Research Publications (Systems Science)

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Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems
(Hindawi Limited, 2020-08-01) Aibinu, Mathew O.; Thakur, Surendra C.; Moyo, Sibusiso
Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of (p, {\eta})-strongly monotone type, where {\eta} > 0, p > 1. An example is presented for the nonlinear equations of (p, {\eta})-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.
Child and youth care workers: Profile, nutrition knowledge and food safety and hygiene practices
(AOSIS OpenJournals, 2014-08-06) Grobbelaar, Hendrina Helena; Napier, Carin E.
Background: Facilities concerned with children ‘in need of care’ should not only be considered as a last resort for a child’s care, but also as an intervention that requires more than addressing a child’s basic physical needs. The nutritional needs of children are particularly important to consider as they are a fundamental part of the care provided. Objectives: The purpose of this descriptive quantitative study was to investigate the profile, nutrition knowledge, food safety and hygiene practices of child and youth care workers (CCWs) in residential care settings in order to guide the development of a food preparation and nutrition manual. Method: The residential care settings included in this study were three that were selected randomly in Durban. CCWs (N = 40) employed permanently or part-time were included. Convenience purposive sampling of the CCWs was undertaken. A structured self-administered questionnaire, developed and tested for this purpose, was used to gather information on the profile, nutrition knowledge, food safety and hygiene practices. The data were analysed for descriptive statistics (means and frequencies). Results: The majority of CCWs were women aged 18−34 years. Very few had completed a relevant tertiary qualification. The results indicated that the respondents’ knowledge was fair on general nutrition guidelines, but there were areas of concern. Specifically, knowledge on recommended fruit and vegetable intake, correct serving sizes and importance of a variety in the diet were lacking. Some knowledge about food safety and hygiene practices was demonstrated, but not in totality. Conclusion: The overall findings supported the development of a comprehensive food preparation and nutrition manual for child residential care facilities.
Consumption threshold used to investigate stability and ecological dominance in consumer-resource dynamics
(Elsevier, 2015) Collins, Obiora Cornelius; Duffy, Kevin Jan
Understanding consumer resource population dynamics can be important to an understanding of the overall ecology of systems. For example, the tree-grass continuum dynamics of savannas, an important ecological biome, is inﬂuenced by the population dynamics. Here we investigate herbivory driven popu-lation dynamics of a savanna using a simple model of the interactions of the dominant players, namely: trees, grasses, browsers, grazers and mixed browsers-grazers. We introduce a consumption threshold that summarises some of the parameters and this is used as a guide to understanding the dynamics. This number is used in investigating system stability and sensitivity to parameter ﬂuctuations. It is also used to identify degrees of ecological dominance.
Heavy impact on seedlings by the impala suggests a central role in woodland dynamics
(Cambridge University Press, 2012-04-12) O'Kane, Christopher A. J.; Duffy, Kevin Jan; Page, Bruce R.; Macdonald, David W.
Research has increasingly established that mesoherbivores influence the regeneration of woody plants. However the relationship between mesoherbivore density and degree of impact, and the spatial component of this impact, has not been well established. Using a novel sampling design, we assessed in iMfolozi Park, South Africa, the impact of impala (Aepyceros melampus) across the full complement of woody species within the home range, evaluating its spatial component and relationship to impala density. We used four GPS collars, in separate breeding herds, and a GIS to detect zones of different density of impala in the landscape, thus defining a fine-grain browsing gradient. We assessed impact on woody recruits (≤ 0.5 m height) across this gradient by means of 1600 random 1 × 1-m quadrats. Densities of woody seedlings, and mean percentage of remaining canopy, were significantly less in areas of high impala density versus low-density areas. There was a significant correlation between increasing impala density and decreasing density of favoured woody recruits. We propose a hypothesis of impala-induced patch dynamics. It seems likely that the ubiquitous impala may create and sustain a shifting mosaic of patches, and thus function as a key determinant of landscape heterogeneity.
Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold
(Elsevier, 2016) Duffy, Kevin Jan; Collins, Obiora Cornelius
The existence, or not, of cyclic dynamics is one of the pivotal aspects of ecological populations. This work considers a consumer resource model found in ecology that can describe both cyclic and non-cyclic dynamics depending on parameter conditions. A threshold consumption number C0 is introduced, similar to the basic reproduction in epidemiological models. It is shown that consumer survival requires C0 > 1 and that a Hopf bifurcation occurs at , where is defined here and is greater than 1. This result is discussed with an example and extensions to other more complicated models.
Indigenous strategies and empirical models for adaptability of the maize-bean intercropping system to climate change
(UZ Foundatoin, 2016-12) Mapanda, S.; Chitja, J. M.; Duffy, Kevin Jan
This review article discusses on different ways of indigenous strategies and empirical models as an adaptation to climate change by smallholder farmers in Africa. Indigenous adaptation strategies are methods that enable individuals or communities to adjust to the impacts of climate change in local areas. Some of the strategies practiced are: zero tillage, mulching, soil management techniques, organic agriculture and fallow system of cultiva-tion, intercropping with legumes, early planting and use of tolerant varieties to drought, water conservation and crop diversification. Scientists developed many empirical models that are used to project the impact of climate change to agriculture. Some of the empirical models include: CERES-Maize Crop Model, Global Circulation Models (GCM) and histori-cal data records. There is also use of empirical evidence such as indigenous land unit framework, indigenous early warning systems, use of rainmakers, movement of birds, ants and crying of dogs by the indigenous smallholder farmers in Africa. Intercropping system is the best practice used as a strategy to climate change adaptability, and one of the most suitable intercropping systems is that of maize and bean. However, the current research findings revealed that there is a lack of consideration of indigenous knowledge that could enhance livelihoods that depend on natural resources directly affected by climate change.
Linear Quantum Entropy and Non-Hermitian Hamiltonians
(MDPI, 2016-12-16) Sergi, Alessandro; Giaquinta, Paolo V.
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered
Microbiological water quality along Vaal Gamagara’s potable water distribution system
(Business Perspectives, 2015) Mokhosi, Agnes; Dzwairo, Bloodless
Safe drinking water is essential to all life forms. Thus analysis for microbiological parameters is critical as this assists in declaring the fitness of potable water for human consumption, among other sustainable and “green uses”. The aim of this paper is to investigate the microbiological quality of potable water along Vaal Gamagara Water Treatment Plant’s (VGWTP) distribution system. A total of 10 samples were collected weekly along the system. The samples were col-lected from January to December 2013 in order to analyze for Escherichia coli (E.coli), total coliforms (TC) and Hete-rotrophic plate counts (HPC). The results showed that only 0.1% and 0.4% of samples analyzed were positive for E. coli and total coliforms, respectively. However, HPC results showed that 40% of the samples analyzed from June to December 2013 had higher counts than the recommended standard limit. The chlorine residual showed an increase from June to December 2013. An assessment of the results indicated that the integrity of the system was compromised for the research period. Water quality failures in a distribution system are unacceptable because they threaten human health and sometimes result in loss of life. Thus the assessment called for an urgent need to boost chlorine residual especially at points further away from the treatment plant. This was envisaged to provide a safety net for microbial compliance while the system was critically and continuously monitored, and further investigations were performed. Studies on chlorine decay were recommended as a priority in order to optimize disinfection and maintain good quality drinking water throughout the system.
Model highlights likely long-term inﬂuences of mesobrowsers versus those of elephants on woodland dynamics
(Wiley Online Library, 2014-06) O'Kane, Christopher A. J.; Duffy, Kevin Jan; Page, Bruce R.; Macdonald, David W.
The potential long-term inﬂuences of mesobrowsers versus those of savannah elephants on woodland dynamics have not been explored. This may be a critical omission especially in southern African savannahs, where efforts to preserve existing woodlands are typically directed at elephant man-agement. We describe a simple browse–browser model, parameterized from an extensive review of the literature and our own data, including quantitative assessment of impala impact, from the study site, iMfolozi Park, South Africa. As there is a paucity of species-speciﬁc demographic data on savannah woody species, we modelled, in a novel approach, functional groups of plant species typical of Acacia wood-lands. Outputs suggest that over the long term (100 years), low-to-moderate densities of impala will have a similar impact on woodland structure, in terms of density of adult trees, as low-to-moderate densities of elephant. Further, the outputs highlight the apparently strong synergistic effect impala and elephant impacts combined have on woodland dynamics, suggesting that reduction or removal of either impala or elephant will radically reduce long-term destruc-tion of savannah woodlands. Recorded changes in adult tree numbers in iMfolozi broadly supported the model’s outputs.
