Direct sedimentation analysis of interference optical data in analytical ultracentrifugation

Sedimentation data acquired with the interference optical scanning system of the Optima XL-I analytical ultracentrifuge can exhibit time-invariant noise components, as well as small radial-invariant baseline offsets, both superimposed onto the radial fringe shift data resulting from the macromolecular solute distribution. A well-established method for the interpretation of such ultracentrifugation data is based on the analysis of time-differences of the measured fringe profiles, such as employed in the g(s*) method. We demonstrate how the technique of separation of linear and nonlinear parameters can be used in the modeling of interference data by unraveling the time-invariant and radial-invariant noise components. This allows the direct application of the recently developed approximate analytical and numerical solutions of the Lamm equation to the analysis of interference optical fringe profiles. The presented method is statistically advantageous since it does not require the differentiation of the data and the model functions. The method is demonstrated on experimental data and compared with the results of a g(s*) analysis. It is also demonstrated that the calculation of time-invariant noise components can be useful in the analysis of absorbance optical data. They can be extracted from data acquired during the approach to equilibrium, and can be used to increase the reliability of the results obtained from a sedimentation equilibrium analysis.     

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.     

Analysis of intentional head gestures to assist computer access by physically disabled people

Any human-computer interface requires both a means of transducing information flowing from the person and a way of classifying this information in a form that can be used by an application program. Since several interface devices exploit the head movements of disabled people to control computers, this paper includes a discussion of existing technologies based on head movements. As an alternative to simple techniques based on pointing to classify this information, this paper studies the possibility of using a combination of pointing and movement gestures to control an application program. By using hidden Markov models to classify movements into ‘yes’, ‘no’ and spurious gestures, it was possible to control a simple graphics application program. Subsequent analysis showed that the hidden Markov models achieved a 74% success rate.     

Linking the green and brown worlds through nonconsumptive predator effects

Predators can indirectly affect lower trophic levels by either consuming their prey (consumptive effect, CE) or by changing the physiology or behavior of their prey (nonconsumptive effect, NCE). Cascading effects of predators on primary producers are common, and can be propagated by CEs, NCEs, or a combination of both mechanisms. Predator impacts in detrital food webs (the ‘brown world’) have received considerably less attention than their effects on systems with primary producers at the base (the ‘green world’), and only recently have we begun to appreciate the importance of above‐ground predators indirectly impacting below‐ground processes. Numerous studies reveal the total impact (CEs and NCEs) of predators in brown food webs, but our understanding of the role of isolated NCEs is limited. Many habitats and major taxa have not been studied, and patterns are difficult to distinguish due to frequent reporting of mixed effects. Predators play an important role as connectors between brown and green worlds when they feed from both food webs (multichannel feeding). We are only beginning to understand how NCEs influence detrital food webs, and it is unknown whether multichannel fear is an essential component of predator–prey ecology that regulates ecosystem function. Synthesis Predators have been shown to impact ecosystems through both consumptive and nonconsumptive effects on their prey Historically, herbivory‐based ‘green’ systems have been the venue for documenting these predator effects, while detritus‐based ‘brown’ systems received considerably less attention. However, similar mechanisms exist in green and brown worlds, suggesting strong parallels. We review and synthesize predator effects in detrital systems, highlighting important shortcomings in current understanding. Furthermore, we build upon the idea of multichannel feeding (i.e. consumption of prey from both green and brown food webs) to propose the existence of ‘multichannel fear’. We provide a framework for documenting multichannel fear to facilitate continued exploration of how predators link seemingly disparate systems.     

