Analytical modeling and sensitivity analysis for travel time estimation on signalized urban networks

This paper presents a model for estimation of average travel time and its variability on signalized urban networks using cumulative plots. The plots are generated based on the availability of data: a) case-D, for detector data only; b) case-DS, for detector data and signal timings; and c) case-DSS, for detector data, signal timings and saturation flow rate. The performance of the model for different degrees of saturation and different detector detection intervals is consistent for case-DSS and case-DS whereas, for case-D the performance is inconsistent. The sensitivity analysis of the model for case-D indicates that it is sensitive to detection interval and signal timings within the interval. When detection interval is integral multiple of signal cycle then it has low accuracy and low reliability. Whereas, for detection interval around 1.5 times signal cycle both accuracy and reliability are high.

Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

An androgen receptor mutation in the MDA-MB-453 cell line model of molecular apocrine breast cancer compromises receptor activity

Recent evidence indicates that the estrogen receptor-a-negative, androgen receptor (AR)- positive molecular apocrine subtype of breast cancer is driven by AR signaling. The MDA-MB-453 cell line is the prototypical model of this breast cancer subtype; its proliferation is stimulated by androgens such as 5a-dihydrotestosterone (DHT) but inhibited by the progestin medroxyprogesterone acetate (MPA) via AR-mediated mechanisms. We report here that the AR gene in MDAMB- 453 cells contains a G-T transversion in exon 7, resulting in a receptor variant with a glutamine to histidine substitution at amino acid 865 (Q865H) in the ligand binding domain. Compared with wild-type AR, the Q865H variant exhibited reduced sensitivity to DHT and MPA in transactivation assays in MDA-MB-453 and PC-3 cells but did not respond to non-androgenic ligands or receptor antagonists. Ligand binding, molecular modeling, mammalian two-hybrid and immunoblot assays revealed effects of the Q865H mutation on ligand dissociation, AR intramolecular interactions, and receptor stability. Microarray expression profiling demonstrated that DHT and MPA regulate distinct transcriptional programs in MDA-MB-453 cells. Gene Set Enrichment Analysis revealed that DHT- but not MPA-regulated genes were associated with estrogen-responsive transcriptomes from MCF-7 cells and the Wnt signaling pathway. These findings suggest that the divergent proliferative responses of MDA-MB-453 cells to DHT and MPA result from the different genetic programs elicited by these two ligands through the AR-Q865H variant. This work highlights the necessity to characterize additional models of molecular apocrine breast cancer to determine the precise role of AR signaling in this breast cancer subtype. Endocrine-Related Cancer (2012) 19 599–613

A simple model for the establishment of tick-borne pathogens of Ixodes scapularis : a global sensitivity analysis of R0

The basic reproduction number of a pathogen, R 0, determines whether a pathogen will spread (R0>1R 0>1), when introduced into a fully susceptible population or fade out (R0<1R 0<1), because infected hosts do not, on average, replace themselves. In this paper we develop a simple mechanistic model for the basic reproduction number for a group of tick-borne pathogens that wholly, or almost wholly, depend on horizontal transmission to and from vertebrate hosts. This group includes the causative agent of Lyme disease, Borrelia burgdorferi, and the causative agent of human babesiosis, Babesia microti, for which transmission between co-feeding ticks and vertical transmission from adult female ticks are both negligible. The model has only 19 parameters, all of which have a clear biological interpretation and can be estimated from laboratory or field data. The model takes into account the transmission efficiency from the vertebrate host as a function of the days since infection, in part because of the potential for this dynamic to interact with tick phenology, which is also included in the model. This sets the model apart from previous, similar models for R0 for tick-borne pathogens. We then define parameter ranges for the 19 parameters using estimates from the literature, as well as laboratory and field data, and perform a global sensitivity analysis of the model. This enables us to rank the importance of the parameters in terms of their contribution to the observed variation in R0. We conclude that the transmission efficiency from the vertebrate host to Ixodes scapularis ticks, the survival rate of Ixodes scapularis from fed larva to feeding nymph, and the fraction of nymphs finding a competent host, are the most influential factors for R0. This contrasts with other vector borne pathogens where it is usually the abundance of the vector or host, or the vector-to-host ratio, that determine conditions for emergence. These results are a step towards a better understanding of the geographical expansion of currently emerging horizontally transmitted tick-borne pathogens such as Babesia microti, as well as providing a firmer scientific basis for targeted use of acaricide or the application of wildlife vaccines that are currently in development.

Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the statistics literature and "the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic ("thermodynamic integration via importance sampling") for qualifying the role of the bridging sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.

A sensitivity analysis of train speed and its effect on railway capacity

Increasing train speeds is conceptually a simple and straight forward method to expand railway capacity, for example in comparison to other more extensive and elaborate alternatives. In this article an analytical capacity model has been investigated as a means of performing a sensitivity analysis of train speeds. The results of this sensitivity analysis can help improve the operation of this railway system and to help it cope with additional demands in the future. To test our approach a case study of the Rah Ahane Iran (RAI) national railway network has been selected. The absolute capacity levels for this railway network have been determined and the analysis shows that increasing trains speeds may not be entirely cost effective in all circumstances.

Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

A mathematical model of chlamydial infection incorporating movement of chlamydial particles

We present a spatiotemporal mathematical model of chlamydial infection, host immune response and spatial movement of infectious particles. The re- sulting partial differential equations model both the dynamics of the infection and changes in infection profile observed spatially along the length of the host genital tract. This model advances previous chlamydia modelling by incorporating spatial change, which we also demonstrate to be essential when the timescale for movement of infectious particles is equal to, or shorter than, the developmental cycle timescale. Numerical solutions and model analysis are carried out, and we present a hypothesis regarding the potential for treatment and prevention of infection by increasing chlamydial particle motility.

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Hypertrophic scars arise when there is an overproduction of collagen during wound healing. These are often associated with poor regulation of the rate of programmed cell death(apoptosis) of the cells synthesizing the collagen or by an exuberant inflammatory response that prolongs collagen production and increases wound contraction. Severe contractures that occur, for example, after a deep burn can cause loss of function especially if the wound is over a joint such as the elbow or knee. Recently, we have developed a morphoelastic mathematical model for dermal repair that incorporates the chemical, cellular and mechanical aspects of dermal wound healing. Using this model, we examine pathological scarring in dermal repair by first assuming a smaller than usual apoptotic rate for myofibroblasts, and then considering a prolonged inflammatory response, in an attempt to determine a possible optimal intervention strategy to promote normal repair, or terminate the fibrotic scarring response. Our model predicts that in both cases it is best to apply the intervention strategy early in the wound healing response. Further, the earlier an intervention is made, the less aggressive the intervention required. Finally, if intervention is conducted at a late time during healing, a significant intervention is required; however, there is a threshold concentration of the drug or therapy applied, above which minimal further improvement to wound repair is obtained.