Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

The role of basic nutritional research in pediatric liver disease : an historical perspective

The advent of liver transplantation for end-stage liver disease (ESLD) in children has necessitated a major rethink in the preoperative preparation and management from simple palliative care to active directed intervention. This is particularly evident in the approach to the nutritional care of these patients with the historical understanding of the nutritional pertubations in ESLD being described from a single pediatric liver transplant center. ESLD in children is a hypermetabolic process adversely affecting nutritional status, metabolic, and non-metabolic body compartments. There is a complex dynamic process affecting metabolic activity within the metabolically active body cell mass, as well as lipid oxidation during fasting and at rest, with other factors operating in conjunction with daily activities. We have proposed that immediately ingested nutrients are a more important source of energy in patients with ESLD than in healthy children, among whom energy may be stored in various body compartments.

The nutritional management of acute diarrhea in young infants : effect of carbohydrate ingested

To compare the efficacy of a low-lactose hy-drolyzed milk formula, a lactose-free corn syrup-based milk formula, and a standard lactose-containing formula during refeeding after rehydration in infants with gastroenteritis, 135 patients older than 2 years were studied by randomized trial. Clearly demonstrated disadvantages in terms of early weight loss and longer duration of diarrhea were observed with the lactose-based formula compared with early weight gains on both the low-lactose formulae, and thus the lactose-containing formula was discontinued after 91 patients. The early weight loss with the lactose-containing formula was statistically significantly related to the degree of relative (rehydrated) underweight. The two low-lactose formulae were further compared in the remaining 44 patients. Early weight gain (48 h) was sig-nificantly greater with the lactose-hydrolyzed formula compared with the corn syrup-based formula, but no statistically significant differences were observed in duration of diarrhea, energy intake, treatment failures, or late weight gain. We conclude that the routine use of a low-lactose formula during refeeding after rehydration in infants with gastroenteritis may have some advantages in underweight infants and toddlers in whom it is important to prevent further weight loss. © 1994 Raven Press Ltd, New York.

Smoothed rank-based procedure for censored data

A smoothed rank-based procedure is developed for the accelerated failure time model to overcome computational issues. The proposed estimator is based on an EM-type procedure coupled with the induced smoothing. "The proposed iterative approach converges provided the initial value is based on a consistent estimator, and the limiting covariance matrix can be obtained from a sandwich-type formula. The consistency and asymptotic normality of the proposed estimator are also established. Extensive simulations show that the new estimator is not only computationally less demanding but also more reliable than the other existing estimators.

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

Protein turnover in malnourished patients with cystic fibrosis: Effects of elemental and nonelemental nutritional supplements

To evaluate the relative efficacy of nonele-mental versus semielemental enteral supplements for nutritional rehabilitation of cystic fibrosis (CF) patients, whole-body protein turnover using the [15N]glycine method was studied in nine malnourished CF patients during enteral feedings, in a block design study compar-ing a semielemental formula (Criticare), a higher protein density but nonelemental formula (Traumacal) (T), and a nonelemental formula that had been modified to become isocaloric and isonitrogenous to the semielemental formula (modified Traumacal, MT). No significant differences in rates of protein synthesis or catabolism were observed comparing the three formulas. However the higher protein density nonelemental formula resulted in higher net protein deposition compared to the other two formulas (T + 0.42 g kg-110 h-1versus 0.33 g kg-110 h-1for Criticare and-0.59 g kg-110 h-1for MT), although this was significant (p < 0.05) for the MT versus T comparison only. This study lends support to the use of less expensive nonelemental formulas for the nutritional management of malnourished patients with CF. © 1990 Raven Press Ltd, New York.

