On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.

Development and survival of the diamondback moth (Lepidoptera : Plutellidae) at constant and alternating temperatures

Survival and development time from egg to adult emergence of the diamondback moth, Plutella xylostella (L.), were determined at 19 constant and 14 alternating temperature regimes from 4 to 40degreesC. Plutella xylostella developed successfully front egg to adult emergence at constant temperatures from 8 to 32degreesC. At temperatures from 4 to 6degreesC or from 34 to 40degreesC, partial or complete development of individual stages or instars was possible, with third and fourth instars having the widest temperature limits. The insect developed successfully from egg to adult emergence under alternating regimes including temperatures as low as 4degreesC or as high as 38degreesC. The degree-day model, the logistic equation, and the Wang model were used to describe the relationships between temperature and development rate at both constant and alternating temperatures. The degree-day model described the relationships well from 10 to 30degreesC. The logistic equation and the Wang model fit the data well at temperatures 32degreesC. Under alternating regimes, all three models gave good simulations of development in the mid-temperature range, but only the logistic equation gave close simulations in the low temperature range, and none gave close or consistent simulations in the high temperature range. The distribution of development time was described satisfactorily by a Weibull function. These rate and time distribution functions provide tools for simulating population development of P. xylostella over a wide range of temperature conditions.

Competition between disorder and exchange splitting in superconducting ZrZn2

We propose a simple picture for the occurrence of superconductivity and the pressure dependence of the superconducting critical temperature, T-SC, in ZrZn2. According to our hypothesis the pairing potential is independent of pressure, but the exchange splitting, E-xc leads to a pressure dependence in the (spin dependent) density of states at the Fermi level, D-sigma (epsilon(F)). Assuming p-wave pairing T-SC is dependent on D-sigma (epsilonF) which ensures that, in the absence of non-magnetic impurities, T-SC decreases as pressure is applied until it reaches a minimum in the paramagnetic state. Disorder reduces this minimum to zero, this gives the illusion that the superconductivity disappears at the same pressure as ferromagnetism does.

Jointly radial and translation homothetic preferences: generalized constant risk aversion

The paper identifies the structural restrictions on preferences required for them to exhibit both translation homotheticity in particular direction and radial homotheticity. The results are illustrated by an application to an asset allocation problem in the absence of riskless asset.

Diabetes, my constant companion

Forty-five years as a doctor with diabetes has given Alan Stocks personal insight into how to manage life and practice when living with a chronic illness. Diabetes has proved beneficial to his career, rather than a disadvantage.

Pulsed EPR studies of a bacterial sulfite-oxidizing enzyme with pH-invariant hyperfine interactions from exchangeable protons

Variable-frequency pulsed electron paramagnetic resonance studies of the molybdenum(V) center of sulfite dehydrogenase (SDH) clearly show couplings from nearby exchangeable protons that are assigned to a (MoOHn)-O-v group. The hyperfine parameters for these exchangeable protons of SDH are the same at both low and high pH and similar to those for the high-pH forms of sulfite oxidases (SOs) from eukaryotes. The SDH proton parameters are distinctly different from the low-pH forms of chicken and human so.

Hypoxic/ischemic models in newborn piglet: Comparison of constant FiO(2) versus variable FiO(2) delivery

A comparison of a constant (continuous delivery of 4% FiO(2)) and a variable (initial 5% FiO(2) with adjustments to induce low amplitude EEG (LAEEG) and hypotension) hypoxic/ischemic insult was performed to determine which insult was more effective in producing a consistent degree of survivable neuropathological damage in a newborn piglet model of perinatal asphyxia. We also examined which physiological responses contributed to this outcome. Thirty-nine 1-day-old piglets were subjected to either a constant hypoxic/ischemic insult of 30- to 37-min duration or a variable hypoxic/ischemic insult of 30-min low peak amplitude EEG (LAEEG < 5 mu V) including 10 min of low mean arterial blood pressure (MABP < 70% of baseline). Control animals (n = 6) received 21% FiO(2) for the duration of the experiment. At 72 h, the piglets were euthanased, their brains removed and fixed in 4% paraformaldehyde and assessed for hypoxic/ischemic injury by histological analysis. Based on neuropathology scores, piglets were grouped as undamaged or damaged; piglets that did not survive to 72 h were grouped separately as dead. The variable insult resulted in a greater number of piglets with neuropathological damage (undamaged = 12.5%, damaged = 68.75%, dead = 18.75%) while the constant insult resulted in a large proportion of undamaged piglets (undamaged = 50%, damaged = 22.2%, dead = 27.8%). A hypoxic insult varied to maintain peak amplitude EEG < 5 mu V results in a greater number of survivors with a consistent degree of neuropathological damage than a constant hypoxic insult. Physiological variables MABP, LAEEG, pH and arterial base excess were found to be significantly associated with neuropathological outcome. (c) 2006 Elsevier B.V. All rights reserved.

