Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Gain control network conditions in early sensory coding

Gain control is essential for the proper function of any sensory system. However, the precise mechanisms for achieving effective gain control in the brain are unknown. Based on our understanding of the existence and strength of connections in the insect olfactory system, we analyze the conditions that lead to controlled gain in a randomly connected network of excitatory and inhibitory neurons. We consider two scenarios for the variation of input into the system. In the first case, the intensity of the sensory input controls the input currents to a fixed proportion of neurons of the excitatory and inhibitory populations. In the second case, increasing intensity of the sensory stimulus will both, recruit an increasing number of neurons that receive input and change the input current that they receive. Using a mean field approximation for the network activity we derive relationships between the parameters of the network that ensure that the overall level of activity of the excitatory population remains unchanged for increasing intensity of the external stimulation. We find that, first, the main parameters that regulate network gain are the probabilities of connections from the inhibitory population to the excitatory population and of the connections within the inhibitory population. Second, we show that strict gain control is not achievable in a random network in the second case, when the input recruits an increasing number of neurons. Finally, we confirm that the gain control conditions derived from the mean field approximation are valid in simulations of firing rate models and Hodgkin-Huxley conductance based models

Recent breast cancer trends among Asian/Pacific Islander, Hispanic, and African-American women in the US: changes by tumor subtype

Abstract available at publisher's website

Multiple populations in globular clusters. Lessons learned from the Milky Way globular clusters

Recent progress in studies of globular clusters has shown that they are not simple stellar populations, being rather made of multiple generations. Evidence stems both from photometry and spectroscopy. A new paradigm is then arising for the formation of massive star clusters, which includes several episodes of star formation. While this provides an explanation for several features of globular clusters, including the second parameter problem, it also opens new perspectives about the relation between globular clusters and the halo of our Galaxy, and by extension of all populations with a high specific frequency of globular clusters, such as, e.g., giant elliptical galaxies. We review progress in this area, focusing on the most recent studies. Several points remain to be properly understood, in particular those concerning the nature of the polluters producing the abundance pattern in the clusters and the typical timescale, the range of cluster masses where this phenomenon is active, and the relation between globular clusters and other satellites of our Galaxy.Comment: In press (The Astronomy and Astrophysics Review

Impacts of climate change on plant diseases – opinions and trends

There has been a remarkable scientific output on the topic of how climate change is likely to affect plant diseases in the coming decades. This review addresses the need for review of this burgeoning literature by summarizing opinions of previous reviews and trends in recent studies on the impacts of climate change on plant health. Sudden Oak Death is used as an introductory case study: Californian forests could become even more susceptible to this emerging plant disease, if spring precipitations will be accompanied by warmer temperatures, although climate shifts may also affect the current synchronicity between host cambium activity and pathogen colonization rate. A summary of observed and predicted climate changes, as well as of direct effects of climate change on pathosystems, is provided. Prediction and management of climate change effects on plant health are complicated by indirect effects and the interactions with global change drivers. Uncertainty in models of plant disease development under climate change calls for a diversity of management strategies, from more participatory approaches to interdisciplinary science. Involvement of stakeholders and scientists from outside plant pathology shows the importance of trade-offs, for example in the land-sharing vs. sparing debate. Further research is needed on climate change and plant health in mountain, boreal, Mediterranean and tropical regions, with multiple climate change factors and scenarios (including our responses to it, e.g. the assisted migration of plants), in relation to endophytes, viruses and mycorrhiza, using long-term and large-scale datasets and considering various plant disease control methods

An agent-based model of the response to angioplasty and bare-metal stent deployment in an atherosclerotic blood vessel

