Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Foreseeability of pure economic loss and causation

In Bonny Glen Pty Ltd v Country Energy [2009] NSWCA 26 (24 February 2009) the New South Wales Court of Appeal held that the pure economic loss suffered by the appellant was recoverable. However, rather than arguments as to whether the appellant was vulnerable and a member of an ascertainable class, whether the respondent had knowledge of the risk to the appellant and was in a position of control and considerations as to indeterminate liability as in Perre v Apand Pty Ltd (1999) 198 CLR 180, the arguments raised related to the foreseeability of the loss and causation.

Appetite sensations and satiety quotient : predictors of energy intake and weight loss

PURPOSE: The aim of this study was to further evaluate the validity and clinical meaningfulness of appetite sensations to predict overall energy intake as well as body weight loss. METHODS: Men (n=176) and women (n=139) involved in six weight loss studies were selected to participate in this study. Visual analogue scales were used to measure appetite sensations before and after a fixed test meal. Fasting appetite sensations, 1 h post-prandial area under the curve (AUC) and the satiety quotient (SQ) were used as predictors of energy intake and body weight loss. Two separate measures of energy intake were used: a buffet style ad libitum test lunch and a three-day self-report dietary record. RESULTS: One-hour post-prandial AUC for all appetite sensations represented the strongest predictors of ad libitum test lunch energy intake (p0.001). These associations were more consistent and pronounced for women than men. Only SQ for fullness was associated with ad libitum test lunch energy intake in women. Similar but weaker relationships were found between appetite sensations and the 3-day self-reported energy intake. Weight loss was associated with changes in appetite sensations (p0.01) and the best predictors of body weight loss were fasting desire to eat; hunger; and PFC (p0.01). CONCLUSIONS: These results demonstrate that appetite sensations are relatively useful predictors of spontaneous energy intake, free-living total energy intake and body weight loss. They also confirm that SQ for fullness predicts energy intake, at least in women.

Predicting loss and fragmentation of habitat of the vulnerable subtropical rainforest tree Macadamia integrifolia with models developed from compiled ecological data

Habitat models are widely used in ecology, however there are relatively few studies of rare species, primarily because of a paucity of survey records and lack of robust means of assessing accuracy of modelled spatial predictions. We investigated the potential of compiled ecological data in developing habitat models for Macadamia integrifolia, a vulnerable mid-stratum tree endemic to lowland subtropical rainforests of southeast Queensland, Australia. We compared performance of two binomial models—Classification and Regression Trees (CART) and Generalised Additive Models (GAM)—with Maximum Entropy (MAXENT) models developed from (i) presence records and available absence data and (ii) developed using presence records and background data. The GAM model was the best performer across the range of evaluation measures employed, however all models were assessed as potentially useful for informing in situ conservation of M. integrifolia, A significant loss in the amount of M. integrifolia habitat has occurred (p < 0.05), with only 37% of former habitat (pre-clearing) remaining in 2003. Remnant patches are significantly smaller, have larger edge-to-area ratios and are more isolated from each other compared to pre-clearing configurations (p < 0.05). Whilst the network of suitable habitat patches is still largely intact, there are numerous smaller patches that are more isolated in the contemporary landscape compared with their connectedness before clearing. These results suggest that in situ conservation of M. integrifolia may be best achieved through a landscape approach that considers the relative contribution of small remnant habitat fragments to the species as a whole, as facilitating connectivity among the entire network of habitat patches.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

The effects of exercise-induced weight loss on appetite-related peptides and motivation to eat

Context: The magnitude of exercise-induced weight loss depends on the extent of compensatory responses. An increase in energy intake is likely to result from changes in the appetite control system toward an orexigenic environment; however, few studies have measured how exercise impacts on both orexigenic and anorexigenic peptides. ---------- Objective: The aim of the study was to investigate the effects of medium-term exercise on fasting/postprandial levels of appetite-related hormones and subjective appetite sensations in overweight/obese individuals. ---------- Design and Setting: We conducted a longitudinal study in a university research center. ---------- Participants and Intervention: Twenty-two sedentary overweight/obese individuals (age, 36.9 ± 8.3 yr; body mass index, 31.3 ± 3.3 kg/m2) took part in a 12-wk supervised exercise programme (five times per week, 75% maximal heart rate) and were requested not to change their food intake during the study. ---------- Main Outcome Measures: We measured changes in body weight and fasting/postprandial plasma levels of glucose, insulin, total ghrelin, acylated ghrelin (AG), peptide YY, and glucagon-like peptide-1 and feelings of appetite. ---------- Results: Exercise resulted in a significant reduction in body weight and fasting insulin and an increase in AG plasma levels and fasting hunger sensations. A significant reduction in postprandial insulin plasma levels and a tendency toward an increase in the delayed release of glucagon-like peptide-1 (90–180 min) were also observed after exercise, as well as a significant increase (127%) in the suppression of AG postprandially. ---------- Conclusions: Exercise-induced weight loss is associated with physiological and biopsychological changes toward an increased drive to eat in the fasting state. However, this seems to be balanced by an improved satiety response to a meal and improved sensitivity of the appetite control system.