Nutritional status and food intake data on children and adolescents in residential care facilities in Durban
(Health and Medical Publications Group (HMPG), 2013) Grobbelaar, Hendrina Helena; Oldewage-Theron, Wilna; Napier, Carin E.
Objective: The aim of this study was to examine growth indicators and dietary intake patterns of children aged 4-18 years residing in residential care facilities in Durban. Method: Thirty-three girls and 110 boys, aged 5-18 years, in three different children’s homes participated in the study. Anthropometric measurements included weight and height and were analysed using the World Health Organization’s AnthroPlus® version 1.0.2 statistical software. The seven-day-cycle menus were analysed for nutrient and energy intake using the FoodFinder® version 3 software programme. Daily nutrient intakes were reported as means and standard deviations, and comparisons were made with the dietary reference intakes for specific age groups. Average served portion sizes were established by plate waste studies and observation. Results: The results showed that stunting and overweight were prevalent in this group. 4.7% of the boys aged 4-8 years and 3.3% of the boys aged 14-18 years were severely stunted. 13.3% of the girls aged 9-13 years and 20% of the girls aged 14-18 years were stunted. The body mass index for age reported that a small number (6.7% of the girls aged 9-13 years and 3.3% of the boys aged 14-18 years) were wasted. The results also showed that 33.3% of the girls aged 4-8 years and 33.4% of the girls aged 9-13 years were at risk of being overweight. 26.7% of the girls aged 14-18 years were overweight (> + 2 standard deviations). Most of the children in the 4-8 age group (83.3% of the boys and 100% of the girls) fell in the normal range for weight for age, while only one boy was underweight. One hundred per cent or more of the dietary reference intakes for energy, protein, carbohydrate and most of the micronutrients were met, except for calcium and iodine. A low intake of vitamin C among older boys and girls was reported. None of the groups met the recommended fibre intake. Conclusion: The results indicated a need for the development and implementation of a comprehensive nutrition education programme for both child care workers and children.
Optimal control of maize foliar diseases using the plants population dynamics
(Taylor and Fancis, 2015-09-28) Collins, Obiora Cornelius; Duffy, Kevin Jan
Pathogens and insects can have important negative effects on yields of crops cultivated by humans. These effects can be important for the food security or financial well-being of individuals. In particular, maize is a very important staple crop worldwide and is vulnerable to diseases. We formulate here a mathematical model to evaluate the impacts of foliar diseases on the population dynamics of maize plants. Qualitative analyses of the important mathematical features of the model are carried out. We show how this methodology can be extended to reducing the spread of foliar diseases through effective control measures with minimum costs.
Quantum entropy of systems described by non-Hermitian Hamiltonians
(IOP Science, 2016-03-02) Sergi, Alessandro; Zloshchastiev, Konstantin G.
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non-Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning.
Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides
(American Physical Society, 2016) Zloshchastiev, Konstantin G.
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schr¨odinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operatorwhich describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general non-Hermitian Hamiltonians, we derive a master equation that describes the statistical ensembles of EM wave modes. The method also describes the quantum dissipative and decoherence processes which happen during the wave’s propagation, and, among other things, it reveals the conditions that are necessary to control the energy and information loss inside the above-mentioned materials.
