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.

The anodic dissolution of magnesium in chloride and sulphate solutions

The electrochemical behaviour of magnesium was studied in representative chloride and sulphate solutions including NaCl, Na2SO4, NaOH and their mixed solutions, HCl, and H2SO4: (1) by measuring electrochemical polarisation curves, (2) by using electrochemical impedance spectroscopy (EIS), and (3) by simultaneous measurement of hydrogen gas evolution and measurement of magnesium dissolution rates using inductively coupled plasma atomic emission spectrophotometry (ICPEAS). These experiments showed that a partially protective surface film played an important role in the dissolution of magnesium in chloride and sulphate solutions. Furthermore, the experimental data were consistent with the involvement of the intermediate species Mg+ in magnesium dissolution at film imperfections or on a film-free surface. At such sites, magnesium first oxidised electrochemically to the intermediate species Mg+, and then the intermediate species chemically reacted with water to produce hydrogen and Mg2+. The presence of Cl- ions increased the film free area, and accelerated the electrochemical reaction rate from magnesium metal to Mg+. (C) 1997 Elsevier Science Ltd.

ERP 'old/new' effects: memory strength and decisional factor(s)

Event-related potentials (ERPs) were recorded while subjects made old/new recognition judgments on new unstudied words and old words which had been presented at study either once ('weak') or three times ('strong'). The probability of an 'old' response was significantly higher for strong than weak words and significantly higher for weak than new words. Comparisons were made initially between ERPs to new, weak and strong words, and subsequently between ERPs associated with six strength-by-response conditions. The N400 component was found to be modulated by memory trace strength in a graded manner. Its amplitude was most negative in new word ERPs and most positive in strong word ERPs. This 'N400 strength effect' was largest at the left parietal electrode (in ear-referenced ERPs). The amplitude of the late positive complex (LPC) effect was sensitive to decision accuracy (and perhaps confidence). Its amplitude was larger in ERPs evoked by words attracting correct versus incorrect recognition decisions. The LPC effect had a left > right, centro-parietal scalp topography (in ear-referenced ERPs). Hence, whereas, the majority of previous ERP studies of episodic recognition have interpreted results from the perspective of dual-process models, we provide alternative interpretations of N400 and LPC old/new effects in terms of memory strength and decisional factor(s). (C) 2002 Elsevier Science Ltd. All rights reserved.

Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

Restricted mating dispersal and strong breeding group structure in a mid-sized marsupial mammal (Petrogale penicillata)

Ecological genetic studies have demonstrated that spatial patterns of mating dispersal, the dispersal of gametes through mating behaviour, can facilitate inbreeding avoidance and strongly influence the structure of populations, particularly in highly philopatric species. Elements of breeding group dynamics, such as strong structuring and sex-biased dispersal among groups, can also minimize inbreeding and positively influence levels of genetic diversity within populations. Rock-wallabies are highly philopatric mid-sized mammals whose strong dependence on rocky terrain has resulted in series of discreet, small colonies in the landscape. Populations show no signs of inbreeding and maintain high levels of genetic diversity despite strong patterns of limited gene flow within and among colonies. We used this species to investigate the importance of mating dispersal and breeding group structure to inbreeding avoidance within a 'small' population. We examined the spatial patterns of mating dispersal, the extent of kinship within breeding groups, and the degree of relatedness among brush-tailed rock-wallaby breeding pairs within a colony in southeast Queensland. Parentage data revealed remarkably restricted mating dispersal and strong breeding group structuring for a mid-sized mammal. Breeding groups showed significant levels of female kinship with evidence of male dispersal among groups. We found no evidence for inbreeding avoidance through mate choice; however, anecdotal data suggest the importance of life history traits to inbreeding avoidance between first-degree relatives. We suggest that the restricted pattern of mating dispersal and strong breeding group structuring facilitates inbreeding avoidance within colonies. These results provide insight into the population structure and maintenance of genetic diversity within colonies of the threatened brush-tailed rock-wallaby.

Modeling diffraction in free-space optical interconnects by the mode expansion method

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka et al. [IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems. (C) 2003 Optical Society of America.

Phase diagram of the three-band half-filled Cu-O two-leg ladder

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu d(x)(2)-y(2) and the O p(x) and p(y) orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

Refinement-robust fairness

We motivate and study the robustness of fairness notions under refinement of transitions and places in Petri nets. We show that the classical notions of weak and strong fairness are not robust and we propose a hierarchy of increasingly strong, refinement-robust fairness notions. That hierarchy is based on the conflict structure of transitions, which characterizes the interplay between choice and synchronization in a fairness notion. Our fairness notions are defined on non-sequential runs, but we show that the most important notions can be easily expressed on sequential runs as well. The hierarchy is further motivated by a brief discussion on the computational power of the fairness notions.

