scientists needed to foster and consolidate CD prevention programmes; in the future, both patient care and long-term vector control would nonetheless benefit from more sharply focused, problem-oriented research

The Integral Burst Alert System (IBAS)

We describe the INTEGRAL Burst Alert System (IBAS): the automatic software for the rapid distribution of the coordinates of the Gamma-Ray Bursts detected by INTEGRAL. IBAS is implemented as a ground based system, working on the near-real time telemetry stream. During the first six months of operations, six GRB have been detected in the field of view of the INTEGRAL instruments and localized by IBAS. Positions with an accuracy of a few arcminutes are currently distributed by IBAS to the community for follow-up observations within a few tens of seconds of the event.Comment: 7 pages, latex, 5 figures, Accepted for publication on A&A Special Issue on First Science with INTEGRA