A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Mass spectrometry-based metabolomics towards understanding of gene functions with a diversity of biological contexts

Currently, mass spectrometry-based metabolomics studies extend beyond conventional chemical categorization and metabolic phenotype analysis to understanding gene function in various biological contexts (e.g., mammalian, plant, and microbial). These novel utilities have led to many innovative discoveries in the following areas: disease pathogenesis, therapeutic pathway or target identification, the biochemistry of animal and plant physiological and pathological activities in response to diverse stimuli, and molecular signatures of host-pathogen interactions during microbial infection. In this review, we critically evaluate the representative applications of mass spectrometry-based metabolomics to better understand gene function in diverse biological contexts, with special emphasis on working principles, study protocols, and possible future development of this technique. Collectively, this review raises awareness within the biomedical community of the scientific value and applicability of mass spectrometry-based metabolomics strategies to better understand gene function, thus advancing this application's utility in a broad range of biological fields

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Ion-acoustic waves in a complex plasma with negative ions

A wave propagation in a complex dusty plasma with negative ions was considered. The relevant processes such as ionization, electron attachment, diffusion, positive-negative ion recombination, plasma particle collisions, as well as elastic Coulomb and inelastic dust-charging collisions were taken self-consistently. It was found that the equilibrium of the plasma as well as the propagation of ion waves were modified to various degrees by these effects.

Charging and trapping of macroparticles in near-electrode regions of fluorocarbon plasmas with negative ions

Charging and trapping of macroparticles in the near-electrode region of fluorocarbon etching plasmas with negative ions is considered. The equilibrium charge and forces on particles are computed as a function of the local position in the plasma presheath and sheath. The ionic composition of the plasma corresponds to the etching experiments in 2.45 GHz surface-wave sustained and 13.56 MHz inductively coupled C4F8+Ar plasmas. It is shown that despite negligible negative ion currents collected by the particles, the negative fluorine ions affect the charging and trapping of particulates through modification of the sheath/presheath structure.

Ion-acoustic waves in a complex plasma with negative ions

Negative ions and negatively charged micro- to nano-meter sized dust grains are ubiquitous in astrophysical as well as industrial processing plasmas. The negative ions can appear in electro-negative plasmas as a result of elementary processes such as dissociative or non-dissociative electron attachment to neutrals. They are usually rather small in number, and in general do not affect the overall plasma behavior. On the other hand, since the dust grains are almost always highly negative, even in small numbers they can take up a considerable proportion of the total negative charge in the system. The presence of dusts can affect the characteristics of most collective processes of the plasma since the charge balance in both the steady and dynamic states can be significantly altered. Another situation that often occurs is that the electron number density becomes small because of their absorption by the dust grains or the discharge walls. In this case the negative ions in the plasma can play a very important role. Here, a self-consistent theory of linear waves in complex laboratory plasmas containing dust grains and negative ions is presented. A comprehensive model for such plasmas including source and sink effects associated with the presence of dust grains and negative ions is introduced. The stationary state of the plasma as well as the dispersion and damping characteristics of the waves are investigated. All relevant processes, such as ionization, diffusion, electron attachment, negative-positive ion recombination, dust charge relaxation, and dissipation due to electron and ion elastic collisions with neutrals and dust particles, as well as charging collisions with the dusts, are taken into consideration.

Shared generation of pseudo-random functions with cumulative maps

In Crypto’95, Micali and Sidney proposed a method for shared generation of a pseudo-random function f(·) among n players in such a way that for all the inputs x, any u players can compute f(x) while t or fewer players fail to do so, where 0 ≤ t < u ≤ n. The idea behind the Micali-Sidney scheme is to generate and distribute secret seeds S = s1, . . . , sd of a poly-random collection of functions, among the n players, each player gets a subset of S, in such a way that any u players together hold all the secret seeds in S while any t or fewer players will lack at least one element from S. The pseudo-random function is then computed as where f s i (·)’s are poly-random functions. One question raised by Micali and Sidney is how to distribute the secret seeds satisfying the above condition such that the number of seeds, d, is as small as possible. In this paper, we continue the work of Micali and Sidney. We first provide a general framework for shared generation of pseudo-random function using cumulative maps. We demonstrate that the Micali-Sidney scheme is a special case of this general construction.We then derive an upper and a lower bound for d. Finally we give a simple, yet efficient, approximation greedy algorithm for generating the secret seeds S in which d is close to the optimum by a factor of at most u ln 2.

Protein-energy malnutrition exists and is associated with negative outcomes in morbidly obese hospital patients

Prevalence of protein-energy malnutrition (PEM), food intake inadequacy and associated health-related outcomes in morbidly obese (Body Mass Index ≥ 40 kg/m2) acute care patients are unknown. This study reports findings in morbidly obese participants from the Australasian Nutrition Care Day Survey (ANCDS) conducted in 2010. The ANCDS was a cross-sectional survey involving acute care patients from 56 Australian and New Zealand hospitals. Hospital-based dietitians evaluated participants’ nutritional status (defined by Subjective Global Assessment, SGA) and 24-hour food intake (as 0%, 25%, 50%, 75%, and 100% of the offered food). Three months later, outcome data, including length of stay (LOS) and 90-day in-hospital mortality, were collected. Of the 3122 participants, 4% (n = 136) were morbidly obese (67% females, 55 ± 14 years, BMI: 48 ± 8 kg/m2). Eleven percent (n = 15) of the morbidly obese patients were malnourished, and most (n = 11/15, 73%)received standard hospital diets without additional nutritional support. Malnourished morbidly obese patients had significantly longer LOS and greater 90-day in-hospital mortality than well-nourished counterparts (23 days vs. 9 days, p = 0.036; 14% vs. 0% mortality, p = 0.011 respectively). Thirteen morbidly obese patients (10%) consumed only 25% of the offered meals with a significantly greater proportion of malnourished (n = 4, 27%) versus well-nourished (n = 9, 7%) (p = 0.018). These results provide new knowledge on the prevalence of PEM and poor food intake in morbidly obese patients in Australian and New Zealand hospitals. For the first time internationally, the study establishes that PEM is significantly associated with negative outcomes in morbidly obese patients and warrants timely nutritional support during hospitalisation.

