Faculty of Science

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Open Access
Spline solutions for nonlinear two point boundary value problems
(1980-1-1) Usmani, Riaz A.
Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four techniques.
Open Access
Rings with involution whose symmetric elements are central
(1980-1-1) Lim, Taw Pin
In a ring R with involution whose symmetric elements S are central, the skew-symmetric elements K form a Lie algebra over the commutative ring S. The classification of such rings which are 2-torsion free is equivalent to the classification of Lie algebras K over S equipped with a bilinear form f that is symmetric, invariant and satisfies [[x,y],z]=f(y,z)x−f(z,x)y. If S is a field of char ≠2, f≠0 and dimK>1 then K is a semisimple Lie algebra if and only if f is nondegenerate. Moreover, the derived algebra K′ is either the pure quaternions over S or a direct sum of mutually orthogonal abelian Lie ideals of dim≤2.
Open Access
Longitudinal dispersion of tracer particles in a channel bounded by Porous media using slip condition
(1984-1-1) Pal, Dulal; Veerabhadraiah, R.; Shivakumar, P. N.; Rudraiah, N.
Longitudinal dispersion of solute in a channel bounded by porous layers is studied using the analysis of Taylor [4] with BJ slip condition. The results of the present analysis are compared with those of Fung and Tang [2] obtained from using the no-slip condition. It is found that the effect of slip is significant only in the case when the membrane is permeable to solvent but not to the tracer. However, in the case when the membrane is permeable to both the tracer and the solvent, we find that our results coincide with those of Fung and Tang [2].
Open Access
Numerical methods for approximating eigenvalues of boundary value problems
(1986-1-1) Usmani, Kiaz A.; Isa, Mohammad
This paper describes some new finite difference methods for the approximation of eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation of the type (py″)′′−(qy′)′+(r−λs)y=0. The smallest positive eigenvalue of some typical eigensystems is computed to demonstrate the practical usefulness of the numerical techniques developed.
Open Access
Finite difference methods for computing eigenvalues of fourth order boundary value problems
(1986-1-1) Usmani, Riaz A.
This brief report describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation y(4)+(p(x)−λq(x))y=0. These methods are derived from the formulah4y1(4)=(δ4−16δ6+7240δ8−…)yi.Numerical results are included to demonstrate practical usefulness of our methods.
Open Access
Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem
(1987-1-1) Usmani, Riaz A.; Sakai, Manabu
This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form (py″)′′+(q−λr)y=0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.
Open Access
Play-the-winner rule and adaptive designs of clinical trials
(2000-1-1) Wang, Xikui; Pullman, Daryl
In another paper, we have argued that the traditional randomized design of clinical trials is ethically infeasible in desperate medical situations and adaptive designs are morally required. We have also argued that in such situations, the appropriate designs must satisfy what we call the Principle of interchangeability. In this statistics paper, we show that the statistical model of bandit processes satisfies this principle of interchangeability. Moreover, we demonstrate that when such a model is used as an adaptive design, the total regret of successes lost is smaller when compared with simple randomization. We illustrate the results by the simple deterministic play-the-winner design.
Open Access
Toeplitz operators with BMO symbols and the Berezin transform
(2002-1-1) Zorboska, Nina
We prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol is either a positive L1-function or an L∞ function.
Open Access
A New Mathematical Model for Assessing Therapeutic Strategies for HIV Infection
(2002-1-1) Gumel, A. B.; Zhang, Xue-Wu; Shivakumar, P. N.; Garba, M. L.; Sahai, B. M.
The requirements for the eradication of HIV in infected individuals are unknown. Intermittent administration of the immune activator interleukin-2 (IL-2) in combination with highly-active antiretroviral therapy (HAART) has been suggested as an effective strategy to realize long-term control of HIV replication in vivo. However, potential latent virus reservoirs are considered to be a major impediment in achieving this goal. In this paper, a new mathematical model is designed and used to monitor the interactions between HIV, CD4+ T-cells, CD8+ T-cells, productively infected and latently infected CD4+ T-cells, and to evaluate therapeutic strategies during the first 3 years of HIV infection. The model shows that current anti-HIV therapies, including intermittent IL-2 and HAART, are insufficient in achieving eradication of HIV. However, it suggests that the HIV eradication may indeed be theoretically feasible if such therapy is administered continuously (without interruption) under some specified conditions. These conditions may realistically be achieved using an agent (such as a putative anti-HIV vaccine) that brings about a concomitant increase in the proliferation of HIVspecific CD4+ T- and CD8+ T-cells and the differentiation of CD8+ T-cells into anti-HIV cytotoxic T lymphocytes (CTLs).
Open Access
Could Condoms Stop the AIDS Epidemic?
