The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Expression and distribution of cell-surface proteoglycans in the normal Lewis rat molar periodontium

Cell-surface proteoglycans participate in several biological functions such as cell cell and cell-matrix interactions, cell adhesion, the binding to various growth factors as co-receptors and repair. To understand better the expression and distribution of cell-surface proteoglycans in the periodontal tissues, an immunohistochemical evaluation of the normal Lewis rat molar periodontium using panels of antibodies for syndecan-1, -2, -4, glypican and betaglycan was carried out. Our results demonstrated the expression and distribution of all proteoglycans in the suprabasal gingival epithelium, soft and hard connective tissues. Both cellular and matrix localization was evident within the various periodontal compartments. The presence of these cell-surface proteoglycans indicates the potential for roles in the process of tissue homeostasis, repair or regeneration in periodontium of which each function requires further study.

More men than women make mucosal IgA antibodies to human papillomavirus type 16 (HPV-16) and HPV-18: A study of oral HPV and oral HPV antibodies in a normal healthy population

Background: We have previously shown the high prevalence of oral anti-human papillomavirus type 16 (HPV-16) antibodies in women with HPV-associated cervical neoplasia. It was postulated that the HPV antibodies were initiated after HPV antigenic stimulation at the cervix via the common mucosal immune system. The present study aimed to further evaluate the effectiveness of oral fluid testing for detecting the mucosal humoral response to HPV infection and to advance our limited understanding of the immune response to HPV. Methods: The prevalence of oral HPV infection and oral antibodies to HPV types 16, 18 and 11 was determined in a normal, healthy population of children, adolescents and adults, both male and female, attending a dental clinic. HPV types in buccal cells were determined by DNA sequencing. Oral fluid was collected from the gingival crevice of the mouth by the OraSure method. HPV-16, HPV-18 and HPV-11 antibodies in oral fluid were detected by virus-like particle-based enzyme-linked immunosorbent assay. As a reference group 44 women with cervical neoplasia were included in the study. Results: Oral HPV infection was h ighest in children (9/114, 7.9%), followed by adolescents (4/78, 5.1%), and lowest in normal adults (4/116, 3.5%). The predominant HPV type found was HPV-13 (7/22, 31.8%) followed by HPV-32 (5/22, 22.7%). The prevalence of oral antibodies to HPV-16, HPV-18 and HPV-11 was low in children and increased substantially in adolescents and normal adults. Oral HPV-16 IgA was significantly more prevalent in women with cervical neoplasia (30/44, 68.2%) than the women from the dental clinic (18/69, 26.1% P = 0.0001). Significantly more adult men than women displayed oral HPV-16 IgA (30/47 compared with 18/69, OR 5.0, 95% CI 2.09-12.1, P < 0.001) and HPV-18 IgA (17/47 compared with 13/69, OR 2.4, 95% CI 0.97-6.2, P = 0.04). Conclusion: The increased prevalence of oral HPV antibodies in adolescent individuals compared with children was attributed to the onset of sexual activity. The increased prevalence of oral anti-HPV IgA in men compared with women was noteworthy considering reportedly fewer men than women make serum antibodies, and warrants further investigation. © 2006 Marais et al; licensee BioMed Central Ltd.

Organotypic culture of normal, dysplastic and squamous cell carcinoma-derived oral cell lines reveals loss of spatial regulation of CD44 and p75(NTR) in malignancy

Oral squamous cell carcinomas (OSCC) often arise from dysplastic lesions. The role of cancer stem cells in tumour initiation is widely accepted, yet the potential existence of pre-cancerous stem cells in dysplastic tissue has received little attention. Cell lines from oral diseases ranging in severity from dysplasia to malignancy provide opportunity to investigate the involvement of stem cells in malignant progression from dysplasia. Stem cells are functionally defined by their ability to generate hierarchical tissue structures in consortium with spatial regulation. Organotypic cultures readily display tissue hierarchy in vitro; hence, in this study, we compared hierarchical expression of stem cell-associated markers in dermis-based organotypic cultures of oral epithelial cells from normal tissue (OKF6-TERT2), mild dysplasia (DOK), severe dysplasia (POE-9n) and OSCC (PE/CA P J15). Expression of CD44, p75NTR, CD24 and ALDH was studied in monolayers by flow cytometry and in organotypic cultures by immunohistochemistry. Spatial regulation of CD44 and p75NTR was evident for organotypic cultures of normal (OKF6-TERT2) and dysplasia (DOK and POE-9n) but was lacking for OSCC (PE/CA PJ15)-derived cells. Spatial regulation of CD24 was not evident. All monolayer cultures exhibited CD44, p75NTR, CD24 antigens and ALDH activity (ALDEFLUOR® assay), with a trend towards loss of population heterogeneity that mirrored disease severity. In monolayer, increased FOXA1 and decreased FOXA2 expression correlated with disease severity, but OCT3/4, Sox2 and NANOG did not. We conclude that dermis-based organotypic cultures give opportunity to investigate the mechanisms that underlie loss of spatial regulation of stem cell markers seen with OSCC-derived cells.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