Plasmon nanofocusing with negative refraction in a high-index dielectric wedge

Here, we describe a metal-insulator-insulator nanofocusing structure formed by a high-permittivity dielectric wedge on a metal substrate. The structure is shown to produce nanofocusing of surface plasmon polaritons (SPPs) in the direction opposite to the taper of the wedge, including a range of nanoplasmonic effects such as nanofocusing of SPPs with negative refraction, formation of plasmonic caustics within a nanoscale distance from the wedge tip, mutual transformation of SPP modes, and significant local field enhancements in the adiabatic and strongly nonadiabatic regimes. A combination of approximate analytical and rigorous numerical approaches is used to analyze the strength and position of caustics in the structure. In particular, it is demonstrated that strong SPP localization within spatial regions as small as a few tens of nanometers near the caustic is achievable in the considered structures. Contrary to other nanofocusing configurations, efficient nanofocusing is shown to occur in the strongly nonadiabatic regime with taper angles of the dielectric wedge as large as ∼40° and within uniquely short distances (as small as a few dozens of nanometers) from the tip of the wedge. Physical interpretations of the obtained results are also presented and discussed.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

The effect of social support derived from World of Warcraft on negative psychological symptoms

Previous research examining players of Massively-Multiplayer Online Games (MMOGs) suggests that players form meaningful relationships with each other. Other research indicates that people may derive social support from online sources and this social support has been associated with greater wellbeing. This study used an online survey of players (N = 206) of the MMOG “World of Warcraft” (WoW) to examine if social support can be derived from MMOGs, and to examine its relationship with negative psychological symptoms. Players of WoW were found to derive social support from playing and a positive relationship was found between game engagement and levels of in-game social support. Higher levels of in-game social support were associated with fewer negative psychological symptoms, although this effect was not maintained after accounting for social support derived from the offline sources. Additionally, a small subsample of players (N = 21) were identified that played for between 44 and 82 hours per week (M = 63.33). These players had significantly lower levels of offline social support and higher levels of negative symptoms compared to the rest of the sample. This study provides evidence that social support can be derived from MMOGs and the associated potential to promote well being, but also highlights the potential harm from spending excessive hours playing.

Reasons for cannabis use in men with and without psychosis

Psychoses are relatively low prevalence disorders that have a disproportionately negative impact on individuals and society. Cannabis use is one factor that can exacerbate the negative consequences associated with psychotic disorders. Relatively few studies have examined the effects or reasons for using cannabis self-reported by individuals with psychosis. The present study is the first known to compare directly such factors in individuals with and without psychosis, within a single study. At baseline and follow-up participants with psychosis most commonly reported using cannabis for positive mood alteration (36% and 42%), coping with negative affect (27% and 29%) and for social activity reasons (38% and 29%). The control group most commonly reported using cannabis for relaxation (34% and 43%) and social activity reasons (49% and 51%). Participants with psychosis were less likely to report relaxation as the most important effect after use (27%) or expect it at follow-up (49%) compared to the control group (53% and 70%). In both groups, addiction and positive affect enhancement were the composite variable scores correlated most consistently with concurrent amount and frequency of use.

Longitudinal patterns of weight in women diagnosed with breast cancer [Conference Abstract]

Introduction: Weight gain is a common concern following breast cancer and has been associated with negative health outcomes. As such, prevention of weight gain is of clinical interest. This work describes weight change between 6- and 18-months following a breast cancer diagnosis and explores the personal, treatment and behavioural characteristics associated with gains in weight. Methods: Body mass index was objectively assessed, at three-monthly intervals, on a population-based sample of women newly diagnosed with unilateral breast cancer (n=185). Changes in BMI between 6- and 18-months post-diagnosis were calculated, with gains of one or more being considered clinically detrimental to future health. Results: Approximately 60% of participants were overweight or obese at 6-months post-diagnosis. While BMI remained relatively stable across the testing period (range=27.3-27.8), 24% of participants experienced clinically relevant gains in BMI (median gains=1.9). Following adjustment for potential confounders, younger age (<45 years; Odds ratio, OR=9.8), being morbidly obese at baseline (OR=4.6) and receiving hormone therapy (OR=4.8) were characteristics associated with an increased odds (p<0.05) of gaining BMI. Other characteristics associated with gains in BMI were more extensive surgery and having a history of smoking, although these relationships were not supported statistically. In contrast, caring for younger children was associated with reduced risk of gaining BMI (OR=0.3, p=0.20). Conclusions: Clinically relevant weight gain between 6- and 18-months post-breast cancer diagnosis is an issue for one in four women, with certain subgroups being particularly susceptible. However, the majority of women diagnosed with breast cancer are overweight or obese and gains in body weight are common. Thus, interventions that address the importance of achieving and sustaining a healthy body weight, delivered to all women with breast cancer, may have greater public health impact than interventions targeting any specific breast cancer subgroup.

Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.