Pre-operative nutritional support in children with end-stage liver disease accepted for liver transplantation: An approach to management

Pre-operative nutritional support was studied in 28 children with end-stage liver disease awaiting orthotopic liver transplantation. Nasogastric supplemental administration of a standard semi-elemental enteral nutritional formula was compared with a similar formula enriched with branched chain amino acids, and with a group receiving oral nutrition only. The duration of treatment in all groups was similar (mean 90 days). Energy intakes in the supplemented groups were 120-150% of recommended daily intakes (RDI), whereas ad libitum intakes in the oral group ranged 58-100% RDI. A significant improvement in mean Z-score for body weight (denoting catch-up) was noted only in those children who received nasogastric supplements enriched with branched-chain amino acids. The standard enterally-fed group maintained their body weight and Z-scores did not change significantly. In contrast, body weight Z-scores in those fed orally declined significantly. Nutritional supportive therapy of malnourished children with end-stage liver disease can minimize or improve nutritional status in children awaiting liver transplantation. The use of nutritional formulae rich in branche-chain amino acids may have nutritional advantages in children with chronic liver disease which require further study and evaluation.

The ontogeny of serum immunoreactive pancreatic lipase and cationic trypsinogen in the premature human infant

We evaluated the development of the exocrine pancreas in 16 healthy preterm infants (29.3 ± 1.6 weeks). The infants were fed breast milk with formula supplements (n=8) or formula alone (n=8). Growth was monitored weekly for 12 weeks then at 3, 6, 9, 12 months. At the same intervals sera were determined for pancreatic lipase and cationic trypsinogen. In addition, cord blood samples were analysed from another 33 preterm (27.6 ± 5.2 weeks) and 75 healthy full-term infants. Serum pancreatic lipase in the cord blood of term (3.7 ± 0.4 μg/l) and preterm infants (1.8 ± 0.2 μg/l) was significantly below values reported for older children (10.5 ± 0.9 μg/l; p < 0.001). In the preterm infant, serum lipase was also significantly lower than values obtained at term (p < 0.001). At birth, serum trypsinogen for preterm (16.8 ± 1.3 μg/l) and term infants (23.3 ± 1.9 μg/l) were below those for older children (31.4 ± 3.7 μg/l; p < 0.05). Over the first 3 weeks of life, serum lipase and trypsinogen increased significantly. From 3 weeks to 12 months of age, serum trypsinogen values remained unchanged, but serum lipase increased dramatically after 10 weeks of age. Thus, at 6 and 12 months of age, the preterm infants had significantly higher serum lipase values than infants of the same age born at term. These two pancreatic enzymes appear to show independent age-related maturation in infants born before term. The rate of maturation of lipase appears to be accelerated by exposure to the extrauterine environment.

CBCT image guidance in head and neck irradiation: The impact of daily and weekly imaging protocols

Purpose This study evaluated the impact of a daily and weekly image-guided radiotherapy protocols in reducing setup errors and setting of appropriate margins in head and neck cancer patients. Materials and methods Interfraction and systematic shifts for the hypothetical day 1–3 plus weekly imaging were extrapolated from daily imaging data from 31 patients (964 cone beam computed tomography (CBCT) scans). In addition, residual setup errors were calculated by taking the average shifts in each direction for each patient based on the first three shifts and were presumed to represent systematic setup error. The clinical target volume (CTV) to planning target volume (PTV) margins were calculated using van Herk formula and analysed for each protocol. Results The mean interfraction shifts for daily imaging were 0·8, 0·3 and 0·5 mm in the S-I (superior-inferior), L-R (left-right) and A-P (anterior-posterior) direction, respectively. On the other hand the mean shifts for day 1–3 plus weekly imaging were 0·9, 1·8 and 0·5 mm in the S-I, L-R and A-P direction, respectively. The mean day 1–3 residual shifts were 1·5, 2·1 and 0·7 mm in the S-I, L-R and A-P direction, respectively. No significant difference was found in the mean setup error for the daily and hypothetical day 1–3 plus weekly protocol. However, the calculated CTV to PTV margins for the daily interfraction imaging data were 1·6, 3·8 and 1·4 mm in the S-I, L-R and A-P directions, respectively. Hypothetical day 1–3 plus weekly resulted in CTV–PTV margins of 5, 4·2 and 5 mm in the S-I, L-R and A-P direction. Conclusions The results of this study show that a daily CBCT protocol reduces setup errors and allows setup margin reduction in head and neck radiotherapy compared to a weekly imaging protocol.

