Multifractal characterisation and analysis of complex networks

Complex networks have been studied extensively due to their relevance to many real-world systems such as the world-wide web, the internet, biological and social systems. During the past two decades, studies of such networks in different fields have produced many significant results concerning their structures, topological properties, and dynamics. Three well-known properties of complex networks are scale-free degree distribution, small-world effect and self-similarity. The search for additional meaningful properties and the relationships among these properties is an active area of current research. This thesis investigates a newer aspect of complex networks, namely their multifractality, which is an extension of the concept of selfsimilarity. The first part of the thesis aims to confirm that the study of properties of complex networks can be expanded to a wider field including more complex weighted networks. Those real networks that have been shown to possess the self-similarity property in the existing literature are all unweighted networks. We use the proteinprotein interaction (PPI) networks as a key example to show that their weighted networks inherit the self-similarity from the original unweighted networks. Firstly, we confirm that the random sequential box-covering algorithm is an effective tool to compute the fractal dimension of complex networks. This is demonstrated on the Homo sapiens and E. coli PPI networks as well as their skeletons. Our results verify that the fractal dimension of the skeleton is smaller than that of the original network due to the shortest distance between nodes is larger in the skeleton, hence for a fixed box-size more boxes will be needed to cover the skeleton. Then we adopt the iterative scoring method to generate weighted PPI networks of five species, namely Homo sapiens, E. coli, yeast, C. elegans and Arabidopsis Thaliana. By using the random sequential box-covering algorithm, we calculate the fractal dimensions for both the original unweighted PPI networks and the generated weighted networks. The results show that self-similarity is still present in generated weighted PPI networks. This implication will be useful for our treatment of the networks in the third part of the thesis. The second part of the thesis aims to explore the multifractal behavior of different complex networks. Fractals such as the Cantor set, the Koch curve and the Sierspinski gasket are homogeneous since these fractals consist of a geometrical figure which repeats on an ever-reduced scale. Fractal analysis is a useful method for their study. However, real-world fractals are not homogeneous; there is rarely an identical motif repeated on all scales. Their singularity may vary on different subsets; implying that these objects are multifractal. Multifractal analysis is a useful way to systematically characterize the spatial heterogeneity of both theoretical and experimental fractal patterns. However, the tools for multifractal analysis of objects in Euclidean space are not suitable for complex networks. In this thesis, we propose a new box covering algorithm for multifractal analysis of complex networks. This algorithm is demonstrated in the computation of the generalized fractal dimensions of some theoretical networks, namely scale-free networks, small-world networks, random networks, and a kind of real networks, namely PPI networks of different species. Our main finding is the existence of multifractality in scale-free networks and PPI networks, while the multifractal behaviour is not confirmed for small-world networks and random networks. As another application, we generate gene interactions networks for patients and healthy people using the correlation coefficients between microarrays of different genes. Our results confirm the existence of multifractality in gene interactions networks. This multifractal analysis then provides a potentially useful tool for gene clustering and identification. The third part of the thesis aims to investigate the topological properties of networks constructed from time series. Characterizing complicated dynamics from time series is a fundamental problem of continuing interest in a wide variety of fields. Recent works indicate that complex network theory can be a powerful tool to analyse time series. Many existing methods for transforming time series into complex networks share a common feature: they define the connectivity of a complex network by the mutual proximity of different parts (e.g., individual states, state vectors, or cycles) of a single trajectory. In this thesis, we propose a new method to construct networks of time series: we define nodes by vectors of a certain length in the time series, and weight of edges between any two nodes by the Euclidean distance between the corresponding two vectors. We apply this method to build networks for fractional Brownian motions, whose long-range dependence is characterised by their Hurst exponent. We verify the validity of this method by showing that time series with stronger correlation, hence larger Hurst exponent, tend to have smaller fractal dimension, hence smoother sample paths. We then construct networks via the technique of horizontal visibility graph (HVG), which has been widely used recently. We confirm a known linear relationship between the Hurst exponent of fractional Brownian motion and the fractal dimension of the corresponding HVG network. In the first application, we apply our newly developed box-covering algorithm to calculate the generalized fractal dimensions of the HVG networks of fractional Brownian motions as well as those for binomial cascades and five bacterial genomes. The results confirm the monoscaling of fractional Brownian motion and the multifractality of the rest. As an additional application, we discuss the resilience of networks constructed from time series via two different approaches: visibility graph and horizontal visibility graph. Our finding is that the degree distribution of VG networks of fractional Brownian motions is scale-free (i.e., having a power law) meaning that one needs to destroy a large percentage of nodes before the network collapses into isolated parts; while for HVG networks of fractional Brownian motions, the degree distribution has exponential tails, implying that HVG networks would not survive the same kind of attack.