A study of the diffusion characteristics of normal, delipidized and relipidized articular cartilage using magnetic resonance imaging

This paper assesses the capacity to provide semipermeability of the synthetic layer of surface-active phospholipids created to replace the depleted surface amorphous layer of articular cartilage. The surfaces of articular cartilage specimens in normal, delipidized, and relipidized conditions following incubation in dipalmitoyl-phosphatidylcholine and palmitoyl-oleoyl-phosphatidylcholine components of the joint lipid mixture were characterized nanoscopically with the atomic force microscope and also imaged as deuterium oxide (D2O) diffused transiently through these surfaces in a magnetic resonance imaging enclosure. The MR images were then used to determine the apparent diffusion coefficients in a purpose-built MATLAB®-based algorithm. Our results revealed that all surfaces were permeable to D2O, but that there was a significant difference in the semipermeability of the surfaces under the different conditions, relative to the apparent diffusion coefficients. Based on the results and observations, it can be concluded that the synthetic lipid that is deposited to replace the depleted SAL of articular cartilage is capable of inducing some level of semipermeability.

Morphology of osteocyte cells in normal and hyper-gravity

Osteocyte cells are the most abundant cells in human bone tissue. Due to their unique morphology and location, osteocyte cells are thought to act as regulators in the bone remodelling process, and are believed to play an important role in astronauts’ bone mass loss after long-term space missions. There is increasing evidence showing that an osteocyte’s functions are highly affected by its morphology. However, changes in an osteocyte’s morphology under an altered gravity environment are still not well documented. Several in vitro studies have been recently conducted to investigate the morphological response of osteocyte cells to the microgravity environment, where osteocyte cells were cultured on a two-dimensional flat surface for at least 24 hours before microgravity experiments. Morphology changes of osteocyte cells in microgravity were then studied by comparing the cell area to 1g control cells. However, osteocyte cells found in vivo are with a more 3D morphology, and both cell body and dendritic processes are found sensitive to mechanical loadings. A round shape osteocyte’s cells support a less stiff cytoskeleton and are more sensitive to mechanical stimulations compared with flat cellular morphology. Thus, the relative flat and spread shape of isolated osteocytes in 2D culture may greatly hamper their sensitivity to a mechanical stimulus, and the lack of knowledge on the osteocyte’s morphological characteristics in culture may lead to subjective and noncomprehensive conclusions of how altered gravity impacts on an osteocyte’s morphology. Through this work empirical models were developed to quantitatively predicate the changes of morphology in osteocyte cell lines (MLO-Y4) in culture, and the response of osteocyte cells, which are relatively round in shape, to hyper-gravity stimulation has also been investigated. The morphology changes of MLO-Y4 cells in culture were quantified by measuring cell area and three dimensionless shape features including aspect ratio, circularity and solidity by using widely accepted image analysis software (ImageJTM). MLO-Y4 cells were cultured at low density (5×103 per well) and the changes in morphology were recorded over 10 hours. Based on the data obtained from the imaging analysis, empirical models were developed using the non-linear regression method. The developed empirical models accurately predict the morphology of MLO-Y4 cells for different culture times and can, therefore, be used as a reference model for analysing MLO-Y4 cell morphology changes within various biological/mechanical studies, as necessary. The morphological response of MLO-Y4 cells with a relatively round morphology to hyper-gravity environment has been investigated using a centrifuge. After 2 hours culture, MLO-Y4 cells were exposed to 20g for 30mins. Changes in the morphology of MLO-Y4 cells are quantitatively analysed by measuring the average value of cell area and dimensionless shape factors such as aspect ratio, solidity and circularity. In this study, no significant morphology changes were detected in MLO-Y4 cells under a hyper-gravity environment (20g for 30 mins) compared with 1g control cells.

A closed-form approximation for pricing temperature-based weather derivatives

This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If the deviations of daily temperatures from their expected values are modelled as an Ornstein-Uhlenbeck process with timevarying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records are a particularly poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.

Beyond normal competencies : understanding organisation designs to develop and sustain IT-related capabilities

It is apparent that IT resources are important for organisations. It is also clear that organisations unique competencies, their IT-related capabilities, leverage the IT resources uniquely to create and sustain competitive advantage. However, IT resources are dynamic, and evolve at an exponential rate. This means that organisations will need to sustain their competencies to leverage opportunities offered by new IT resources. Research on ways to sustain IT-related capabilities is limited and a deeper understanding of this situation is important. Amongst other factors, a possible reason for this lack of progress in this area could be due to the lack of validated measurement items of the theoretical constructs to conduct such studies. We suggest an environment in which organisations could build new and sustain their existing IT-related capabilities. We then report on the development of valid and reliable measures for this environment. The validated measures would be useful in extending our understanding on how firms could sustain their IT-related capabilities. This effort will provide a deeper understanding of how firms can secure sustainable IT-related business value from their acquired IT resources.

