Estimating variable returns to scale production frontiers with alternative stochastic assumptions

Two stochastic production frontier models are formulated within the generalized production function framework popularized by Zellner and Revankar (Rev. Econ. Stud. 36 (1969) 241) and Zellner and Ryu (J. Appl. Econometrics 13 (1998) 101). This framework is convenient for parsimonious modeling of a production function with returns to scale specified as a function of output. Two alternatives for introducing the stochastic inefficiency term and the stochastic error are considered. In the first the errors are added to an equation of the form h(log y, theta) = log f (x, beta) where y denotes output, x is a vector of inputs and (theta, beta) are parameters. In the second the equation h(log y,theta) = log f(x, beta) is solved for log y to yield a solution of the form log y = g[theta, log f(x, beta)] and the errors are added to this equation. The latter alternative is novel, but it is needed to preserve the usual definition of firm efficiency. The two alternative stochastic assumptions are considered in conjunction with two returns to scale functions, making a total of four models that are considered. A Bayesian framework for estimating all four models is described. The techniques are applied to USDA state-level data on agricultural output and four inputs. Posterior distributions for all parameters, for firm efficiencies and for the efficiency rankings of firms are obtained. The sensitivity of the results to the returns to scale specification and to the stochastic specification is examined. (c) 2004 Elsevier B.V. All rights reserved.

Exploration of the cell-cycle genes found within the RIKEN FANTOM2 data set

The cell cycle is one of the most fundamental processes within a cell. Phase-dependent expression and cell-cycle checkpoints require a high level of control. A large number of genes with varying functions and modes of action are responsible for this biology. In a targeted exploration of the FANTOM2-Variable Protein Set, a number of mouse homologs to known cell-cycle regulators as well as novel members of cell-cycle families were identified. Focusing on two prototype cell-cycle families, the cyclins and the NIMA-related kinases (NEKs), we believe we have identified all of the mouse members of these families, 24 cyclins and 10 NEKs, and mapped them to ENSEMBL transcripts. To attempt to globally identify all potential cell cycle-related genes within mouse, the MGI (Mouse Genome Database) assignments for the RIKEN Representative Set (RPS) and the results from two homology-based queries were merged. We identified 1415 genes with possible cell-cycle roles, and 1758 potential paralogs. We comment on the genes identified in this screen and evaluate the merits of each approach.

Accuracy of SRM and power tap power monitoring systems for bicycling

Purpose: Although manufacturers of bicycle power monitoring devices SRM and Power Tap (PT) claim accuracy to within 2.5%, there are limited scientific data available in support. The purpose of this investigation was to assess the accuracy of SRM and PT under different conditions. Methods: First, 19 SRM were calibrated, raced for 11 months, and retested using a dynamic CALRIG (50-1000 W at 100 rpm). Second, using the same procedure, five PT were repeat tested on alternate days. Third, the most accurate SRM and PT were tested for the influence of cadence (60, 80, 100, 120 rpm), temperature (8 and 21degreesC) and time (1 h at similar to300 W) on accuracy. Finally, the same SRM and PT were downloaded and compared after random cadence and gear surges using the CALRIG and on a training ride. Results: The mean error scores for SRM and PT factory calibration over a range of 50-1000 W were 2.3 +/- 4.9% and -2.5 +/- 0.5%, respectively. A second set of trials provided stable results for 15 calibrated SRM after 11 months (-0.8 +/- 1.7%), and follow-up testing of all PT units confirmed these findings (-2.7 +/- 0.1%). Accuracy for SRM and PT was not largely influenced by time and cadence; however. power output readings were noticeably influenced by temperature (5.2% for SRM and 8.4% for PT). During field trials, SRM average and max power were 4.8% and 7.3% lower, respectively, compared with PT. Conclusions: When operated according to manufacturers instructions, both SRM and PT offer the coach, athlete, and sport scientist the ability to accurately monitor power output in the lab and the field. Calibration procedures matching performance tests (duration, power, cadence, and temperature) are, however, advised as the error associated with each unit may vary.