Prevalence of malnutrition risk and its relationship with risk factors of hospital re-admission in older adults

Background: Risk of malnutrition in older people continues to be a global problem. Malnutrition is often unrecognized and under-treated across health care settings and may result in undesirable health consequences, impaired recovery from illness and a poorer quality of life. Aim: This study aimed to determine the prevalence of malnutrition risk in a sample of older people at high risk of hospital re-admission. The association between risk factors of hospital re-admission and risk of malnutrition were also explored. Methods: One hundred and twenty five hospitalised patients aged 65 years and older at risk of hospital readmission (24% male, 76% female, mean age 77 ± 6 years) were recruited from a tertiary metropolitan hospital in Australia. The valid and reliable Malnutrition Screen Tool (MST) was employed to screen for malnutrition risk. It consists of two questions related to recent weight loss and appetite. Results: Prevalence of older adults at risk of malnutrition was 27.4%. Risk of malnutrition was not associated with age, gender and living arrangement. However, among risk factors of hospital readmission, lack of social support (χ2 = 4.18, N = 125, p = 0.028), and fair –poor self-rating of health (χ2 = 4.13, N = 125, p = 0.042) were statistically significant associated with risk of malnutrition. Conclusion: Risk of malnutrition in older people continues to be a concern in health care, and increasing psycho social support may help shed light on reducing risk of malnutrition.

Socioeconomic inequalities in weight status among mid-aged adults : the contribution of perceptions of weight status and weight-control behaviours