Caffeine ingestion and cycling power output in a low or normal muscle glycogen state

Purpose Commencing selected workouts with low muscle glycogen availability augments several markers of training adaptation compared with undertaking the same sessions with normal glycogen content. However, low glycogen availability reduces the capacity to perform high-intensity (>85% of peak aerobic power (V·O2peak)) endurance exercise. We determined whether a low dose of caffeine could partially rescue the reduction in maximal self-selected power output observed when individuals commenced high-intensity interval training with low (LOW) compared with normal (NORM) glycogen availability. Methods Twelve endurance-trained cyclists/triathletes performed four experimental trials using a double-blind Latin square design. Muscle glycogen content was manipulated via exercise–diet interventions so that two experimental trials were commenced with LOW and two with NORM muscle glycogen availability. Sixty minutes before an experimental trial, subjects ingested a capsule containing anhydrous caffeine (CAFF, 3 mg-1·kg-1 body mass) or placebo (PLBO). Instantaneous power output was measured throughout high-intensity interval training (8 × 5-min bouts at maximum self-selected intensity with 1-min recovery). Results There were significant main effects for both preexercise glycogen content and caffeine ingestion on power output. LOW reduced power output by approximately 8% compared with NORM (P < 0.01), whereas caffeine increased power output by 2.8% and 3.5% for NORM and LOW, respectively, (P < 0.01). Conclusion We conclude that caffeine enhanced power output independently of muscle glycogen concentration but could not fully restore power output to levels commensurate with that when subjects commenced exercise with normal glycogen availability. However, the reported increase in power output does provide a likely performance benefit and may provide a means to further enhance the already augmented training response observed when selected sessions are commenced with reduced muscle glycogen availability. It has long been known that endurance training induces a multitude of metabolic and morphological adaptations that improve the resistance of the trained musculature to fatigue and enhance endurance capacity and/or exercise performance (13). Accumulating evidence now suggests that many of these adaptations can be modified by nutrient availability (9–11,21). Growing evidence suggests that training with reduced muscle glycogen using a “train twice every second day” compared with a more traditional “train once daily” approach can enhance the acute training response (29) and markers representative of endurance training adaptation after short-term (3–10 wk) training interventions (8,16,30). Of note is that the superior training adaptation in these previous studies was attained despite a reduction in maximal self-selected power output (16,30). The most obvious factor underlying the reduced intensity during a second training bout is the reduction in muscle glycogen availability. However, there is also the possibility that other metabolic and/or neural factors may be responsible for the power drop-off observed when two exercise bouts are performed in close proximity. Regardless of the precise mechanism(s), there remains the intriguing possibility that the magnitude of training adaptation previously reported in the face of a reduced training intensity (Hulston et al. (16) and Yeo et al.) might be further augmented, and/or other aspects of the training stimulus better preserved, if power output was not compromised. Caffeine ingestion is a possible strategy that might “rescue” the aforementioned reduction in power output that occurs when individuals commence high-intensity interval training (HIT) with low compared with normal glycogen availability. Recent evidence suggests that, at least in endurance-based events, the maximal benefits of caffeine are seen at small to moderate (2–3 mg·kg-1 body mass (BM)) doses (for reviews, see Refs. (3,24)). Accordingly, in this study, we aimed to determine the effect of a low dose of caffeine (3 mg·kg-1 BM) on maximal self-selected power output during HIT commenced with either normal (NORM) or low (LOW) muscle glycogen availability. We hypothesized that even under conditions of low glycogen availability, caffeine would increase maximal self-selected power output and thereby partially rescue the reduction in training intensity observed when individuals commence HIT with low glycogen availability.

The effects and interactions of GABAergic and dopaminergic agents in the prevention of form deprivation myopia by brief periods of normal vision

Intravitreal injections of GABA antagonists, dopamine agonists and brief periods of normal vision have been shown separately to inhibit form-deprivation myopia (FDM). Our study had three aims: (i) establish whether GABAergic agents modify the myopia protective effect of normal vision, (ii) investigate the receptor sub-type specificity of any observed effect, and (iii) consider an interaction with the dopamine (DA) system. Prior to the period of normal vision GABAergic agents were applied either (i) individually, (ii) in combination with other GABAergic agents (an agonist with an antagonist), or (iii) in combination with DA agonists and antagonists. Water injections were given to groups not receiving drug treatments so that all experimental eyes received intravitreal injections. As shown previously, constant form-deprivation resulted in high myopia and when diffusers were removed for 2 h per day the period of normal vision greatly reduced the FDM that developed. GABA agonists inhibited the protective effect of normal vision whereas antagonists had the opposite effect. GABAA/C agonists and D2 DA antagonists when used in combination were additive in suppressing the protective effect of normal vision. A D2 DA agonist restored some of the protective effect of normal vision that was inhibited by a GABA agonist (muscimol). The protective effect of normal vision against form-deprivation is modifiable by both the GABAergic and DAergic pathways.