The chemical composition of α cen A: Strong lines and the ABO theory of collisional line broadening

The mean abundances of Mg, Si, Ca, Ti, Cr, and Fe based on both strong and weak lines of alpha CenAare determined by matching the observed line profiles with those synthesised from stellar atmospheric models and comparing these results with a similar analysis for the Sun. There is good agreement between the abundances from strong and weak lines. Strong lines should generally be an excellent indicator of abundance and far easier to measure than the weak lines normally used. Until the development of the Anstee, Barklem, and O'Mara ( ABO) theory for collisional line broadening, the uncertainty in the value of the damping constant prevented strong lines being used for abundance determinations other than in close differential analyses. We found that alpha Cen A has a mean overabundance of 0.12 +/- 0.06 dex compared to solar mean abundances. This result agrees remarkably well with previous studies that did not use strong lines or the ABO theory for collisional line broadening. Our result supports the conclusion that reliable abundances can be derived from strong lines provided this new theory for line broadening is used to calculate the van derWaals damping.

A model of migrants' remittances with human capital investment and intrafamilial transfers

This study analyzes data on migrants' remittances using a two-period theory of intergenerational transfers based on an informal, intrafamilial loan arrangement using weak altruism, a behavior between strong altruism and pure self-interest. The model provides an integrated theory of migrants' remittances, human capital investment decisions, and intrafamilial transfers applicable to low-income countries with no official pension schemes and imperfect capital markets. Propositions, derived from the theory, are tested, re-analyzing original survey data on remittances of Pacific island migrants in Sydney. When weak altruism and strong altruism yield opposite predictions, the econometric results tend to confirm the former hypothesis and invalidate the latter.

Photodegradation of irinotecan (CPT-11) in aqueous solutions: Identification of fluorescent products and influence of solution composition

The photodegradation of irinotecan (CPT-11), the semisynthetic derivative of the antitumor alkaloid 20(S)-camptothecin, has been investigated. The drug was exposed to laboratory light for up to 5 days in 0.9% saline solution (pH 8.5). Five significant photodegradation products were observed and a high-performance liquid chromatography (HPLC) assay was employed to isolate them from CPT-11 using gradient conditions. The structures were elucidated by nuclear magnetic resonance spectroscopy and tandem mass spectrometry and shown to be the result of extensive modifications of the lactone ring of CPT-11. Three of the compounds were found to belong to the mappicine group of alkaloids. In addition, the effect of light on the stability of CPT-11 in aqueous solutions and biological fluids was also assessed, Potassium phosphate buffers (0.05 M, pH 5.0-8.2) and saline, plasma, urine, and bile solutions containing 20 mu M CPT-11 were equilibrated in the dark for 24 h before being exposed to laboratory light for up to 171 h at ambient temperature. Four of the five identified photodegradation products were observed and quantitated by isocratic HPLC, using a different detection mode (fluorescence) than the one used for gradient elution, In general, CPT-11 was found to be unstable under neutral and alkaline conditions for all solutions investigated, with the exception of bile. We conclude that CPT-11 is photolabile and that care should be taken to protect samples, particularly those intended for the isolation and identification of novel metabolites of CPT-11.

Spatial structure and habitat variation in a grasshopper hybrid zone

A hybrid zone between the grasshoppers Chorthippus brunneus and C. jacobsi (Orthoptera: Acrididae) in northern Spain has been analyzed for variation in morphology and ecology. These species are readily distinguished by the number of stridulatory pegs on the hind femur. Both sexes are fully winged and inhabit disturbed habitats throughout the study area. We develop a maximum-likelihood approach to fitting a two-dimensional cline to geographical variation in quantitative traits and for estimating associations of population mean with local habitat. This method reveals a cline in peg number approximately 30 km south of the Picos de Europa Mountains that shows substantial deviations in population mean compared with the expectations of simple tension zone models. The inclusion of variation in local vegetation in the model explains a significant proportion of the residual variation in peg number, indicating that habitat-genotype associations contribute to the observed spatial pattern. However, this association is weak, and a number of populations continue to show strong deviations in mean even after habitat is included in the final model. These outliers may be the result of long-distance colonization of sites distant from the cline center or may be due to a patchy pattern of initial contact during postglacial expansion. As well as contrasting with the smooth hybrid zones described for Chorthippus parallelus, this situation also contrasts with the mosaic hybrid zones observed in Gryllus crickets and in parts of the hybrid zone between Bombina toad species, where habitat-genotype associations account for substantial amounts of among-site variation.

Comparison of adsorption capacity of p-Cresol & p-Nitrophenol by activated carbon in single and double solute

Adsorption of p-Cresol and p-Nitrophenol by untreated activated carbon in single and multisolute solutions was carried out at 301 K and at controlled pH conditions. In acidic conditions, well below the pK(a) of both solutes, it was observed that the adsorbate solubility and the electron density of aromatic rings influenced the extent of adsorption by affecting the extent of London dispersion forces. The fitted parameters obtained from single-solute Langmuir equation show that Q(max) and the adsorption affinity of carbon for the compound with low pK(a) decrease more significantly. In higher solution pH conditions, on the other hand, it was found that electrostatic forces played a significant role on the extent of adsorption. The presence of another compound decreases Q(max) and the adsorption affinity of carbon for the principal compound. The effect of pH, on the carbon surface and on the solute molecules, must be considered. Adsorption of the solute at higher pH values was found to be dependent on the concentration of anionic form of the solute. The isotherm data were fitted to the Langmuir isotherm equation for both single and double solute solutions.