Background Socioeconomically-disadvantaged adults in developed countries experience a higher prevalence of a number of chronic diseases, such as cardiovascular disease, type 2 diabetes, osteoarthritis and some forms of cancer. Overweight and obesity are major risk factors for these diseases. Lower socioeconomic groups have a greater prevalence of overweight and obesity and this may contribute to their higher morbidity and mortality. International studies suggest that socioeconomic groups may differ in their self-perceptions of weight status and their engagement in weightcontrol behaviours (WCBs). Research has shown that lower socioeconomic adults are more likely to underestimate their weight status, and are less likely to engage in WCBs. This may contribute (in part) to the marked inequalities in weight status observed at the population level. There are few, and somewhat limited, Australian studies that have examined the types of weight-control strategies people adopt, the barriers to their weight control, the determinants of their perceived weight status and WCBs. Furthermore, there are no known Australian studies that have examined socioeconomic differences in these factors to better understand the reasons for socioeconomic inequalities in weight status. Hence, the overall aim of this Thesis is to examine why socioeconomically-disadvantaged group experience a greater prevalence of overweight and obesity than their more-advantaged counterparts. Methods This Thesis used data from two sources. Men and women aged 45 to 60 years were examined from both data source. First, the longitudinal Australian Diabetes, Obesity and Lifestyle (AusDiab) Study were used to advance our knowledge and understanding of socioeconomic differences in weight change, perceived weight status and WCBs. A total of 2753 participants with measured weights at both baseline (1999-2000) and follow-up (2004-2005) were included in the analyses. Percent weight change over the five-year interval was calculated and perceived weight status, WCBs and highest attained education were collected at baseline. Second, the Candidate conducted a postal questionnaire from 1013 Brisbane residents (69.8 % response rate) to investigate the relationship between socioeconomic position, determinants of perceived weight status, WCBs, and barriers and reasons to weight control. A test-retest reliability study was conducted to determine the reliability of the new measures used in the questionnaire. Most new measures had substantial to almost perfect reliability when considering either kappa coefficient or crude agreement. Results The findings from the AusDiab Study (accepted for publication in the Australian and New Zealand Journal of Public Health) showed that low-educated men and women were more likely to be obese at baseline compared to their higheducated respondents (O.R. = 1.97, 95 % C.I. = 1.30-2.98 and O.R. = 1.52, 95 % C.I. = 1.03-2.25, respectively). Over the five year follow-up period (1999-2000 to 2004- 05) there were no socioeconomic differences in weight change among men, however socioeconomically-disadvantaged women had greater weight gains. Participants perceiving themselves as overweight gained less weight than those who saw themselves as underweight or normal weight. There was no relationship between engaging in WCBs and five-year weight change. The postal questionnaire data showed that socioeconomically-disadvantaged groups were less likely to engage in WCBs. If they did engage in weight control, they were less likely to adopt exercise strategies, including moderate and vigorous physical activities but were more likely to decrease their sitting time to control their weight. Socioeconomically-disadvantaged adults reported more barriers to weight control; such as perceiving weight loss as expensive, requiring a lot of cooking skills, not being a high priority and eating differently from other people in the household. These results have been accepted for publication in Public Health Nutrition. The third manuscript (under review in Social Science and Medicine) examined socioeconomic differences in determinants of perceived weight status and reasons for weight control. The results showed that lower socioeconomic adults were more likely to specify the following reasons for weight control: they considered themselves to be too heavy, for occupational requirements, on recommendation from their doctor, family members or friends. Conversely, high-income adults were more likely to report weight control to improve their physical condition or to look more attractive compared with those on lower-incomes. There were few socioeconomic differences in the determinants of perceived weight status. Conclusions Education inequalities in overweight/obesity among men and women may be due to mis-perceptions of weight status; overweight or obese individuals in loweducated groups may not perceive their weight as problematic and therefore may not pay attention to their energy-balance behaviours. Socioeconomic groups differ in WCBs, and their reasons and perceived barriers to weight control. Health promotion programs should encourage weight control among lower socioeconomic groups. More specifically, they should encourage the engagement of physical activity or exercise and dietary strategies among disadvantaged groups. Furthermore, such programs should address potential barriers for weight control that disadvantaged groups may encounter. For example, disadvantaged groups perceive that weight control is expensive, requires cooking skills, not a high priority and eating differently from other people in the household. Lastly, health promotion programs and policies aimed at reducing overweight and obesity should be tailored to the different reasons and motivations to weight control experienced by different socioeconomic groups. Weight-control interventions targeted at higher socioeconomic groups should use improving physical condition and attractiveness as motivational goals; while, utilising social support may be more effective for encouraging weight control among lower socioeconomic groups.

The 'obesity paradox' in chronic obstructive pulmonary disease

Poor nutritional status in chronic obstructive pulmonary disease (COPD) is associated with increased mortality independently of disease-severity (Collins et al).1 Epidemiological studies have suggested a protective role of obesity against mortality in COPD (Vestbo et al)2 which is contrary to data from the general population where obesity is associated with decreased life expectancy. This relationship has been referred to as the ‘obesity paradox’ and has been demonstrated in a number of chronic wasting conditions (Kalantar-Zadeh et al).3 This study investigated the existence of the obesity paradox in outpatients with COPD by examining the effect of body mass index (BMI) on 1-year healthcare use and clinical outcome in terms of hospital admission rates, length of hospital stay, outpatient appointments and mortality. BMI was assessed in 424 outpatients with COPD, with measurements performed by specialist respiratory nurses during outpatient clinics. 1-year healthcare use was retrospectively collected from the date of BMI measurement. Abstract S163 Table 1 Patients classified as overweight (25.0–29.9 kg/m2) or obese (>30 kg/m2) experienced significantly fewer emergency hospital admissions, as well as a reduced length of hospital stay, in comparison to normal weight (20.0–24.9 kg/m2) or underweight (<20 kg/m2) outpatients. There was a significant negative trend between BMI classification and mortality. This study supports the existence of the ‘obesity paradox’ in COPD, not only in relation to reduced 1 year mortality rates but also in terms of reduced emergency hospital admissions and reduced length of hospital stay.