Feeding mode of Australian infants in the first 12 months of life: An assessment against national breastfeeding indicators

Background: In 2011, Australia published a set of 6 population-level indicators assessing breastfeeding, formula use, and the introduction of soft/semisolid/solid foods. Objectives: This study aimed to report the feeding practices of Australian infants against these indicators and determine the predictors of early breastfeeding cessation and introduction of solids. Methods: Mother–infant dyads (N = 1470) were recruited postnatally in 2 Australian capital cities and regional areas of 1 state between February 2008 and March 2009. Demographic and feeding intention data were collected by self-completed questionnaire at infant birth, with feeding practices (current feeding mode, age of breastfeeding cessation, age of formula and/or solids introduction) reported when the infant was between 4 and 7 months of age, and around 13 months of age. Multiple logistic regression was used to determine the predictors of breastfeeding cessation and solids introduction. Results: Although initiation of breastfeeding was almost universal (93.3%), less than half of the infants were breastfed to 6 months (41.7%) and 33.3% were receiving solids by 4 months. Women who were socially disadvantaged, younger, less educated, unpartnered, primiparous, and/or overweight were most likely to have ceased breastfeeding before 6 months of age, and younger and/or less educated women were most likely to have introduced solid food by 4 months of age. Not producing adequate milk was the most common reason provided for cessation of breastfeeding. Conclusion: The feeding behaviors of Australian infants in the first 12 months fall well short of recommendations. Women need anticipatory guidance as to the indicators of breastfeeding success and the tendency of women to doubt the adequacy of their breast milk supply warrants further investigation.

Mechanical performances of track-shaped rebar stiffened concrete-filled steel tubular (SCFRT) stub columns under axial compression

This paper presents a combined experimental, numerical, and theoretical study on the mechanical behaviors of track-shaped concrete-filled steel tubular (SCFRT) stub columns stiffened by rebars under compressive load. A total of 18 track-shaped concrete-filled steel tubular specimens including 12 specimens stiffened by rebars and 6 non-stiffened counterparts are tested, with consideration of parameters including flakiness ratio, concrete strength, and stiffeners. Failure pattern, bearing capacity, and ductility are all analyzed and discussed based on the experimental results. The numerical simulation by finite element (FE) software ABAQUS is also conducted. Based on both experimental and numerical results, theoretical formula to predict the load-bearing capacity of SCFRT stub columns subjected to axial compression loading is established according to the superposition principle of ultimate load-bearing capacity with rational simplification. The proposed theoretical method provides accurate predictions on the load bearing capacity by comparing with experimental results from 18 groups of specimens.

Autonomous UAVs wildlife detection using thermal imaging, predictive navigation and computer vision

There is an increased interest on the use of Unmanned Aerial Vehicles (UAVs) for wildlife and feral animal monitoring around the world. This paper describes a novel system which uses a predictive dynamic application that places the UAV ahead of a user, with a low cost thermal camera, a small onboard computer that identifies heat signatures of a target animal from a predetermined altitude and transmits that target’s GPS coordinates. A map is generated and various data sets and graphs are displayed using a GUI designed for easy use. The paper describes the hardware and software architecture and the probabilistic model for downward facing camera for the detection of an animal. Behavioral dynamics of target movement for the design of a Kalman filter and Markov model based prediction algorithm are used to place the UAV ahead of the user. Geometrical concepts and Haversine formula are applied to the maximum likelihood case in order to make a prediction regarding a future state of the user, thus delivering a new way point for autonomous navigation. Results show that the system is capable of autonomously locating animals from a predetermined height and generate a map showing the location of the animals ahead of the user.

Kafka on the Shore

Kafka On The Shore consists of three simple concrete letterforms floating on a gallery wall. Reminiscent of minimalist sculpture, the mathematical expression of the letterforms states that ‘r’ is greater than ‘g’. Despite this material simplicity, the solemn presentation of the formula suggests a sense of foreboding, a quiet menace. The work was created as a response to the economic theories of Thomas Piketty presented in his book Capital in the Twenty-First Century. The primary finding of Piketty’s data-driven research is the formula presented by the work; that historically, wealth and inequity both flourish when the rate of return on capital (r) is greater than the rate of economic growth (g). With this simple mathematical summary the book acts as a sobering indictment on the present state of economic inequality.