Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.

Partial state bounding with a pre-specified time of non-linear discrete systems with time-varying delays

In this study, the authors address a new problem of finding, with a pre-specified time, bounds of partial states of non-linear discrete systems with a time-varying delay. A novel computational method for deriving the smallest bounds is presented. The method is based on a new comparison principle, a new algorithm for finding the infimum of a fractal function, and linear programming. The effectiveness of our obtained results is illustrated through a numerical example.

Chemical structure based prediction of PAN and oxidized PAN fiber density through a non-linear mathematical model

The production of carbon fiber, particularly the oxidation/stabilization step, is a complex process. In the present study, a non-linear mathematical model has been developed for the prediction of density of polyacrylonitrile (PAN) and oxidized PAN fiber (OPF), as a key physical property for various applications, such as energy and material optimization, modeling, and design of the stabilization process. The model is based on the available functional groups in PAN and OPF. Expected functional groups, including [Formula presented], [Formula presented], –CH2, [Formula presented], and [Formula presented], were identified and quantified through the full deconvolution analysis of Fourier transform infrared attenuated total reflectance (FT-IR ATR) spectra obtained from fibers. These functional groups form the basis of three stabilization rendering parameters, representing the cyclization, dehydrogenation and oxidation reactions that occur during PAN stabilization, and are used as the independent variables of the non-linear predictive model. The k-fold cross validation approach, with k = 10, has been employed to find the coefficients of the model. This model estimates the density of PAN and OPF independent of operational parameters and can be expanded to all operational parameters. Statistical analysis revealed good agreement between the governing model and experiments. The maximum relative error was less than 1% for the present model.

Is guanxi always good for employee self-development in China? Examining non-linear and moderated relationships

The nature of work and careers in China are constantly evolving as a result of market-oriented economic transition in the country. Increasingly, employees are required to be proactive and self-starting in skill and competency improvement for employability. Employee self-development (ESD) involves considerations embedded in a wide range of relationships including both work and non-work domains. This research draws from social exchange theory and information processing theory to investigate how guanxi, a relational phenomenon unique to traditional Chinese culture, influences ESD. Drawing from the experience of a sample (n = 404) of employees in China, an inverted U-shaped relationship between guanxi and ESD is found, suggesting that initial positive influences of guanxi on ESD diminish after reaching an inflexion point. We also found that these influences are stronger for gender congruent employee-supervisor dyads. The theoretical and managerial implications that too much guanxi is not necessarily good for ESD, particularly in the presence of gender congruence, are also discussed.

Hydrologic response of a tropical watershed to urbanization

 Urbanization has profound influence on the hydrologic response of landscapes. Urban transformation affects the storages and processes that determine the generation of hydrologic fluxes. It also changes the time-scales associated with hydrologic processes. Shifts in hydrologic response of the watershed unit due to urban transformation may be more complex than the simple linear mixing (weighted sum) of responses from the urbanized and non-urbanized fractions of the landscape. This may especially be the case for tropical watersheds where the precipitation forcing of the watershed is frequent and intense - interacting with the shifting time-scales and changing storages with increasing urbanization. In this study, a fully distributed hydrological model (MOBIDIC) that captures hydrologic dynamics during storms and interstorms is applied in order to characterize the potentially nonlinear response of a tropical watershed to urban transformation. Indices that quantify the departures from linear response are introduced and used to test the effects of urbanization on different hydrologic processes and fluxes in a mixed (urban and non-urban) watershed. The tropical Kranji watershed in Singapore is used in this study. Fortunately two sub-watersheds within Kranji that have streamflow gaging stations are well-suited for the calibration of the model. One sub-watershed is nearly fully urbanized and another is pristine (non-urban). As a result the contrasting components (urban and non-urban) can be calibrated in the model. The simulation system is then used to assess the hydrologic response due to changing levels of urbanization. For some fluxes and storages, the hydrologic response due to changing urban fraction cannot be simply predicted from a linear mixing model.

Primary voltage control of a single-phase inverter using linear quadratic regulator with integrator

This paper proposes a linear quadratic regulator with integral action, ensuring fast dynamic response and resisting capability of voltage deviation from instantaneous reference grid voltage, to control the inverter voltage that can also be used in a microgrid. The proposed control strategy is based on a linear quadratic regulator, minimizing the cost function of the system, with integral action used to impede voltage degradation from a reference voltage for outside disturbances of the system, such as abrupt load change. The combined integral term assists to recover the voltage difference between grid and reference grid voltage. The validity of the proposed controller has been tested with linear and non-linear loads under various conditions. In both cases, the effectiveness of the controller has been proved. The result of the proposed controller is good to track the instantaneous reference grid voltage.