Exercise, appetite and weight management: understanding the compensatory responses in eating behaviour and how they contribute to variability in exercise-induced weight loss

Does exercise promote weight loss? One of the key problems with studies assessing the efficacy of exercise as a method of weight management and obesityis that mean data are presented and the individual variability in response is overlooked. Recent data have highlighted the need to demonstrate and characterise the individual variability in response to exercise. Do people who exercise compensate for the increase in energy expenditure via compensatory increases in hunger and food intake? The authors address the physiological, psychological and behavioural factors potentially involved in the relationship between exercise and appetite, and identify the research questions that remain unanswered. A negative consequence of the phenomena of individual variability and compensatory responses has been the focus on those who lose little weight in response to exercise; this has been used unreasonably as evidence to suggest that exercise is a futile method of controlling weight and managing obesity. Most of the evidence suggests that exercise is useful for improving body composition and health. For example, when exercise-induced mean weight loss is <1.0 kg, significant improvements in aerobic capacity (+6.3 ml/kg/min), systolic (−6.00 mm Hg) and diastolic (−3.9 mm Hg) blood pressure, waist circumference (−3.7 cm) and positive mood still occur. However, people will vary in their responses to exercise; understanding and characterising this variability will help tailor weight loss strategies to suit individuals.

Knee extensor strength differences in obese and healthy-weight 10-13 year olds

The purpose of this study was to investigate if obese children have reduced knee extensor (KE) strength and to explore the relationship between adiposity and KE strength. An observational case-control study was conducted in three Australian states, recruiting obese [n=107 (51 female, 56 male)] and healthy-weight [n=132 (56 female, 76 male)] 10–13 year old children. Body mass index, body composition (dual energy X-ray absorptiometry), isokinetic/isometric peak KE torques (dynamometry) and physical activity (accelerometry) were assessed. Results revealed that compared with their healthy-weight peers, obese children had higher absolute KE torques (P≤0.005), equivocal KE torques when allometrically normalized for fat-free mass (FFM) (P≥0.448) but lower relative KE torques when allometrically normalized for body mass (P≤0.008). Adjustments for maternal education, income and accelerometry had little impact on group differences, except for isometric KE torques relative to body mass which were no longer significantly lower in obese children (P≥0.013, not significant after controlling for multiple comparisons). Percent body fat was inversely related to KE torques relative to body mass (r= -0.22 to -0.35, P≤0.002), irrespective of maternal education, income or accelerometry. In conclusion, while obese children have higher absolute KE strength and FFM, they have less functional KE strength (relative to mass) available for weight-bearing activities than healthy-weight children. The finding that FFM-normalized KE torques did not differ suggests that the intrinsic contractile properties of the KE muscles are unaffected by obesity. Future research is needed to see if deficits in KE strength relative to mass translate into functional limitations in weight-bearing activities.

Language affects length of stay in emergency departments in Queensland public hospitals

BACKGROUND: A long length of stay (LOS) in the emergency department (ED) associated with overcrowding has been found to adversely affect the quality of ED care. The objective of this study is to determine whether patients who speak a language other than English at home have a longer LOS in EDs compared to those whose speak only English at home. METHODS: A secondary data analysis of a Queensland state-wide hospital EDs dataset (Emergency Department Information System) was conducted for the period, 1 January 2008 to 31 December 2010. RESULTS: The interpreter requirement was the highest among Vietnamese speakers (23.1%) followed by Chinese (19.8%) and Arabic speakers (18.7%). There were significant differences in the distributions of the departure statuses among the language groups (Chi-squared=3236.88, P<0.001). Compared with English speakers, the Beta coeffi cient for the LOS in the EDs measured in minutes was among Vietnamese, 26.3 (95%CI: 22.1–30.5); Arabic, 10.3 (95%CI: 7.3–13.2); Spanish, 9.4 (95%CI: 7.1–11.7); Chinese, 8.6 (95%CI: 2.6–14.6); Hindi, 4.0 (95%CI: 2.2–5.7); Italian, 3.5 (95%CI: 1.6–5.4); and German, 2.7 (95%CI: 1.0–4.4). The fi nal regression model explained 17% of the variability in LOS. CONCLUSION: There is a close relationship between the language spoken at home and the LOS at EDs, indicating that language could be an important predictor of prolonged LOS in EDs and improving language services might reduce LOS and ease overcrowding in EDs in Queensland's public hospitals.