Stable isotope turnover and variability in tail hairs of captive and free-ranging African elephants (Loxodonta africana) reveal dietary niche differences within populations
(NRC Research Press, 2013) Codron, Jacqueline; Kirkman, Kevin; Duffy, Kevin Jan; Sponheimer, Matt; Lee-Thorp, Julia A.; Ganswindt, Andre; Clauss, Marcus; Codron, Daryl
Many herbivore species expand their dietary niche breadths by switching from browse-rich diets in dry seasons to grass-rich diets in rainy seasons, in response to phenological changes in plant availability and quality. We analyzed stable isotope series along tail hairs of captive and free-ranging African elephant (Loxodonta africana (Blumenbach, 1797)) to compare patterns of seasonal dietary variability across individuals. Results from elephants translocated from the wild into captivity, where their diets are semicontrolled, revealed tail hair growth rates of 0.34 mm/day, on average, and relatively rapid isotope turnover through the transition from wild into captivity. Sampling hairs at 10 mm increments thus archives dietary chronologies at a resolution suitable for tracking diet switches at seasonal, and even subseasonal, scales. Hairs of free-ranging elephants showed extensive carbon isotopic variability within individuals, consistent with seasonal switches between C3-browsing and C4-grazing. Similarly extensive, but asynchronous, shifts in nitrogen isotope ratios were also observed, suggesting an influence of factors other than seasonality. Across individuals, switching patterns differed across habitats, and across age classes, with older, larger animals including increasing amounts of C3 browse into their diets. These results demonstrate how stable isotope approaches characterize complex patterns of resource use in wildlife populations.
Symmetrized exponential oscillator
(World Scientific Publishing, 2016-09-01) Znojil, Miloslav
Several properties of bound states in potential V(x) = g² exp(Formula presented.)x(Formula presented.) are studied. Firstly, with the emphasis on the reliability of our arbitrary-precision construction, wave functions are considered in the two alternative (viz. asymptotically decreasing or regular) exact Bessel-function forms which obey the asymptotic or matching conditions, respectively. The merits of the resulting complementary transcendental secular equation approaches are compared and their applicability is discussed.
Time correlation functions for non-Hermitian quantum systems
(American Physical Society, 2015-06-09) Sergi, Alessandro; Zloshchastiev, Konstantin G.
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semidefiniteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.
Understanding multiple species ecosystem dynamics using a consumer resource model
(Wiley, 2016) Collins, Obiora Cornelius; Duffy, Kevin Jan
Most ecological systems comprise multiple species coex-isting and the dynamics of these multiple species can be important for understanding, management, and conservation. One method to study such ecological system dynamics is the use of heterogeneous models. Here we for-mulate and analyze a multiple species (n patches or groups) consumer re-source model. Initial insights are gained by analyzing the special cases n =1 and n = 2. A threshold consumption number C0 is used to investigate system stability and hence the long-term dynamics of the system. It is shown how this threshold consumption number can measure the eﬀects and extent of multiple species coexistence in the system.
Using Maximum Entropy modeling to predict the potential distributions of large trees for conservation planning
(Ecological Society of America, 2012-06) Smith, Alain; Page, Bruce R.; Duffy, Kevin Jan; Slotow, Rob
Large trees, as keystone structures, are functionally important in savanna ecosystems, and low recruitment and slow growth makes their conservation important. Understanding factors influencing their distribution is essential for mitigation of excessive mortality, for example from management fires or large herbivores. We recorded the locations of large trees in Hluhluwe-Imfolozi Park (HiP) using GPS to record trees along 43 km of 10 m-wide transects. Maximum entropy modeling (MaxEnt) uses niche modeling to predict the distribution of a species from the probability of finding it within raster squares, based on environmental variables and recorded locations. MaxEnt is typically applied at a regional spatial scale, and here we assessed its usefulness when predicting the distribution of species at a small (local) scale. HiP has variable topography, heterogeneous soils, and a strong rainfall gradient, resulting in a wide variety of habitat types. We used locations of 179 Acacia nigrescens and 106 Sclerocarya birrea (large trees ≥ 5m), and raster environmental layers for: aspect, elevation, geology, annual rainfall, slope, soil and vegetation. A. nigrescens was largely restricted to the Imfolozi section, while S. birrea had a wider distribution across the reserve. Understanding the interaction of environmental variables dictating tree distribution may facilitate habitat restoration, and will assist planning decisions for persistence of large trees within reserves, including options to reduce fire frequency or herbivore impacts. Though the AUC (Area Under the Curve) values used to test model predictions were high for both species, the ground truthing test data showed that distribution for A. nigrescens was more accurate than that for S. birrea, highlighting the need for independent test data to assess model accuracy. We emphasize that MaxEnt can be used at finer spatial scales than those typically used for species occurrence, but models must be tested using spatially independent test data.