Invariant and dual subtraction games resolving the Duch\^e-Rigo conjecture

We prove a recent conjecture of Duch\^ene and Rigo, stating that every complementary pair of homogeneous Beatty sequences represents the solution to an \emph{invariant} impartial game. Here invariance means that each available move in a game can be played anywhere inside the game-board. In fact, we establish such a result for a wider class of pairs of complementary sequences, and in the process generalize the notion of a \emph{subtraction game}. Given a pair of complementary sequences $(a_n)$ and $(b_n)$ of positive integers, we define a game $G$ by setting $\{\{a_n, b_n\}\}$ as invariant moves. We then introduce the invariant game $G^\star$, whose moves are all non-zero $P$-positions of $G$. Provided the set of non-zero $P$-positions of $G^\star$ equals $\{\{a_n,b_n\}\}$, this \emph{is} the desired invariant game. We give sufficient conditions on the initial pair of sequences for this 'duality' to hold.Comment: 11 pages, 2 figure

Fuel cells for power generation and organic waste treatment on the island of Mull

In-situ use of biomass and organic waste streams have the potential to provide the key to energy self sustainability for islands and remote communities. Traditionally biogas fuels have been used in combustion engines for electric power generation. However, fuel cells offer the prospect of achieving higher generating efficiencies, and additionally, important environmental benefits can be achieved by way of mitigating greenhouse gas emissions, whilst providing a carbon sink. This paper presents the design details of a biogas gas plant and fuel cell installation that will provide a practical solution on an island (and be applicable in other remote and rural areas) where connection to the grid can be expensive, and where biofuels can be produced on site at no significant extra cost

Antiphase dynamics in a multimode semiconductor laser with optical injection

A detailed experimental study of antiphase dynamics in a two-mode semiconductor laser with optical injection is presented. The device is a specially designed Fabry-Perot laser that supports two primary modes with a THz frequency spacing. Injection in one of the primary modes of the device leads to a rich variety of single and two-mode dynamical scenarios, which are reproduced with remarkable accuracy by a four dimensional rate equation model. Numerical bifurcation analysis reveals the importance of torus bifurcations in mediating transitions to antiphase dynamics and of saddle-node of limit cycle bifurcations in switching of the dynamics between single and two-mode regimes.Comment: 7 pages, 9 figure

The Role of Gestures in Mental Animation

We examined the use of hand gestures while people solved spatial reasoning problems in which they had to infer how components of a mechanical device will move from a static diagram of the device (mental animation problems). In Experiment 1, participants were asked to think aloud while solving mental animation problems. They gestured on more than 90% of problems, and most gestures expressed information about the component motions that was not stated in words. Two further experiments examined whether the gestures functioned in the mechanical inference process, or whether they merely served functions of expressing or communicating the results of this process. In these experiments, we examined the effects of instructions to think aloud, restricting participants' hand motions, and secondary tasks on mental animation performance. Although participants who were instructed to think aloud gestured more than control groups, some gestures occurred even in control conditions. A concurrent spatial tapping task impaired performance on mechanical reasoning, whereas a simple tapping task and restricting hand motions did not. These results indicate that gestures are a natural way of expressing the results of mental animation processes and suggest that spatial working memory and premotor representations are involved in mental animation. They provide no direct evidence that gestures are functional in the thought process itself, but do not rule out a role for overt gestures in this type of spatial thinking

Flight test pilot evaluation of a delayed flap approach procedure

Using NASA's CV-990 aircraft, a delayed flap approach procedure was demonstrated to nine guest pilots from the air transport industry. Four demonstration flights and 37 approaches were conducted under VFR weather conditions. A limited pilot evaluation of the delayed flap procedure was obtained from pilot comments and from questionaires they completed. Pilot acceptability, pilot workload, and ATC compatibility were quantitatively rated. The delayed flap procedure was shown to be feasible, and suggestions for further development work were obtained

Delayed flap approach procedures for noise abatement and fuel conservation

The NASA/Ames Research Center is currently investigating the delayed flap approach during which pilot actions are determined and prescribed by an onboard digital computer. The onboard digital computer determines the proper timing for the deployment of the landing gear and flaps based on the existing winds and airplane gross weight. Advisory commands are displayed to the pilot. The approach is flown along the conventional ILS glide slope but is initiated at a higher airspeed and in a clean aircraft configuration that allows for low thrust and results in reduced noise and fuel consumption. Topics discussed include operational procedures, pilot acceptability of these procedures, and fuel/noise benefits resulting from flight tests and simulation

Flight tests of IFR landing approach systems for helicopters

Joint NASA/FAA helicopter flight tests were conducted to investigate airborne radar approaches (ARA) and microwave landing system (MLS) approaches. Flight-test results were utilized to prove NASA with a data base to be used as a performance measure for advanced guidance and navigation concepts, and to provide FAA with data for establishment of TERPS criteria. The first flight-test investigation consisted of helicopter IFR approaches to offshore oil rigs in the Gulf of Mexico, using weather/mapping radar, operational pilots, and a Bell 212 helicopter. The second flight-test investigation consisted of IFR MLS approaches at Crows Landing (near Ames Research Center), with a Bell UH-1H helicopter, using NASA, FAA, and operational industry pilots. Tests are described and results discussed

Quantitative sensory testing in children with sickle cell disease: additional insights and future possibilities.

Quantitative sensory testing (QST) is used in a variety of pain disorders to characterize pain and predict prognosis and response to specific therapies. In this study, we aimed to confirm results in the literature documenting altered QST thresholds in sickle cell disease (SCD) and assess the test-retest reliability of results over time. Fifty-seven SCD and 60 control subjects aged 8-20 years underwent heat and cold detection and pain threshold testing using a Medoc TSAII. Participants were tested at baseline and 3 months; SCD subjects were additionally tested at 6 months. An important facet of our study was the development and use of a novel QST modelling approach, allowing us to model all data together across modalities. We have not demonstrated significant differences in thermal thresholds between subjects with SCD and controls. Thermal thresholds were consistent over a 3- to 6-month period. Subjects on whom hydroxycarbamide (HC) was initiated shortly before or after baseline testing (new HC users) exhibited progressive decreases in thermal sensitivity from baseline to 6 months, suggesting that thermal testing may be sensitive to effective therapy to prevent vasoocclusive pain. These findings inform the use of QST as an endpoint in the evaluation of preventative pain therapies