Combining distances of ballistic and myrmecochorous seed dispersal in Adriana quadripartita (Euphorbiaceae)

The separate contributions of different vectors to net seed dispersal curves of diplochorous systems have rarely been characterised. In Australia, myrmecochory is a common seed dispersal syndrome and in the majority of such systems, seeds are initially dispersed ballistically. We measured ballistic and myrmecochorous seed dispersal distances in relation to canopies of Adriana quadripartita (Euphorbiaceae) and used a simulation model to estimate the net dispersal curve. We also compared seed removal rates and ant abundances under, and outside, plant canopies to examine how foraging patterns by ants may affect net dispersal.Overall ant abundance did not show a significant numerical response to seedfall; however, the abundance of the main seed dispersing ant, Rhytidoponera ‘metallica’ did. Despite this, seed removal rates did not differ significantly between canopy and open locations. Rhytidoponera ‘metallica’ account for 93% of observed seed dispersal events. On average, the ants dispersed seeds 1.54 m and in doing so, moved seed a mean radial distance of 0.76 m away from canopy edges. This contribution to net dispersal distance by ants is considerable since ballistic dispersal moved seeds a median distance of 7.5 cm. Our simulation model indicated that the combination of ballistic and ant seed dispersal is expected to result in seeds being transported a median net radial dispersal distance of 1.05 m from the canopy edge.Thus in this system, an important function of diplochory may simply be to move a higher proportion of seeds from under the canopy of parent plants than is possible by ballistic dispersal alone. This ‘dispersal-for-distance’ may result in reduced parent–offspring competition or may increase the probability that seeds reach rare safe sites for germination and recruitment.     

A non-linear least-squares approach to the resolution of heterogeneous fluorescence from multitryptophan proteins

Protein heterogeneous fluorescence results from the different microenvironment of each emitting chromophore. The structural and dynamic information contained in this emission can be extracted to some extent by selective quenching experiments. In this work, graphical and numerical methods are described for the analysis of protein emission in terms of three separated contributions: a fluorescence fraction which is not accessible to the quencher and two additional fractions with different solvent exposure. ‘Static quenching’ deviations from Stern-Volmer behaviour are also discussed. The application of these methods is exemplified on simulated quenching experiments and real data on acrylamide quenching of lysozyme fluorescence.     

Living is Information Processing: From Molecules to Global Systems

We extend the concept that life is an informational phenomenon, at every level of organisation, from molecules to the global ecological system. According to this thesis: (a) living is information processing, in which memory is maintained by both molecular states and ecological states as well as the more obvious nucleic acid coding; (b) this information processing has one overall function—to perpetuate itself; and (c) the processing method is filtration (cognition) of, and synthesis of, information at lower levels to appear at higher levels in complex systems (emergence). We show how information patterns, are united by the creation of mutual context, generating persistent consequences, to result in ‘functional information’. This constructive process forms arbitrarily large complexes of information, the combined effects of which include the functions of life. Molecules and simple organisms have already been measured in terms of functional information content; we show how quantification may be extended to each level of organisation up to the ecological. In terms of a computer analogy, life is both the data and the program and its biochemical structure is the way the information is embodied. This idea supports the seamless integration of life at all scales with the physical universe. The innovation reported here is essentially to integrate these ideas, basing information on the ‘general definition’ of information, rather than simply the statistics of information, thereby explaining how functional information operates throughout life.     

Notes on the genus Amorphophallus (Araceae) – 13. Evolution of pollen ornamentation and ultrastructure in Amorphophallus and Pseudodracontium

A strict consensus tree based on chloroplast and nuclear sequences (rbcL, matK, trnL, FLint2) from 46 Amorphophallus species, two Pseudodracontium species and six outgroups is used to develop a hypothesis for the evolution of ornamentation and ectexine ultrastructure in the pollen of Amorphophallus. There are four main clades: an exclusively African, largely psilate clade (‘African clade’), an Asian, largely psilate clade (‘Asian psilate clade’) and an Asian, largely striate clade consisting of a mainly continental SE Asian clade (‘continental SE Asian striate clade’) and one centred in Malesia (‘Malesian striate clade’). Ultrastructure provides a valuable contribution towards understanding pollen ornamentation in Amorphophallus. Pollen with a thin psilate ectexine without dark granules might be plesiomorphic in Amorphophallus. Then the diverse striate type would be derived. Within both striate clades, reversals to the psilate type occur. Striate pollen with psilate caps, which is nested in the continental SE Asian striate clade, is a synapomorphy of Pseudodracontium. The fossulate type is also diverse, and its distribution in the tree indicates a polyphyletic origin. Areolate, echinate and verrucate ornamentation, occur in single species in the tree, but are found also in species not included in the molecular analysis. All three are heterogeneous and probably polyphyletic too. Reticulate, scabrate and striate/scabrate ornamentation are autapomorphies, of which the reticulate type and the striate/scabrate type may derive from psilate and striate ornamentation, respectively. Of the four main clades, the Asian psilate and African clade seem to be basal, while both striate clades might have evolved from the Asian psilate clade via a species like A. rhizomatosus. Dark granules evolved more than once, which might explain their diverse size, shape and distribution.     

