Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

An atomistic simulation of solid state sintering using Monte Carlo methods

This paper presents results on the simulation of the solid state sintering of copper wires using Monte Carlo techniques based on elements of lattice theory and cellular automata. The initial structure is superimposed onto a triangular, two-dimensional lattice, where each lattice site corresponds to either an atom or vacancy. The number of vacancies varies with the simulation temperature, while a cluster of vacancies is a pore. To simulate sintering, lattice sites are picked at random and reoriented in terms of an atomistic model governing mass transport. The probability that an atom has sufficient energy to jump to a vacant lattice site is related to the jump frequency, and hence the diffusion coefficient, while the probability that an atomic jump will be accepted is related to the change in energy of the system as a result of the jump, as determined by the change in the number of nearest neighbours. The jump frequency is also used to relate model time, measured in Monte Carlo Steps, to the actual sintering time. The model incorporates bulk, grain boundary and surface diffusion terms and includes vacancy annihilation on the grain boundaries. The predictions of the model were found to be consistent with experimental data, both in terms of the microstructural evolution and in terms of the sintering time. (C) 2002 Elsevier Science B.V. All rights reserved.

A four-stage index 2 Diagonally Implicit Runge-Kutta method

High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge-Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge-Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions., numerical examples are used to test the proposed method using fixed and variable step size implementations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

The impact of participation in activities while on vacation on senior's psychological well-being: A path model application

This article extends earlier research regarding the relationships between senior travelers’ participation in activities while on vacation, their overall satisfaction with their travel experiences, and their psychological well-being. A path model was developed to depict the direct and indirect relationships between these variables by using a sample of senior tourists traveling on North American escorted tour itineraries. Whereas the direct effect accounted for 98% of the relationships between the senior tourists’ levels of participation in activities and their psychological well-being, the indirect effect was negligible. The study concluded that senior tourists’activity levels were significantly related to their psychological well-being, but their satisfaction with the tours was not.

Estimation of total body water from bioelectrical impedance analysis in patients with pancreatic cancer - agreement between three methods of prediction

Introduction Bioelectrical impedance analysis (BIA) is a useful field measure to estimate total body water (TBW). No prediction formulae have been developed or validated against a reference method in patients with pancreatic cancer. The aim of this study was to assess the agreement between three prediction equations for the estimation of TBW in cachectic patients with pancreatic cancer. Methods Resistance was measured at frequencies of 50 and 200 kHz in 18 outpatients (10 males and eight females, age 70.2 +/- 11.8 years) with pancreatic cancer from two tertiary Australian hospitals. Three published prediction formulae were used to calculate TBW - TBWs developed in surgical patients, TBWca-uw and TBWca-nw developed in underweight and normal weight patients with end-stage cancer. Results There was no significant difference in the TBW estimated by the three prediction equations - TBWs 32.9 +/- 8.3 L, TBWca-nw 36.3 +/- 7.4 L, TBWca-uw 34.6 +/- 7.6 L. At a population level, there is agreement between prediction of TBW in patients with pancreatic cancer estimated from the three equations. The best combination of low bias and narrow limits of agreement was observed when TBW was estimated from the equation developed in the underweight cancer patients relative to the normal weight cancer patients. When no established BIA prediction equation exists, practitioners should utilize an equation developed in a population with similar critical characteristics such as diagnosis, weight loss, body mass index and/or age. Conclusions Further research is required to determine the accuracy of the BIA prediction technique against a reference method in patients with pancreatic cancer.

Control of Aedes vectors of dengue in three provinces of Vietnam by use of Mesocyclops (Copepoda) and community-based methods validated by entomologic, clinical, and serological surveillance

We describe remarkable success in controlling dengue vectors, Aedes aegypti (L.) and Aedes albopictus (Skuse), in 6 communes with 11,675 households and 49,647 people in the northern provinces of Haiphong, Hung Yen, and Nam Dinh in Vietnam. The communes were selected for high-frequency use of large outdoor concrete tanks and wells. These were found to be the source of 49.6-98.4% of Ae. aegypti larvae, which were amenable to treatment with local Mesocyclops, mainly M. woutersi Van der Velde, M. aspericornis (Daday) and M. thermocyclopoides Harada. Knowledge, attitude, and practice surveys were performed to determine whether the communities viewed dengue and dengue hemorrhagic fever as a serious health threat; to determine their knowledge of the etiology, attitudes, and practices regarding control methods including Mesocyclops; and to determine their receptivity to various information methods. On the basis of the knowledge, attitude, and practice data, the community-based dengue control program comprised a system of local leaders, health volunteer teachers, and schoolchildren, supported by health professionals. Recycling of discards for economic gain was enhanced, where appropriate, and this, plus 37 clean-up campaigns, removed small containers unsuitable for Mesocyclops treatment. A previously successful eradication at Phan Boi village (Hung Yen province) was extended to 7 other villages forming Di Su commune (1,750 households) in the current study. Complete control was also achieved in Nghia Hiep (Hung Yen province) and in Xuan Phong (Nam Dinh province); control efficacy was greater than or equal to 99.7% in the other 3 communes (Lac Vien in Haiphong, Nghia Dong, and Xuan Kien in Nam Dinh). Although tanks and wells were the key container types of Ae. aegypti productivity, discarded materials were the source of 51% of the standing crop of Ae. albopictus. Aedes albopictus larvae were eliminated from the 3 Nam Dinh communes, and 86-98% control was achieved in the other 3 communes. Variable dengue attack rates made the clinical and serological comparison of control and untreated communes problematic, but these data indicate that clinical surveillance by itself is inadequate to monitor dengue transmission.

Structure of the gut contents of Trichogramma australicum Girault (Hymenoptera : Trichogrammatidae) larvae fixed in situ in eggs of its host Helicoverpa armigera (Hubner) (Lepidoptera : Noctuidae)

Trichogramma australicum larvae develop most rapidly in younger eggs of its host, the pest lepidopteran Helicoverpa armigera . To establish how the developmental stage of the host affects the diet of T. australicum , larvae were fixed in situ in eggs of H. armigera of different ages and the structure of the egg contents and parasitoid gut contents examined histologically. Larvae feeding on newly laid host eggs contain primarily yolk particles in their gut, while larvae feeding on older hosts contain necrotic cells and yolk particles. The gut of T. australicum larvae does not contain organised tissue remnants, indicating that larvae feed primarily by sucking food into their pharynx and feed best on a mixture of particulate semisolids in a liquid matrix. Secretory structures of T. australicum larvae that could be involved in modifying the host environment were examined. The hindgut is modified to form an anal vesicle with a number of attributes suggesting that it may be a specialised secretory structure. The paired salivary glands open to the exterior via a common duct.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Product form approximations for highly linear loss networks with trunk reservation

Admission controls, such as trunk reservation, are often used in loss networks to optimise their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to finding approximation methods. The Erlang Fixed-Point (EFP) approximation, which is based on an independent blocking assumption, has been used for networks both with and without controls. Several more elaborate approximation methods which account for dependencies in blocking behaviour have been developed for the uncontrolled setting. This paper is an exploratory investigation of extensions and synthesis of these methods to systems with controls, in particular, trunk reservation. In order to isolate the dependency factor, we restrict our attention to a highly linear network. We will compare the performance of the resulting approximations against the benchmark of the EFP approximation extended to the trunk reservation setting. By doing this, we seek to gain insight into the critical factors in constructing an effective approximation. (C) 2003 Elsevier Ltd. All rights reserved.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.