Visualization of Cerenkov radiation and the fields of a moving charge

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and. Cerenkov radiation is a visible consequence of a charged particle travelling through a medium at locally superluminal velocities. The Heaviside-Feynman equations for calculating the magnetic and electric fields of a moving charge have been known for many decades, but it is only recently that the computing power to plot the fields of such a particle has become readily available for student use. This paper investigates and illustrates the calculation of Maxwell's D field in homogeneous isotropic media for arbitrary, including superluminal, constant velocity, and uses the results as a basis for discussing energy transfer in the electromagnetic field.

Muscle metabolism during constant- and alternating-intensity exercise around critical power

Few studies have focused on the metabolic responses to alternating high- and low-intensity exercise and, specifically, compared these responses to those seen during constant-load exercise performed at the same average power output. This study compared muscle metabolic responses between two patterns of exercise during which the intensity was either constant and just below critical power (CP) or that oscillated above and below CP. Six trained males (mean +/- SD age 23.6 +/- 2.6 y) completed two 30-minute bouts of cycling (alternating and constant) at an average intensity equal to 90% of CR The intensity during alternating exercise varied between 158% CP and 73% CP. Biopsy samples from the vastus lateralis muscle were taken before (PRE), at the midpoint and end (POST) of exercise and analysed for glycogen, lactate, PCr and pH. Although these metabolic variables in muscle changed significantly during both patterns of exercise, there were no significant differences (p > 0.05) between constant and alternating exercise for glycogen (PRE: 418.8 +/- 85 vs. 444.3 +/- 70; POST: 220.5 +/- 59 vs. 259.5 +/- 126mmol.kg(-1) dw), lactate (PRE: 8.5 +/- 7.7 vs. 8.5 +/- 8.3; POST: 49.9 +/- 19.0 vs. 42.6 +/- 26.6 mmol.kg(-1)dw), phosphocreatine (PRE: 77.9 +/- 11.6 vs. 75.7 +/- 16.9; POST: 65.8 +/- 12.1 vs. 61.2 +/- 12.7mmol.kg(-1)dw) or pH (PRE: 6.99 +/- 0.12 vs. 6.99 +/- 0.08; POST: 6.86 +/- 0.13 vs. 6.85 +/- 0.06), respectively. There were also no significant differences in blood lactate responses to the two patterns of exercise. These data suggest that, when the average power output is similar, large variations in exercise intensity exert no significant effect on muscle metabolism.

A Constant Torque Micro-Viscometer

We present a technique to measure the viscosity of microscopic volumes of liquid using rotating optical tweezers. The technique can be used when only microlitre (or less) sample volumes are available, for example biological or medical samples, or to make local measurements in complicated micro-structures such as cells. The rotation of the optical tweezers is achieved using the polarisation of the trapping light to rotate a trapped birefringent spherical crystal, called vaterite. Transfer of angular momentum from a circularly polarised beam to the particle causes the rotation. The transmitted light can then be analysed to determine the applied torque to the particle and its rotation rate. The applied torque is determined from the change in the circular polarisation of the beam caused by the vaterite and the rotation rate is used to find the viscous drag on the rotating spherical particle. The viscosity of the surrounding liquid can then be determined. Using this technique we measured the viscosity of liquids at room temperature, which agree well with tabulated values. We also study the local heating effects due to absorption of the trapping laser beam. We report heating of 50-70 K/W in the region of liquid surrounding the particle.