Evaluation of shear stress and slip relationship of composite lap joints

Advanced composite materials offer remarkable potential in the strengthening of Civil Engineering structures. This research is targeted to provide in depth knowledge and understanding of bond characteristics of advanced and corrosion resistant material carbon fibre reinforced polymer (CFRP) that has a unique design tailor-ability and cost effective nature. The objective of this research is to investigate and compare the bonding mechanism between CFRP strengthened single and double strap steel joints. Investigations have been made in regards to failure mode, ultimate load and effective bond length for CFRP strengthened double and single strap joints. A series of tensile tests were conducted with different bond lengths for both type of joints. The bond behaviour of these specimens was further investigated by using nonlinear finite element analysis. Finally a bilinear relationship of shear stress-slip has been proposed by using the Finite element model for single and double strap joints.

An interpretative phenomenological analysis of participation in a pro-anorexia Internet site and its relationship to disordered eating

Pro-anorexia Internet sites aim to promote, support and discuss anorexia nervosa. Media coverage has raised concerns that sites may increase the level of eating disorders. This research examines the meaning of participation in a pro-anorexia Internet site and its relationship with disordered eating by using an interpretative phenomenological analysis of fifteen separate message ‘threads’ followed over a six-week period. Four themes were identified: (1) tips and techniques; (2) ‘ana’ v. anorexia nervosa; (3) social support; and (4) need for anorexia. Findings suggest participation was multi-purpose, providing a coping function in relation to weight loss, and the contribution of sites to increased levels of eating disorders is not inevitable.

Genetic response to combined family selection for improved mean harvest weight in giant freshwater prawn (Macrobrachium rosenbergii) in Vietnam

We estimated genetic changes in body and carcass weight traits in a giant freshwater prawn (GFP) (Macrobrachium rosenbergii) population selected for increased body weight at harvest in Vietnam. The data set consisted of 18,387 individual body and 1730 carcass weight records, as well as full pedigree information collected over four generations. Average selection response (per generation) in body weight at harvest (transformed to square root) estimated as the difference between the Selection line and the Control group was 7.4% calculated from least squares mean (LSMs), 7.0% from estimated breeding values (EBVs) and 4.4% calculated from EBVs between two consecutive generations. Favorable correlated selection responses (estimated from LSMs) were found for other body traits including: total length, cephalothorax length, abdominal length, cephalothorax width, and abdominal width (12.1%, 14.5%, 10.4%, 15.5% and 13.3% over three selection generations, respectively). Data in the second generation of selection showed positive correlated responses for carcass weight traits including: abdominal weight, exoskeleton-off weight, and telson-off weight of 8.8%, 8.6% and 8.8%, respectively. We conclude that body weight at harvest responded well to the application of combined (between and within) family selection and correlated responses in carcass weight traits were favorable.

Association of HincII RFLP of low density lipoprotein receptor gene with obesity in essential hypertensives

Obese (BMI ≥ 26 kg/m 2; n = 51) and lean (BMI <26 kg/m 2; n = 61) Caucasian patients with severe, familial essential hypertension, were compared with respect to genotype and allele frequencies of a HincII RFLP of the low density lipoprotein receptor gene (LDLR). A similar analysis was performed in obese (n = 28) and lean (n = 68) normotensives. A significant association of the C allele of the T→C variant responsible for this RFLP was seen with obesity (χ 2 = 4.6, P = 0.029) in the hypertensive, but not in the normotensive, group (odds ratio = 3.0 for the CC genotype and 2.7 for CT). Furthermore, BMI tracked with genotypes of this allele in the hypertensives (P = 0.046). No significant genotypic relationship was apparent for plasma lipids. Significant linkage disequilibrium was, moreover, noted between the HincII RFLP and an ApaLI RFLP (χ 2 = 33, P<0.0005) that has previously shown even stronger association with obesity (odds ratio 19.6 for cases homozygous for the susceptibility allele and 15.2 for het-erozygotes). The present study therefore adds to our previous evidence implicating LDLR as a locus for obesity in patients with essential hypertension.