Prandial subcutaneous injections of glucagon-like peptide-1 cause weight loss in obese human subjects

Recombinant glucagon-like peptide-1 (7–36)amide (rGLP-1) was recently shown to cause significant weight loss in type 2 diabetics when administered for 6 weeks as a continuous subcutaneous infusion. The mechanisms responsible for the weight loss are not clarified. In the present study, rGLP-1 was given for 5d by prandial subcutaneous injections (PSI) (76nmol 30min before meals, four times daily; a total of 302·4nmol/24h) or by continuous subcutaneous infusion (CSI) (12·7nmol/h; a total of 304·8nmol/24h). This was performed in nineteen healthy obese subjects (mean age 44·2 (sem 2·5) years; BMI 39·0 (sem 1·2)kg/m2) in a prospective randomised, double-blind, placebo-controlled, cross-over study. Compared with the placebo, rGLP-1 administered as PSI and by CSI generated a 15% reduction in mean food intake per meal (P=0·02) after 5d treatment. A weight loss of 0·55 (sem 0·2) kg (P<0·05) was registered after 5d with PSI of rGLP-1. Gastric emptying rate was reduced during both PSI (P<0·001) and CSI (P<0·05) treatment, but more rapidly and to a greater extent with PSI of rGLP-1. To conclude, a 5d treatment of rGLP-1 at high doses by PSI, but not CSI, promptly slowed gastric emptying as a probable mechanism of action of increased satiety, decreased hunger and, hence, reduced food intake with an ensuing weight loss.

Improved algebraic cryptanalysis of QUAD, Bivium and Trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks.

A new method for improving reliability and line loss in distribution networks

In this paper, both Distributed Generators (DG) and capacitors are allocated and sized optimally for improving line loss and reliability. The objective function is composed of the investment cost of DGs and capacitors along with loss and reliability which are converted to the genuine dollar. The bus voltage and line current are considered as constraints which should be satisfied during the optimization procedure. Hybrid Particle Swarm Optimization as a heuristic based technique is used as the optimization method. The IEEE 69-bus test system is modified and employed to evaluate the proposed algorithm. The results illustrate that the lowest cost planning is found by optimizing both DGs and capacitors in distribution networks.

Structural equation model of construction contract dispute potential

This paper presents the results of a structural equation model (SEM) for describing and quantifying the fundamental factors that affect contract disputes between owners and contractors in the construction industry. Through this example, the potential impact of SEM analysis in construction engineering and management research is illustrated. The purpose of the specific model developed in this research is to explain how and why contract related construction problems occur. This study builds upon earlier work, which developed a disputes potential index, and the likelihood of construction disputes was modeled using logistic regression. In this earlier study, questionnaires were completed on 159 construction projects, which measured both qualitative and quantitative aspects of contract disputes, management ability, financial planning, risk allocation, and project scope definition for both owners and contractors. The SEM approach offers several advantages over the previously employed logistic regression methodology. The final set of structural equations provides insight into the interaction of the variables that was not apparent in the original logistic regression modeling methodology.

Low fat loss response after medium-term supervised exercise in obese is associated with exercise-induced increase in food reward

Objective: To examine exercise-induced changes in the reward value of food during medium-term supervised exercise in obese individuals. ---------- Subjects/Methods: The study was a 12-week supervised exercise intervention prescribed to expend 500 kcal/day, 5 d/week. 34 sedentary obese males and females were identified as responders (R) or non-responders (NR) to the intervention according to changes in body composition relative to measured energy expended during exercise. Food reward (ratings of liking and wanting, and relative preference by forced choice pairs) for an array of food images was assessed before and after an acute exercise bout. ---------- Results. 20 responders and 14 non-responders were identified. R lost 5.2 kg±2.4 of total fat mass and NR lost 1.7 kg±1.4. After acute exercise, liking for all foods increased in NR compared to no change in R. Furthermore, NR showed an increase in wanting and relative preference for high-fat sweet foods. These differences were independent of 12-weeks regular exercise and weight loss. ---------- Conclusion. Individuals who showed an immediate post-exercise increase in liking and increased wanting and preference for high-fat sweet foods displayed a smaller reduction in fat mass with exercise. For some individuals, exercise increases the reward value of food and diminishes the impact of exercise on fat loss.