Analytical ultracentrifugation as a tool for studying protein interactions

The last two decades have led to significant progress in the field of analytical ultracentrifugation driven by instrumental, theoretical, and computational methods. This review will highlight key developments in sedimentation equilibrium (SE) and sedimentation velocity (SV) analysis. For SE, this includes the analysis of tracer sedimentation equilibrium at high concentrations with strong thermodynamic non-ideality, and for ideally interacting systems, the development of strategies for the analysis of heterogeneous interactions towards global multi-signal and multi-speed SE analysis with implicit mass conservation. For SV, this includes the development and applications of numerical solutions of the Lamm equation, noise decomposition techniques enabling direct boundary fitting, diffusion deconvoluted sedimentation coefficient distributions, and multi-signal sedimentation coefficient distributions. Recently, effective particle theory has uncovered simple physical rules for the co-migration of rapidly exchanging systems of interacting components in SV. This has opened new possibilities for the robust interpretation of the boundary patterns of heterogeneous interacting systems. Together, these SE and SV techniques have led to new approaches to study macromolecular interactions across the entire spectrum of affinities, including both attractive and repulsive interactions, in both dilute and highly concentrated solutions, which can be applied to single-component solutions of self-associating proteins as well as the study of multi-protein complex formation in multi-component solutions.     

Sensitivity of the Welfare Quality® broiler chicken protocol to differences between intensively reared indoor flocks: which factors explain overall classification?

There is a large demand for holistic welfare assessment systems that result in a singular balanced summary of welfare. The Welfare Quality® (WQ) broiler protocol summarizes 18 welfare measures into four principles (‘good feeding’, ‘good housing’, ‘good health’ and ‘appropriate behaviour’), which are then integrated into one overall category (‘excellent’, ‘enhanced’, ‘acceptable’ or ‘not classified’). But the protocol is time consuming which hampers implementation. Furthermore, WQ’s aim to assess animal welfare in a wide range of husbandry systems may decrease its ability to discriminate between flocks from the same system. We applied the protocol in the context of intensive indoor rearing to assess whether it discriminated sufficiently between flocks, could be shortened without losing essential information, and provided a balanced summary of welfare. The vast majority of the flocks (88%) received the same overall classification (acceptable) whilst all other flocks received an adjacent classification (enhanced), suggesting poor discriminative capacity. For 95% of the flocks overall classification was explained by two measures only (‘drinker space’ and ‘stocking density’). A system based on these two measures would reduce assessment time from 3.5 h to a few minutes. However, both measures’ validity can be questioned as they are risk factors for poor welfare rather than animal-based outcome measures and they suffer from methodological weaknesses. Furthermore, the possibility for such an extreme simplification raises doubts on whether the overall classification reflects a balanced summary of different welfare aspects. In line with this, overall classification was not affected by replacing single measures within the ‘good health’ and ‘appropriate behaviour’ principles with realistically attainable minima or maxima for intensively reared flocks. Even replacing either of these two principles entirely with their realistically obtainable minimum or maximum did not affect classification. Such insensitivity to change may discourage attempts to improve the welfare of intensively reared flocks when assessments are made based on the overall classification. This calls for an adjustment of the classification system, which is currently being developed by the Welfare Quality Network.     