(2003-1-1) Moghadas, Seyed M.; Gumel, Abba B.; McLeod, Robert G.; Gordon, Richard
Although therapeutic treatment strategies appear promising for retarding the progression of HIV-related diseases, prevention remains the most effective strategy against the HIV/AIDS epidemic. This paper focuses on the effect of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. There are two primary factors in the use of condoms to halt the HIV/AIDS epidemic: condom efficacy and compliance. Our study is focused on the effect of these factors in stopping the epidemic by constructing a new deterministic mathematical model. The current estimate of condom effectiveness against HIV transmission, based on the latest meta-analysis, is 60–96%, with a mean of 87%. Since the parameter estimates are subject to different kinds of uncertainty, to achieve adequate quality assurance in predictions, uncertainty and sensitivity analyses are carried out using latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs). Using stability and sensitivity analyses, based on a plausible range of parameter values, key parameters that govern the persistence or eradication of HIV are identified. This analysis shows that the product of efficacy and compliance, which we call ‘preventability’ (p), has a negative effect on the epidemic; as increasing p decreases the level of epidemicity. It is also shown that the threshold preventability (pc) increases with increasing average number of HIV-infected partners of susceptible individuals, especially those in the AIDS stage. For populations where the average number of HIV-infected partners is large, the associated preventability threshold is high and perhaps unattainable, suggesting that for such a population, HIV may not be controlled using condoms alone. On the other hand, for a population where the average number of HIV-infected partners is low (within a reasonable range), it is shown that pc is about 75%, suggesting that the epidemic could be stopped using condoms. Thus, for such a population, public health measures that can bring preventability above the threshold and continuous quantitative monitoring to make sure it stays there, are what would be necessary. In other words, for populations with reasonable average numbers of HIV-infected partners, given the will and effort, it is within our means to halt this epidemic using condoms.
Open Access
Long-term trends in spring arrival dates of migrant birds at Delta Marsh, Manitoba, in relation to climate change
(2005-10-31) Murphy-Klassen, HM; Underwood, TJ; Sealy, SG; Czyrnyj, AA
We examined a 63-year data set of dates of first spring sightings for 96 species of migrant birds at Delta Marsh, Manitoba, and considered the influence of local climate change on those arrival dates. Mean monthly spring temperatures increased (0.6-3.8 degrees C) for all four months considered; however, trends for February and March were stronger than those for April and May. Over the 63-year period, 27 species significantly altered their arrival dates. Most of those species arrived significantly earlier; whereas only two species, Greater Yellowlegs (Tringa melanoleuca) and Lesser Yellowlegs (T. flavipes), arrived significantly later over time. About half of the migrants showed significant relationships between arrival dates and mean temperature for their month of arrival. Fifteen species showed significantly earlier arrivals over time and a significant relationship between arrival date and temperature. We also characterized migrants by taxon, breeding status, and wintering location to determine whether there were any trends for altered arrivals within certain groups. Waterfowl, species that breed at Delta Marsh, and short-distance migrants showed slightly higher incidences of advancing arrival dates compared with other groups. Our results provide evidence that climate warming has influenced spring migration arrival dates of several species in Manitoba.
Open Access
Recent developments in volatility modeling and applications
(2006-11-30) Thavaneswaran, A.; Appadoo, S. S.; Bector, C. R.
In financial modeling, it has been constantly pointed out that volatility clustering and conditional nonnormality induced leptokurtosis observed in high frequency data. Financial time series data are not adequately modeled by normal distribution, and empirical evidence on the non-normality assumption is well documented in the financial literature (details are illustrated by Engle (1982) and Bollerslev (1986)). An ARMA representation has been used by Thavaneswaran et al., in 2005, to derive the kurtosis of the various class of GARCH models such as power GARCH, non-Gaussian GARCH, nonstationary and random coefficient GARCH. Several empirical studies have shown that mixture distributions are more likely to capture heteroskedasticity observed in high frequency data than normal distribution. In this paper, some results on moment properties are generalized to stationary ARMA process with GARCH errors. Application to volatility forecasts and option pricing are also discussed in some detail.