Temporal aspects of the VO2 response at the power output associated with VO2peak in well trained cyclists: Implications for interval training prescription

The power output achieved at peak oxygen consumption (VO2 peak) and the time this power can be maintained (i.e., Tmax) have been used in prescribing high-intensity interval training. In this context, the present study examined temporal aspects of the VO2 response to exercise at the cycling power that output well trained cyclists achieve their VO2 peak (i.e., Pmax). Following a progressive exercise test to determine VO2 peak, 43 well trained male cyclists (M age = 25 years, SD = 6; M mass = 75 kg SD = 7; M VO2 peak = 64.8 ml(.)kg(1.)min(-1), SD = 5.2) performed two Tmax tests 1 week apart.1. Values expressed for each participant are means and standard deviations of these two tests. Participants achieved a mean VO2 peak during the Tmax test after 176 s (SD = 40; = 74% of Tmax, SD = 12) and maintained it for 66 s (SD = 39; M = 26% of Tmax, SD = 12). Additionally they obtained mean 95 % of VO2 peak after 147 s (SD = 31; M = 62 % of Tmax, SD = 8) and maintained it for 95 s (SD = 38; M = 38 % of Tmax, SD = 8). These results suggest that 60-70% of Tmax is an appropriate exercise duration for a population of well trained cyclists to attain VO2 peak during exercise at Pmax. However due to intraparticipant variability in the temporal aspects of the VO2 response to exercise at Pmax, future research is needed to examine whether individual high-intensity interval training programs for well trained endurance athletes might best be prescribed according to an athlete's individual VO2 response to exercise at Pmax.

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Modern environmental improvement pathways for the coal power generation industry in Australia

In this work we assess the pathways for environmental improvement by the coal utilization industry for power generation in Australia. In terms of resources, our findings show that coal is a long term resource of concern as coal reserves are likely to last for the next 500 years or more. However, our analysis indicates that evaporation losses of water in power generation will approach 1000 Gl (gigalitres) per year, equivalent to a consumption of half of the Australian residential population. As Australia is the second driest continent on earth, water consumption by power generators is a resource of immediate concern with regards to sustainability. We also show that coal will continue to play a major role in energy generation in Australia and, hence, there is a need to employ new technologies that can minimize environmental impacts. The major technologies to reduce impacts to air, water and soils are addressed. Of major interest, there is a major potential for developing sequestration processes in Australia, in particular by enhanced coal bed methane (ECBM) recovery at the Bowen Basin, South Sydney Basin and Gunnedah Basin. Having said that, CO2 capture technologies require further development to support any sequestration processes in order to comply with the Kyoto Protocol. Current power generation cycles are thermodynamic limited, with 35-40% efficiencies. To move to a high efficiency cycle, it is required to change technologies of which integrated gasification combined cycle plus fuel cell is the most promising, with efficiencies expected to reach 60-65%. However, risks of moving towards an unproven technology means that power generators are likely to continue to use pulverized fuel technologies, aiming at incremental efficiency improvements (business as usual). As a big picture pathway, power generators are likely to play an increasing role in regional development; in particular EcoParks and reclaiming saline water for treatment as pressures to access fresh water supplies will significantly increase.

Implications of seasonal climate forecasts on world wheat trade: a stochastic, dynamic analysis

Improvements in seasonal climate forecasts have potential economic implications for international agriculture. A stochastic, dynamic simulation model of the international wheat economy is developed to estimate the potential effects of seasonal climate forecasts for various countries' wheat production, exports and world trade. Previous studies have generally ignored the stochastic and dynamic aspects of the effects associated with the use of climate forecasts. This study shows the importance of these aspects. In particular with free trade, the use of seasonal forecasts results in increased producer surplus across all exporting countries. In fact, producers appear to capture a large share of the economic surplus created by using the forecasts. Further, the stochastic dimensions suggest that while the expected long-run benefits of seasonal forecasts are positive, considerable year-to-year variation in the distribution of benefits between producers and consumers should be expected. The possibility exists for an economic measure to increase or decrease over a 20-year horizon, depending on the particular sequence of years.

Measuring market power in electricity generation: A long-term perspective using a programming model

This paper focuses on measuring the extent to which market power has been exercised in a recently deregulated electricity generation sector. Our study emphasises the need to consider the concept of market power in a long-run dynamic context. A market power index is constructed focusing on differences between actual market returns and long-run competitive returns, estimated using a programming model devised by the authors. The market power implications of hedge contracts are briefly considered. The state of Queensland Australia is used as a context for the analysis. The results suggest that generators have exercised significant market power since deregulation.