Parametric analysis of the biomechanical response of head subjected to the primary blast loading – a data mining approach

Traumatic brain injury due to primary blast loading has become a signature injury in recent military conflicts and terrorist activities. Extensive experimental and computational investigations have been conducted to study the interrelationships between intracranial pressure response and intrinsic or ‘input’ parameters such as the head geometry and loading conditions. However, these relationships are very complicated and are usually implicit and ‘hidden’ in a large amount of simulation/test data. In this study, a data mining method is proposed to explore such underlying information from the numerical simulation results. The heads of different species are described as a highly simplified two-part (skull and brain) finite element model with varying geometric parameters. The parameters considered include peak incident pressure, skull thickness, brain radius and snout length. Their interrelationship and coupling effect are discovered by developing a decision tree based on the large simulation data-set. The results show that the proposed data-driven method is superior to the conventional linear regression method and is comparable to the nonlinear regression method. Considering its capability of exploring implicit information and the relatively simple relationships between response and input variables, the data mining method is considered to be a good tool for an in-depth understanding of the mechanisms of blast-induced brain injury. As a general method, this approach can also be applied to other nonlinear complex biomechanical systems.     

Land Tenure and Naming Systems in Aboriginal Australia

Naming systems play a prominent role in discussions of land tenure by Aboriginal people. Reference to one area of land and its owners is most commonly in terms of name ‘X’, whereas reference to another area of land and its owners is most commonly made in terms of name ‘Y’. Much of the analytical literature examines how these names refer to groups of people. There is considerable dispute as to whether the reference of these names suffices to determine disjoint groupings of owners that can be described by the term ‘clan’. This paper proposes that the analysis of linkages between names and areas of land should have priority over the analysis of linkages between names and groups of people. The evidence shows that the attachment of names to areas of land is more stable and consistent than their attachment to groups of people. There are differences in the ways that names attach to the landscape, and these differences are significant—they determine whether or not more than one name from the same system may be attached to an area of land. This paper focuses on two areas of Australia: the northern Kakadu‐Oenpelli area and the Timber Creek area (both in the Northern Territory). It shows that naming systems identify disjunctive areas of land as the targets for claims of primary ownership in both areas. These disjunctive areas may reasonably be described with the translation term ‘estates’. In the northern Kakadu‐Oenpelli area, corresponding to these estates, there are disjunctive groupings of owners, which may be termed ‘clans’. However, groupings of owners are not clearly disjunctive in the Timber Creek area, and there is little motivation for using the term ‘clan’. This paper proposes that this difference reflects a general pattern in Aboriginal Australia, with naming systems stably and consistently identifying ‘estates’ across much of the continent. They do not identify ‘clans’ with equivalent stability and consistency.     

CORRECTION FACTORS FOR ‘BINDING’ STUDIES; MODEL SYSTEMS FOR GABA BINDING TO A SYNAPTOSOMAL–MITOCHONDRIAL FRACTION OF RAT CEREBRAL CORTEX1

Correction methods currently used in ‘binding’ experiments have been compared and a new approach is proposed. These methods have been applied to data on the ‘binding’ of GABA to a ‘synaptosomal-mitochondrial’ fraction of rat cerebral cortex under various conditions. Results indicated that values for ‘corrected binding’ can differ greatly, depending upon the method employed. Calculations based on data obtained when using a high concentration of unlabelled GABA to displace ‘specific’ binding of [³H]GABA (‘cold ligand method’) under-estimated the binding, because this method neglects the existence of a biochemically-inert space which exists within the pellet even at 0°C and which traps labelled ligand. The other correction method, in which an inert labelled substance (e.g. sucrose) is used to measure the portion of the pellet occupied by trapped supernatant fluid (‘sucrose space method’), is more accurate, but does not take into account the amount of ligand that may be non-specifically bound to the particulate portion of the pellet. The error with this method is small for ‘high-affinity’ ligand-receptor systems, but may be quite large for lower affinity systems. A method which takes into consideration both the inert space of the pellet and ligand that is non-specifically bound to the pellet (‘fully corrected method’) is proposed. The three correction methods have been applied to a study of the kinetic parameters of GABA binding to a ‘synaptosomal-mitochondrial’ fraction of rat cerebral cortex in the presence and absence of the GABA inhibitor, bicuculline-methiodide. In some cases, the results showed qualitative as well as large quantitative differences, depending on the correction method employed.     