Density based fuzzy c-means clustering of non-convex patterns

We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters.

Nurses' critical event risk assessments : a judgement analysis

Aims. To explore and explain nurses' use of readily available clinical information when deciding whether a patient is at risk of a critical event.

Background. Half of inpatients who suffer a cardiac arrest have documented but unacted upon clinical signs of deterioration in the 24 hours prior to the event. Nurses appear to be both misinterpreting and mismanaging the nursing-knowledge 'basics' such as heart rate, respiratory rate and oxygenation. Whilst many medical interventions originate from nurses, up to 26% of nurses' responses to abnormal signs result in delays of between one and three hours.

Methods. A double system judgement analysis using Brunswik's lens model of cognition was undertaken with 245 Dutch, UK, Canadian and Australian acute care nurses. Nurses were asked to judge the likelihood of a critical event, 'at-risk' status, and whether they would intervene in response to 50 computer-presented clinical scenarios in which data on heart rate, systolic blood pressure, urine output, oxygen saturation, conscious level and oxygenation support were varied. Nurses were also presented with a protocol recommendation and also placed under time pressure for some of the scenarios. The ecological criterion was the predicted level of risk from the Modified Early Warning Score assessments of 232 UK acute care inpatients.

Results. Despite receiving identical information, nurses varied considerably in their risk assessments. The differences can be partly explained by variability in weightings given to information. Time and protocol recommendations were given more weighting than clinical information for key dichotomous choices such as classifying a patient as 'at risk' and deciding to intervene. Nurses' weighting of cues did not mirror the same information's contribution to risk in real patients. Nurses synthesized information in non-linear ways that contributed little to decisional accuracy. The low-moderate achievement (Ra) statistics suggests that nurses' assessments of risk were largely inaccurate; these assessments were applied consistently among 'patients' (scenarios). Critical care experience was statistically associated with estimates of risk, but not with the decision to intervene.

Conclusion. Nurses overestimated the risk and the need to intervene in simulated paper patients at risk of a critical event. This average response masked considerable variation in risk predictions, the need for action and the weighting afforded to the information they had available to them. Nurses did not make use of the linear reasoning required for accurate risk predictions in this task. They also failed to employ any unique knowledge that could be shown to make them more accurate. The influence of time pressure and protocol recommendations depended on the kind of judgement faced suggesting then that knowing more about the types of decisions nurses face may influence information use.

Relevance to clinical practice. Practice developers and educators need to pay attention to the quality of nurses' clinical experience as well as the quantity when developing judgement expertise in nurses. Intuitive unaided decision making in the assessment of risk may not be as accurate as supported decision making. Practice developers and educators should consider teaching nurses normative rules for revising probabilities (even subjective ones) such as Bayes' rule for diagnostic or assessment judgements and also that linear ways of thinking, in which decision support may help, may be useful for many choices that nurses face. Nursing needs to separate the rhetoric of 'holism' and 'expertise' from the science of predictive validity, accuracy and competence in judgement and decision making.