Open Access
The Creatine Kinase/Creatine Connection to Alzheimer's Disease: CK Inactivation, APP-CK Complexes and Focal Creatine Deposits
(2006-4-4) Bürklen, Tanja S.; Schlattner, Uwe; Homayouni, Ramin; Gough, Kathleen; Rak, Margaret; Szeghalmi, Adriana; Wallimann, Theo
Cytosolic brain-type creatine kinase (BB-CK), which is coexpressed with ubiquitous mitochondrial uMtCK, is significantly inactivated by oxidation, in Alzheimer's disease (AD) patients. Since CK has been shown to play a fundamental role in cellular energetics of the brain, any disturbance of this enzyme may exasperate the AD disease process. Mutations in amyloid precursor protein (APP) are associated with early onset AD and result in abnormal processing of APP, and accumulation of Aβ peptide, the main constituent of amyloid plaques in AD brain. Recent data on a direct interaction between APP and the precursor of uMtCK support an emerging relationship between AD, cellular energy levels and mitochondrial function. In addition, recently discovered creatine (Cr) deposits in the brain of transgenic AD mice, as well as in the hippocampus from AD patients, indicate a direct link between perturbed energy state, Cr metabolism and AD. Here, we review the roles of Cr and Cr-related enzymes and consider the potential value of supplementation with Cr, a potent neuroprotective substance. As a hypothesis, we consider whether Cr, if given at an early time point of the disease, may prevent or delay the course of AD-related neurodegeneration.
Open Access
Color variation among nestling brown-headed cowbirds (Molothrus Ater) does not reflect differential success with hosts in Texas
(2007-04-30) Ellison, K; Sealy, SG; McGaha, HR
As brood parasites, nestling Brown-headed Cowbirds (Molothrus ater) may exhibit characters that improve their fledging success when reared alongside host young. The coloration of mouthparts of nestlings can influence adult care and, thus, the polymorphism of yellow or white rictal flanges among nestling Brown-headed Cowbirds may reflect differential success with different hosts on the basis of flange color. Moreover, because Brown-headed Cowbirds in the southern United States co-occur with Bronzed Cowbirds (M. aeneus), whose young have white flanges, cowbird nestlings' flange colors may reflect a means for reducing interspecific competition through partitioning of host species on the basis of nestling flange color. To determine whether flange color influences cowbird fledging success with hosts of either color, we recorded the flange colors of cowbirds and their hosts at a site in Texas. We also tested whether flange color was influenced by nestling sex. Most hosts of Brown-headed Cowbirds had young with yellow flanges (81%, n = 16 spp.), yet Brown-headed Cowbirds with white flanges were more common (61%, n = 107). Bronzed Cowbirds parasitized primarily species whose young had white flanges (86%, n = 348 eggs). Despite the differential use of hosts with regard to flange color, the frequencies of each were similar among nestling and juvenile Brown-headed Cowbirds. Likewise, the frequencies of each color did not differ significantly between the sexes. Therefore, we suggest that a flange color matching that of nestmates is not strongly selected for by hosts.
Open Access
Sensing with One or with Four? A Comparison of Two IEEE 802.15.x Protocols for Use in Sensor Networks
(2007-1-1) Mišić, Vojislav B.; Mišić, Jelena
In this paper we compare the pertinent features of the two emerging technologies for wireless sensor networks: IEEE Standards 802.15.1 and 802.15.4. We review the main features of the MAC protocols defined by those standards, describe their operation, and compare them in terms of characteristics such as performance (access and end-to-end packet delays), bandwidth utilization, and scalability for the deployment of large networks. Our findings indicate that there is no clear winner in all categories; the best protocol (and the underlying technology) to use, are heavily dependent upon the requirements for a particular sensing application. While the main focus of our analysis is the MAC layer, certain important parameters of the Physical (PHY) layer are considered as well, together with some other networking aspects. The results of this analysis should be of interest to the designer and operators of wireless sensor networks.
Open Access
Analysis of Cluster Interconnection Schemes in 802.15.4 Beacon Enabled Networks
(2008-1-1) Mišić, Jelena; Udayshankar, Ranjith
In this paper, we consider the interconnection of IEEE 802.15.4 beacon enabled network clusters. We discuss two types of interconnections. One type can be achieved by using the PAN coordinator node as the bridging device and the other type is achieved by using ordinary network nodes as bridge nodes. We discuss design and performance issues of both kinds of interconnections.
Open Access
Mathematical Assessment of Canada’s Pandemic Influenza Preparedness Plan
(2008-1-1) Gumel, Abba B; Nuño, Miriam; Chowell, Gerardo
OBJECTIVE: The presence of the highly pathogenic avian H5N1 virus in wild bird populations in several regions of the world, together with recurrent cases of H5N1 influenza arising primarily from direct contact with poultry, have highlighted the urgent need for prepared-ness and coordinated global strategies to effectively combat a potential influenza pandemic. The purpose of the present study was to evaluate the Canadian pandemic influenza preparedness plan.PATIENTS AND METHODS: A mathematical model of the transmission dynamics of influenza was used to keep track of the population according to risk of infection (low or high) and infection status (susceptible, exposed or infectious). The model was parametrized using available Canadian demographic data. The model was then used to evaluate the key components outlined in the Canadian plan.RESULTS: The results indicated that the number of cases, mortalities and hospitalizations estimated in the Canadian plan may have been underestimated; the use of antivirals, administered therapeutically, prophylactically or both, is the most effective single intervention followed by the use of a vaccine and basic public health measures; and the combined use of pharmaceutical interventions (antivirals and vaccine) can dramatically minimize the burden of the pending influenza pandemic in Canada. Based on increasing concerns of Oseltamivir resistance (wide-scale implementation), coupled with the expected unavailability of a suitable vaccine during the early stages of a pandemic, the present study evaluated the potential impact of non-pharmaceutical interventions (NPIs) which were not emphasized in the current Canadian plan. To this end, the findings suggest that the use of NPIs can drastically reduce the burden of a pandemic in Canada.CONCLUSIONS: A deterministic model was designed and used to assess Canada’s pandemic preparedness plan. The study showed that the estimates of pandemic influenza burden given in the Canada pandemic preparedness plan may be an underestimate, and that Canada needs to adopt NPIs to complement its preparedness plan.