Sequential and parallel dual labeling of nanoparticles using click chemistry

Bioorthogonal ‘click’ reactions have recently emerged as promising tools for chemistry and biological applications. By using a combination of two different ‘click’ reactions, ‘double-click’ strategies have been developed to attach multiple labels onto biomacromolecules. These strategies require multi-step modifications of the biomacromolecules that can lead to heterogeneity in the final conjugates. Herein, we report the synthesis and characterization of a set of three trifunctional linkers. The linkers having alkyne and cyclooctyne moieties that are capable of participating in sequential copper(I)-catalyzed and copper-free cycloaddition reactions with azides. We have also prepared a linker comprised of an alkyne and a 1,2,4,5-terazine moiety that allows for simultaneous cycloaddition reactions with azides and trans-cyclooctenes, respectively. These linkers can be attached to synthetic or biological macromolecules to create a platform capable of sequential or parallel ‘double-click’ labeling in biological systems. We show this potential using a generation 5 (G5) polyamidoamine (PAMAM) dendrimer in combination with the clickable linkers. The dendrimers were successfully modified with these linkers and we demonstrate both sequential and parallel ‘double-click’ labeling with fluorescent reporters. We anticipate that these linkers will have a variety of application including molecular imaging and monitoring of macromolecule interactions in biological systems.     

Application of the Welfare Quality® assessment system on European beef bull farms

Welfare concerns for intensive beef production have often been raised, but on-farm welfare assessment studies are rare. The aim of this study was to apply the Welfare Quality® (WQ) welfare assessment system for fattening cattle on beef bull farms to evaluate the state of welfare at the level of WQ measures and of aggregated scores, as well as overall classification. In addition, the purpose was to evaluate two ways of providing feedback information to the farmers with regard to possible welfare improvements on the farms. The study was conducted in Austria, Germany and Italy on a total of 63 beef bull farms with deep litter or cubicle-housing systems. Assessments were carried out 3 times (1 month and 7 months apart from the initial visit). In every country, farmers were assigned to two treatment groups (feedback from initial visit as written report, F, written feedback plus oral advice, FA) and a control group (C), which did not receive any feedback. At the criterion level, the highest average welfare scores were obtained from ‘Absence of prolonged hunger’ (94/100 points) followed by ‘Absence of pain induced by management procedures’ (88/100) and ‘Comfort around resting’ (77/100). Most welfare concerns related to the criteria ‘Absence of disease’ (40/100), ‘Expression of social behaviour’ (44/100) and ‘Positive emotional state’ (48/100), thus indicating room for improvements. Two-thirds of the farms achieved the ‘Enhanced’ level, about one-third was judged ‘Acceptable’ and only one farm ‘Excellent’. After 6 months of monitoring period, there was no significant welfare improvement in both the treatment groups as compared with the control group. Reasons for the lack of effect may mainly be seen in the short monitoring period and a lack of external incentives. In conclusion, the WQ assessment system revealed areas for improvement, but longer term studies and investigations on alternative ways of transferring outcomes from on-farm welfare assessments to farmers should be carried out in future.     

Centres of plant endemism in China: places for survival or for speciation?

Aim This study aimed to identify the ‘centres of endemism’ of the Chinese spermatophyte flora in order to indirectly detect the locations of past glacial refugia. The role of these areas as places for plant survival (‘plant museums’) and/or areas for plant evolution and speciation (‘plant cradles’) was also assessed. Location China. Methods Distribution patterns of 555 plant endemic taxa, taken as a representative sample of the Chinese endemic flora, were mapped on a 1° × 1° latitude/longitude grid. For each grid cell, species richness (total count of species) and weighted richness (down‐weighting each species by the inverse of its range) were calculated. Grid cells within the top 5% of highest values of weighted richness were considered centres of endemism. Based on available information, all plant taxa included in this study were classified into palaeoendemics and neoendemics, and their distributional patterns were represented separately. Results Twenty areas of endemism were identified in central and southern China, roughly corresponding to mountain ranges, including the Hengduan and Daxue Mountains, the Yungui Plateau, central China Mountains, the Nanling Mountains, eastern China Mountains, and Hainan and Taiwan. Although almost all centres of endemism contained both palaeoendemic and neoendemic taxa, considerable differences in their respective numbers were recorded, with the majority of neoendemics on the eastern fringe of the Tibetan Plateau (Hengduan Mountains sensu lato) but more palaeoendemics towards the east. Main conclusions Owing to their varied topography, the mountainous regions of central and southern China have provided long‐term stable habitats, which allowed palaeoendemics to persist and facilitated the process of speciation. Contrasting patterns between the palaeoendemics and neoendemics within refugia might be attributable to the geological and tectonic history of specific areas. The eastern fringe of the Tibetan Plateau clearly constitutes the ‘evolutionary front’ of China, probably as a result of the uninterrupted uplift of the plateau since the late Neogene. In contrast, the tectonic stability of central and southern China during the Tertiary may have facilitated the persistence of relict plant lineages.     