Ecology of arboreal marsupials in a network of remnant linear habitats

Linear strips of vegetation set within a less-hospitable matrix are common features of landscapes throughout the world. Depending on location, form and function, these linear landscape elements include hedgerows, fencerows, shelterbelts, roadside or streamside strips and wildlife corridors. In many anthropogenically-modified landscapes, linear strips are important components for conservation because they provide a large proportion of the remaining wooded or shrubby habitat for fauna. They may also function to provide connectivity across the landscape. In some districts, the linear strips form an interconnected network of habitat. The spatial configuration of remnant habitat (size, shape and arrangement) may influence habitat suitability, and hence survival, of many species of plant and animal in modified landscapes. Near Euroa in south-eastern Australia, the clearing and fragmentation of temperate woodlands for agriculture has been extensive and, at present, less than 5% tree cover remains, most of which (83%) occurs as linear strips along roads and streams. The remainder of the woodland occurs as relatively small patches and single isolated trees scattered across the landscape. As an assemblage, arboreal marsupials are woodland dependent and vary in their sensitivity to habitat loss and fragmentation. This thesis focusses on determining the conservation status of arboreal marsupials in the linear network and understanding how they utilise the landscape mosaic. Specifically, the topics examined in this thesis are: (1) the composition of the arboreal marsupial assemblage in linear and non-linear woodland remnants; (2) the status and habitat preferences of species of arboreal marsupial within linear remnants; and (3) the ecology of a population of the Squirrel Glider Petaurus norfolcensis in the linear network, focusing on population dynamics, spatial organisation, and use of den trees. The arboreal marsupial fauna in the linear network was diverse, and comprised seven out of eight species known to occur in the district. The species detected within the strips were P. norfolcensis, the Sugar Glider Petaurus breviceps, Common Brushtail Possum Trichosums vulpecula, Common Ringtail Possum Pseudocheirus peregrinus, Brush-tailed Phascogale Phascogale tapoatafa, Koala Phascolarctos cinereus and Yellow-footed Antechinus Antechinus flavipes. The species not detected was the Feathertail Glider Acrabates pygmaeus. Survey sites in linear remnants (strips of woodland along roads and streams) supported a similar richness and density of arboreal mammals to sites in non-linear remnants (large patches or continuous tracts of woodland nearby). Furthermore, the combined abundance of all species of arboreal marsupials was significantly greater in sites in the linear remnants than in the non-linear remnants. This initial phase of the study provided no evidence that linear woodland remnants support a degraded or impoverished arboreal marsupial fauna in comparison with the nonlinear remnants surveyed. Intensive trapping of arboreal marsupials within a 15 km linear network between February 1997 and June 1998 showed that all species of arboreal marsupial (except A. pygmaeus) were present within the linear strips. Further analyses related trap-based abundance estimates to measures of habitat quality and landscape structure. Width of the linear habitat was significantly positively correlated with the combined abundance of all arboreal marsupials, as well as with the abundance of P. norfolcensis and T. vulpecula. The abundance of T. vulpecula was also significantly positively correlated with variation in overstorey species composition, Acacia density and the number of hollow-bearing trees. The abundance of P. norfolcensis was positively correlated with Acacia density and canopy width, and negatively correlated with distance to the nearest intersection with another linear remnant. No significant variables were identified to explain the abundance of P. tapoatafa, and there were insufficient captures of the remaining species to investigate habitat preferences. Petaurus norfolcensis were resident within the linear network and their density (0.95 -1.54 ha-1) was equal to the maximum densities recorded for this species in continuous forest elsewhere in south-eastern Australia. Rates of reproduction were also similar to those in continuous forest, with births occurring between May and December, a mean natality rate of 1.9, and a mean litter size of 1.7. Sex ratios never differed significantly from parity. Overall, the population dynamics of P. norfolcensis were comparable with published results for the species in contiguous forest, clearly suggesting that the linear remnants currently support a self-sustaining, viable population. Fifty-one P. norfolcensis were fitted with radio transmitters and tracked intermittently between December 1997 and November 1998. Home ranges were small (1.3 - 2.8 ha), narrow (20 - 40 m) and elongated (322 - 839 m). Home ranges were mostly confined to the linear remnants, although 80% of gliders also utilised small clumps of adjacent woodland within farm paddocks for foraging or denning. Home range size was significantly larger at intersections between two or more linear remnants than within straight sections of linear remnants. Intersections appeared to be important sites for social interaction because the overlap of home ranges of members of adjacent social groups was significantly greater at intersections than straight sections. Intersections provided the only opportunity for members of three or more social groups to interact, while still maintaining their territories. The 51 gliders were radiotracked to 143 different hollow-bearing trees on 2081 occasions. On average, gliders used 5.3 den trees during the study (range 1-15), and changed den trees every 4.9 days. The number of den trees used by each glider is likely to be conservative because the cumulative number of den trees continued to increase over the full duration of the study. When gliders shifted between den trees, the mean distance between consecutive den sites was 247 m. Den trees were located throughout a glider's home range, thereby reducing the need to return to a central den site and potentially minimising energy expenditure. Dens were usually located in large trees (mean diameter 88.5 cm) and were selected significantly more often than expected based on their occurrence within the landscape. The overall conclusion of this thesis is that the linear network I studied provides high quality habitat for resident populations of arboreal marsupials. Important factors influencing the suitability of the linear remnants appear to be the high level of network connectivity, the location on soils of high nutrient status, the high density of large trees and an acacia understorey. In highly fragmented landscapes, linear habitats as part of the remaining woodland mosaic have the potential to be an integral component in the conservation of woodland-dependent fauna. The habitat value of linear strips of vegetation should not be underestimated.