Open Access
Delay Analysis of GTS Bridging between IEEE 802.15.4 and IEEE 802.11 Networks for Healthcare Applications
(2008-12-2) Mišić, Jelena; (Sherman) Shen, Xuemin
We consider interconnection of IEEE 802.15.4 beacon-enabled network cluster with IEEE 802.11b network. This scenario is important in healthcare applications where IEEE 802.15.4 nodes comprise patient's body area network (BAN) and are involved in sensing some health-related data. BAN nodes have very short communication range in order to avoid harming patient's health and save energy. Sensed data needs to be transmitted to an access point in the ward room using wireless technology with higher transmission range and rate such as IEEE 802.11b. We model the interconnected network where IEEE 802.15.4-based BAN operates in guaranteed time slot (GTS) mode, and IEEE 802.11b part of the bridge conveys GTS superframe to the 802.11b access point. We then analyze the network delays. Performance analysis is performed using EKG traffic from continuous telemetry, and we discuss the delays of communication due the increasing number of patients.
Open Access
The Manitoba IBD Index: Evidence for a New and Simple Indicator of IBD Activity
(American Journal Gastroenterology, 2009-07) Clara, Ian; Lix, LIsa; Walker, John R.; Graff, Lesley A.; Miller, Norine; Rogala, Linda; Rawsthorne, Patricia; Bernstein, Charles N.
OBJECTIVES: A single-item indicator of disease activity over an extended period of time, the Manitoba Inflammatory Bowel Disease Index (MIBDI), is introduced and compared against several standard measures for assessing activity in patients with Crohn's disease (CD) and ulcerative colitis (UC). METHODS: Participants enrolled in the Manitoba IBD Cohort Study, a population-based longitudinal cohort study (N=353), were assessed semiannually by survey, clinical interview, and blood sample during a 2-year period. The MIBDI is based on patient self-reports of symptom persistence for the previous 6 months, using a 6-level response format. RESULTS: The MIBDI had good sensitivity compared with the Harvey-Bradshaw Index (HB; 0.88), Powell-Tuck Index (PT; 0.84), and Inflammatory Bowel Disease Questionnaire (IBDQ; 0.89), which was maintained at two subsequent annual measurements. Test-retest reliability was also strong (Spearman's r=0.81). Discriminant function analyses identified common discriminating variables of active disease for CD and UC that included HB, PT, and IBDQ subscales of bowel and systemic symptoms, prolonged symptom severity (e.g., abdominal and joint pain, tiredness, diarrhea), and recent persistent pain related to IBD. Unique discriminators included weight problems (CD) and blood in stool (UC). CONCLUSIONS: A single-item, patient-defined disease activity measure, the MIBDI, showed a high degree of sensitivity for classifying individuals with regard to disease status over time compared with the existing disease activity measures, and strong convergent validity with expected proxy measures of disease. These relationships remained consistent over time. Thus, the MIBDI shows promise as a valid, brief tool for measuring disease activity over an extended period.
Open Access
Improving Sensing Accuracy in Cognitive PANs through Modulation of Sensing Probability
(2009-1-1) Mišić, Vojislav B.; Mišić, Jelena
Cognitive radio technology necessitates accurate and timely sensing of primary users' activity on the chosen set of channels. The simplest selection procedure is a simple random choice of channels to be sensed, but the impact of sensing errors with respect to primary user activity or inactivity differs considerably. In order to improve sensing accuracy and increase the likelihood of finding channels which are free from primary user activity, the selection procedure is modified by assigning different sensing probabilities to active and inactive channels. The paper presents a probabilistic analysis of this policy and investigates the range of values in which the modulation of sensing probability is capable of maintaining an accurate view of the status of the working channel set. We also present a modification of the probability modulation algorithm that allows for even greater reduction of sensing error in a limited range of the duty cycle of primary users' activity. Finally, we give some guidelines as to the optimum application ranges for the original and modified algorithm, respectively.