Purpose: While animal models are widely used to investigate the development of restenosis in blood vessels following an intervention, computational models offer another means for investigating this phenomenon. A computational model of the response of a treated vessel would allow investigators to assess the effects of altering certain vessel- and stent-related variables. The authors aimed to develop a novel computational model of restenosis development following an angioplasty and bare-metal stent implantation in an atherosclerotic vessel using agent-based modeling techniques. The presented model is intended to demonstrate the body's response to the intervention and to explore how different vessel geometries or stent arrangements may affect restenosis development. Methods: The model was created on a two-dimensional grid space. It utilizes the post-procedural vessel lumen diameter and stent information as its input parameters. The simulation starting point of the model is an atherosclerotic vessel after an angioplasty and stent implantation procedure. The model subsequently generates the final lumen diameter, percent change in lumen cross-sectional area, time to lumen diameter stabilization, and local concentrations of inflammatory cytokines upon simulation completion. Simulation results were directly compared with the results from serial imaging studies and cytokine levels studies in atherosclerotic patients from the relevant literature. Results: The final lumen diameter results were all within one standard deviation of the mean lumen diameters reported in the comparison studies. The overlapping-stent simulations yielded results that matched published trends. The cytokine levels remained within the range of physiological levels throughout the simulations. Conclusion: We developed a novel computational model that successfully simulated the development of restenosis in a blood vessel following an angioplasty and bare-metal stent deployment based on the characteristics of the vessel crosssection and stent. A further development of this model could ultimately be used as a predictive tool to depict patient outcomes and inform treatment options. © 2014 Curtin, Zhou

New live screening of plant-nematode interactions in the rhizosphere

Abstract Free living nematodes (FLN) are microscopic worms found in all soils. While many FLN species are beneficial to crops, some species cause significant damage by feeding on roots and vectoring viruses. With the planned legislative removal of traditionally used chemical treatments, identification of new ways to manage FLN populations has become a high priority. For this, more powerful screening systems are required to rapidly assess threats to crops and identify treatments efficiently. Here, we have developed new live assays for testing nematode responses to treatment by combining transparent soil microcosms, a new light sheet imaging technique termed Biospeckle Selective Plane Illumination Microscopy (BSPIM) for fast nematode detection, and Confocal Laser Scanning Microscopy for high resolution imaging. We show that BSPIM increased signal to noise ratios by up to 60 fold and allowed the automatic detection of FLN in transparent soil samples of 1.5 mL. Growing plant root systems were rapidly scanned for nematode abundance and activity, and FLN feeding behaviour and responses to chemical compounds observed in soil-like conditions. This approach could be used for direct monitoring of FLN activity either to develop new compounds that target economically damaging herbivorous nematodes or ensuring that beneficial species are not negatively impacted

Pharmacokinetic-Pharmacodynamic Modeling in Pediatric Drug Development, and the Importance of Standardized Scaling of Clearance.

Pharmacokinetic/pharmacodynamic (PKPD) modeling is important in the design and conduct of clinical pharmacology research in children. During drug development, PKPD modeling and simulation should underpin rational trial design and facilitate extrapolation to investigate efficacy and safety. The application of PKPD modeling to optimize dosing recommendations and therapeutic drug monitoring is also increasing, and PKPD model-based dose individualization will become a core feature of personalized medicine. Following extensive progress on pediatric PK modeling, a greater emphasis now needs to be placed on PD modeling to understand age-related changes in drug effects. This paper discusses the principles of PKPD modeling in the context of pediatric drug development, summarizing how important PK parameters, such as clearance (CL), are scaled with size and age, and highlights a standardized method for CL scaling in children. One standard scaling method would facilitate comparison of PK parameters across multiple studies, thus increasing the utility of existing PK models and facilitating optimal design of new studies

Clinical characteristics of different histologic types of breast cancer

Breast cancer is a heterogeneous disease, though little is known about some of its rarer forms, including certain histologic types. Using Surveillance, Epidemiology, and End Results Program data on 135 157 invasive breast cancer cases diagnosed from 1992 to 2001, relationships between nine histologic types of breast cancer and various tumour characteristics were assessed. Among women aged 50–89 years at diagnosis, lobular and ductal/lobular carcinoma cases were more likely to be diagnosed with stage III/IV, ⩾5.0 cm, and node-positive tumours compared to ductal carcinoma cases. Mucinous, comedo, tubular, and medullary carcinomas were less likely to present at an advanced stage. Lobular, ductal/lobular, mucinous, tubular, and papillary carcinomas were less likely, and comedo, medullary, and inflammatory carcinomas were more likely to be oestrogen receptor (ER) negative/progesterone receptor (PR) negative and high grade (notably, 68.2% of medullary carcinomas were ER−/PR− vs 19.3% of ductal carcinomas). In general, similar differences were observed among women diagnosed at age 30–49 years. Inflammatory carcinomas are associated with more aggressive tumour phenotypes, and mucinous, tubular, and papillary tumours are associated with less aggressive phenotypes. The histologic types of breast cancer studied here differ greatly in their clinical presentations, and the differences in their hormone receptor profiles and grades point to their likely different aetiologies