Better off dead? Prices realised for Australian paintings sold at auction

Using auction sales data on Australian paintings over the period 1995 and 2003 we investigate the relationship between artists‟ living status and the price of paintings sold at auction. For deceased artists we consider the time since their death and for living artists their conditional life expectancy. Hedonic regression analysis is applied separately to the data on Indigenous and non-Indigenous paintings. Comparing the modelling results across Indigenous and non-Indigenous paintings we see evidence of two different patterns of response to an artist‟s living status. Both yield non-linear impacts but for Indigenous paintings these are quadratic and for non-Indigenous they are quartic. Thus the response to living status in the more recent market for Indigenous paintings is different to the more established market for non-Indigenous paintings. Whilst the responses differ for the two types of paintings, in answer to the question posed and in terms of the price of a painting at auction an artist is better off long dead or close to death.

Optimizing prediction of binge eating episodes : a comparison approach to test alternative conceptualizations of the affect regulation model

Background : Although a wealth of studies have tested the link between negative mood states and likelihood of a subsequent binge eating episode, the assumption that this relationship follows a typical linear dose–response pattern (i.e., that risk of a binge episode increases in proportion to level of negative mood) has not been challenged. The present study demonstrates the applicability of an alternative, non-linear conceptualization of this relationship, in which the strength of association between negative mood and probability of a binge episode increases above a threshold value for the mood variable relative to the slope below this threshold value (threshold dose response model).

Methods : A sample of 93 women aged 18 to 40 completed an online survey at random intervals seven times per day for a period of one week. Participants self-reported their current mood state and whether they had recently engaged in an eating episode symptomatic of a binge.

Results : As hypothesized, the threshold approach was a better predictor than the linear dose–response modeling of likelihood of a binge episode. The superiority of the threshold approach was found even at low levels of negative mood (3 out of 10, with higher scores reflecting more  negative mood). Additionally, severity of negative mood beyond this threshold value appears to be useful for predicting time to onset of a binge episode.

Conclusions : Present findings suggest that simple dose–response formulations for the association between  negative mood and onset of binge episodes miss vital aspects of this relationship. Most  notably, the impact of mood on binge eating appears to depend on whether a threshold value  of negative mood has been breached, and elevation in mood beyond this point may be useful  for clinicians and researchers to identify time to onset.

Linear optimization for ecological indices based on aggregation functions

We consider an optimization problem in ecology where our objective is to maximize biodiversity with respect to different land-use allocations. As it turns out, the main problem can be framed as learning the weights of a weighted arithmetic mean where the objective is the geometric mean of its outputs. We propose methods for approximating solutions to this and similar problems, which are non-linear by nature, using linear and bilevel techniques.

Ecological allometries and niche use dynamics across Komodo dragon ontogeny

Ontogenetic allometries in ecological habits and niche use are key responses by which individuals maximize lifetime fitness. Moreover, such allometries have significant implications for how individuals influence population and community dynamics. Here, we examined how body size variation in Komodo dragons (Varanus komodoensis) influenced ecological allometries in their: (1) prey size preference, (2) daily movement rates, (3) home range area, and (4) subsequent niche use across ontogeny. With increased body mass, Komodo dragons increased prey size with a dramatic switch from small (≤10 kg) to large prey (≥50 kg) in lizards heavier than 20 kg. Rates of foraging movement were described by a non-linear concave down response with lizard increasinghourly movement rates up until ∼20 kg body mass before decreasing daily movement suggesting reduced foraging effort in larger lizards. In contrast, home range area exhibited a sigmoid response with increased body mass. Intrapopulation ecological niche use and overlap were also strongly structured by body size. Thus, ontogenetic allometries suggest Komodo dragon’s transition from a highly active foraging modeexploiting small prey through to a less active sit and wait feeding strategy focused on killing large ungulates. Further, our results suggest that as body size increases across ontogeny, the Komodo dragon exhibited marked ontogenetic niche shifts that enabled it to function as an entire vertebrate predator guild by exploiting prey across multiple trophic levels.