Relationship between laboratory-measured variables and heart rate during an ultra-endurance triathlon

The aim of the present study was to examine the relationship between the performance heart rate during an ultra-endurance triathlon and the heart rate corresponding to several demarcation points measured during laboratory-based progressive cycle ergometry and treadmill running. Less than one month before an ultra-endurance triathlon, 21 well-trained ultra-endurance triathletes (mean +/- s: age 35 +/- 6 years, height 1.77 +/- 0.05 in, mass 74.0 +/- 6.9 kg, (V) over dot O-2peak = 4.75 +/- 0.42 1 center dot min(-1)) performed progressive exercise tests of cycle ergometry and treadmill running for the determination of peak oxygen uptake ((V) over do O-2peak), heart rate corresponding to the first and second ventilatory thresholds, as well as the heart rate deflection point. Portable telemetry units recorded heart rate at 60 s increments throughout the ultra-endurance triathlon. Heart rate during the cycle and run phases of the ultra-endurance triathlon (148 +/- 9 and 143 +/- 13 beats center dot min(-1) respectively) were significantly (P < 0.05) less than the second ventilatory thresholds (160 +/- 13 and 165 +/- 14 beats center dot min(-1) respectively) and heart rate deflection points (170 +/- 13 and 179 +/- 9 beats center dot min(-1) respectively). However, mean heart rate during the cycle and run phases of the ultra-endurance triathlon were significantly related to (r = 0.76 and 0.66; P < 0.01), and not significantly different from, the first ventilatory thresholds (146 +/- 12 and 148 +/- 15 beats center dot min(-1) respectively). Furthermore, the difference between heart rate during the cycle phase of the ultra-endurance triathlon and heart rate at the first ventilatory threshold was related to marathon run time (r = 0.61; P < 0.01) and overall ultra-endurance triathlon time (r = 0.45; P < 0.05). The results suggest that triathletes perform the cycle and run phases of the ultra-endurance triathlon at an exercise intensity near their first ventilatory threshold

Stochastic dynamic programming for election timing: A game theory approach

In this paper, we consider dynamic programming for the election timing in the majoritarian parliamentary system such as in Australia, where the government has a constitutional right to call an early election. This right can give the government an advantage to remain in power for as long as possible by calling an election, when its popularity is high. On the other hand, the opposition's natural objective is to gain power, and it will apply controls termed as "boosts" to reduce the chance of the government being re-elected by introducing policy and economic responses. In this paper, we explore equilibrium solutions to the government, and the opposition strategies in a political game using stochastic dynamic programming. Results are given in terms of the expected remaining life in power, call and boost probabilities at each time at any level of popularity.

Short-term effects of cycle and treadmill training on exercise tolerance in peripheral arterial disease

Background. To explore the efficacy of cycle training in the treatment of intermittent claudication, the present study compared performance and physiologic effects of cycle training with more conventional treadmill walking training in a group of patients with claudication. Method: Forty-two individuals with peripheral arterial disease and intermittent claudication (24 men, 18 women) were stratified by gender and the presence or absence of type 2 diabetes mellitus and then randomized to a treadmill (n = 13), cycle (n = 15), or control group (n = 14). Treadmill and cycle groups trained three times a week for 6 weeks, whereas the control group did not train during this period. Maximal and pain-free exercise times were measured on graded treadmill and cycle tests before and after training. Results. Treadmill training significantly improved maximal and pain-free treadmill walking times but did not improve cycle performance. Cycle training significantly improved maximal cycle time but did not improve treadmill performance. However, there was evidence of a stronger cross-transfer effect between the training modes for patients who reported a common limiting symptom during cycling and walking at baseline. There was also considerable variation in the training response to cycling, and a subgroup of responsive patients in the cycle group improved their walking performance by more than the average response observed in the treadmill group. Conclusion: These findings suggest that cycle exercise is not effective in improving walking performance in all claudication patients but might be an effective alternative to walking in those who exhibit similar limiting symptoms during both types of exercise.