Physical activity and overweight in children aged 3-5 : relationship to parental activity and obesity

OBJECTIVE To compare the physical activity levels of overweight and non overweight 3- to 5-y-old children while attending preschool. A secondary aim was to evaluate weight-related differences in hypothesized parental determinants of child physical activity behavior. DESIGN Cross-sectional study. SUBJECTS A total of 245, 3- to 5-y-olds (127 girls, 118 boys) and their parent(s) (242 mothers, 173 fathers) recruited from nine preschools. Overweight status determined using the age- and sex-specific 85th percentile for body mass index (BMI) from CDC Growth Charts. MEASUREMENTS Physical activity during the preschool day was assessed on multiple days via two independent objective measures direct observation using the observation system for recording activity in preschools (OSRAP) and real-time accelerometry using the MTI/CSA 7164 accelerometer. Parents completed a take-home survey assessing sociodemographic information, parental height and weight, modeling of physical activity, support for physical activity, active toys and sporting equipment at home, child’s television watching, frequency of park visitation, and perceptions of child competence. RESULTS Overweight boys were significantly less active than their nonoverweight peers during the preschool day. No significant differences were observed in girls. Despite a strong association between childhood overweight status and parental obesity, no significant differences were observed for the hypothesized parental influences on physical activity behavior. CONCLUSIONS Our results suggest that a significant proportion of overweight children may be at increased risk for further gains in adiposity because of low levels of physical activity during the preschool day.

Confirmatory factor analysis of the baby eating behaviour questionnaire and associations with infant weight, gender and feeding mode in an Australian sample

The aim of this study was to evaluate the factor structure of the Baby Eating Behaviour Questionnaire (BEBQ) in an Australian community sample of mother-infant dyads. A secondary aim was to explore the relationship between the BEBQ subscales and infant gender, weight and current feeding mode. Confirmatory factor analysis (CFA) utilising structural equation modelling examined the hypothesised 4-factor model of the BEBQ. Only mothers (N=467) who completed all items on the BEBQ (infant age: M=17 weeks, SD=3 weeks) were included in the analysis. The original 4-factor model did not provide an acceptable fit to the data due to poor performance of the Satiety responsiveness factor. Removal of this factor (3 items) resulted in a well-fitting 3-factor model. Cronbach’s α was acceptable for the Enjoyment of food (α=0.73), Food responsiveness (α=0.78) and Slowness in eating (α=0.68) subscales but low for the Satiety responsiveness (α=0.56) subscale. Enjoyment of food was associated with higher infant weight whereas Slowness in eating and Satiety responsiveness were both associated with lower infant weight. Differences on all four subscales as a function of feeding mode were observed. This study is the first to use CFA to evaluate the hypothesised factor structure of the BEBQ. Findings support further development work on the Satiety responsiveness subscale in particular, but confirm the utility of the Enjoyment of food, Food responsiveness and Slowness in eating subscales.

Can mothers accurately describe their toddler’s weight? Results from the NOURISH cohort

A mother’s perception of her child’s weight may be more important in determining how she feeds her child, than the child’s actual weight status. Use of controlling feeding practices, prompted by perceptions and concerns about weight, may disrupt the child’s innate self-regulation of energy intake. This can promote overeating and overweight (Costanzo & Woody, 1985). This study describes mother’s perception of her child’s weight relative to the child’s actual weight. Mothers in the control group of NOURISH (n=276) were asked to describe their child as underweight, normal weight, or somewhat/very overweight via self-administered questionnaire when children were aged 12-16 months (Daniels et al, 2009). Child’s weight and length were measured by study staff. At assessment, mean age (sd) was 13.7(1.3) months, mean weight-for-age z-score (sd) was 0.6(0.8) (WHO standards, 2008), and 51% were male. Twenty-seven children were perceived as underweight (10%) and twelve children were perceived as overweight (4%). ANOVA revealed significant differences in weight-for-age z-scores across each category of weight perception, mean (sd) -0.2(0.5), 0.6(0.8) and 1.8(0.7) for underweight, normal weight and overweight respectively F(4, 288)= 15.6, (p<0.00). Based on WHO criteria only one of the 27 children was correctly perceived as underweight (WHO 2008). Similarly while 12 children were perceived as overweight, 88 were actually overweight/at risk. At group level, children of mothers who perceived their child as underweight were indeed leaner. However at the individual level mothers could not accurately describe their child’s weight, tending to over-identify underweight and perceive overweight children as normal weight.