Evolution in bioids: Hypercompetitivity as a source of bistability and a possible role of metal complexes as prenucleoprotic mediators of molecular asymmetry

Spontaneous production of optically active compounds can occur through kinetic instability of an asymmetric steady state in open systems, in which two enantiomeric autocatalysts compete for a common prochiral substrate in a stereoselective reaction of ordern>2. For the case ofn=3, a proof of instability of a symmetric reacting state in the general case, and functions of reaction parameters (‘Chemical Reynolds Numbers’) governing the existence and stability of 7 different steady states are derived. The ‘extinct state’ (without autocatalyst) is stable; a finite amount of products is required to shift it into one of the reacting steady states. A mutation from one state into another in such systems (‘bioids’) involves an amplification of different ‘kinds of information’, as ‘stochastic’ (noise into dissipative structures), ‘molecular’ (autocatalysts), and ‘stoichiometric’ information. Stereospecific third order kinetics are believed to be realizable on octahedral metal complexes with two-dentated ligands and to have played a role in the prebiological evolution of optically active compounds.     

Home range,core areas and movement in the ‘critically endangered’ kipunji (Rungwecebus kipunji) in southwest Tanzania

Understanding how threatened forest primates use a heterogeneous landscape is essential to ensuring their survival. Kipunji (Rungwecebus kipunji) are ‘critically endangered’, arboreal monkeys restricted to two sites in Tanzania. Over 90% of the population lives in the degraded Rungwe‐Kitulo forests of the Southern Highlands. In this study, we present the first comprehensive investigation into daily path length and home range size of kipunji, based on data from four groups followed simultaneously over 70 consecutive days on Mt. Rungwe. The mean daily distance travelled was 1293 m (SE 150.82), and daily distance was not significantly correlated to group size. Using fixed kernel density estimation, an area enclosing 90% of the home range calculated using the ‘reference’ method as a smoothing parameter, measured a mean of 306.18 ha (SE 67), and the core area (50% use) was 86.55 ha (SE 18.73). Using the ‘least‐squares cross validation’ method, the mean home range and core area were 205.45 ha (SE 57.02) and 55.45 ha (SE 14.23) respectively. Home range overlap was extensive, although contact between groups was rare, with >97.30% of all observations within 20 min separated by >250 m. The data strongly suggest that kipunji are not territorial.     

Investment in the public good through conditional phenotypes of large effect

We investigate the evolution of an individual's willingness to invest in a public good (what we call, helping) in a patch‐structured population with limited natal dispersal. We assume that an individual's decision to invest is informed by its dispersal status: an individual makes one decision given it is native to the patch on which it breeds, and is free to make a different decision given that it is not native to the patch on which it breeds. Unlike previous work, we assume that investment in the public good, and the public good, itself, both have a large effect on individual fecundity. Kin selection analysis reveals that only extreme investment decisions (i.e. ‘always invest’ or ‘never invest’) can be evolutionarily stable. Numerical results suggest that the evolutionary instability of the ‘never invest’ phenotype (what we call, complete nonhelping) implies the evolutionary stability of ‘always invest’ (what we call, complete helping). In addition, numerical results show that bistability of extreme phenotypes is possible, indicating that the adaptive significance of altruism, in this context, is greater than has been previously recognized. Numerical results are supported by computer simulation, and results, themselves, are briefly discussed in a concluding section.