Optimal control of the propagation of a graph in inhomogeneous media

We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the $H^{-1}$-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

The ordered K-theory of a full extension

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if and only if the extension is stenotic and K-lexicographic. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9 is not correct as stated. See arXiv:1505.05951 for more details. Since Theorem 4.9 is an application to the main results of the paper, the main results of this paper are not affected by the error. Version III comments: Some typos and errors corrected. Some references adde

Factors influencing the relationship between the dose of amlodipine required for blood pressure control and change in blood pressure in hypertensive cats

BACKGROUND: Hypertension is a common problem in elderly cats. In most cats, systolic blood pressure (SBP) of <160 mmHg is achieved in response to amlodipine besylate at either 0.625 or 1.25 mg q24h. The individual cat factors determining dose requirement dose have not been explored. AIMS: To determine whether individual cat factors influence the dose of amlodipine required to achieve adequate blood pressure control and to determine whether factors other than the prescribed dose of drug alter the achieved plasma amlodipine concentrations. METHODS: Fifty‐nine hypertensive cats that required 0.625 mg (A) and 41 cats that required 1.25 mg (B) amlodipine to reach a target SBP of <160 mmHg were identified, and plasma amlodipine concentrations were determined. Comparisons were made between groups, and multivariable linear regression models were performed to investigate predictors of antihypertensive response. RESULTS: Cats that required a greater dose of amlodipine had significantly higher SBP at diagnosis of hypertension (A: (median [25th, 75th percentile]) 182 [175,192] mmHg; B: 207 [194,217] mmHg, P < .001), but comparable blood pressure was achieved after treatment. Plasma amlodipine concentrations were directly related to the dose of amlodipine administered. At diagnosis, cats in group B had significantly lower plasma potassium concentration (A: 4.1 [3.8,4.5]; B: 3.8 [3.6,4.2] mEq/L, P < .01). Weight did not differ between groups. The decrease in SBP was directly and independently associated with the SBP at diagnosis and the plasma amlodipine concentration. CONCLUSIONS AND CLINICAL IMPORTANCE: Cats with higher blood pressure at diagnosis might require a greater dose of amlodipine to control their blood pressure adequately. Differences in amlodipine pharmacokinetics between cats do not seem to play a role in the antihypertensive response

ECONOMICS OF AGRICULTURAL SOIL CARBON SEQUESTRATION IN THE NORTHERN PLAINS

Under the Kyoto protocol of the United Nations Framework Convention on Climate Change the United States is charged with reducing emissions of greenhouse gases to seven percent below their 1990 levels by the period 2008-2012. These reductions could be met from many industries including agriculture. In this paper, an economic simulation model is linked to an ecosystem model to quantify the economic efficiency of policies that might be used to sequester carbon (C) in agricultural soils in the Northern Plains region. Simulations with the Century ecosystem model show that long-term soil C levels associated with a crop/fallow system are less than those for grass alone, but that soil C levels for grass-clover-pasture are greater than for continuously cropped grains. The analysis shows that a CRP-style policy is found to be an inefficient means to increase soil C because the per acre payments to convert crop-land to grass-only draw land from both the crop/fallow system and the continuous cropping system, and costs typically exceed $100 per MT (metric ton) of C. In contrast, payments to adopt continuous cropping were found to produce increases in soil C for between$5 to $70 depending on area and degree of targeting of the payments. The most efficient, lowest cost policy is achieved when payments are targeted to land that was previously in a crop/fallow rotation. In this range, soil C sequestration appears to be competitive with C sequestered from other sources.policy design, economic efficiency, soil carbon, sequestration, valuing soil carbon, Great Plains agriculture, Resource /Energy Economics and Policy, Q2,

ECONOMICS OF AGRICULTURAL SOIL CARBON SEQUESTRATION IN THE NORTHERN GREAT PLAINS

Under the Kyoto protocol of the United Nations Framework Convention on Climate Change the United States is charged with reducing emissions of greenhouse gases to seven percent below their 1990 levels by the period 2008-2012. These reductions could be met from many industries including agriculture. In this paper, an economic simulation model is linked to the CENTURY ecosystem model to quantify the economic efficiency of policies that might be used to sequester carbon (C) in agricultural soils in the Northern Great Plains region. Model outputs are combined to assess the costs of inducing changes in equilibrium levels of soil C through three types of policies. The first is a CRP-style policy that provides producers with per-acre payments for converting crop-land to permanent grass; the second is a policy that provides per-acre payments to all farmers that use continuous cropping, regardless of the land's cropping history; the third is a policy that provides per-acre payments for the use of continuous cropping only on land units that had previously been in a crop/fallow rotation. The analysis shows that a CRP-style policy is found to be an inefficient means to increase soil C resulting in costs that typically exceed $100 per MT (metric ton) of C. In contrast, payments to adopt continuous cropping were found to produce increases in soil C for between$5 to $70/MT depending on the geographic area and degree of targeting of the payments. The most efficient, lowest cost policy is achieved when payments are targeted to land that was previously in a crop/fallow rotation. In this range, soil C sequestration appears to be competitive with C sequestered from other sources.policy design, economic efficiency, soil carbon, sequestration, valuing soil carbon, Great Plains agriculture, Environmental Economics and Policy, Q2,

Determining solar abundances using helioseismology

The recent downward revision of solar photospheric abundances of Oxygen and other heavy elements has resulted in serious discrepancies between solar models and solar structure as determined through helioseismology. In this work we investigate the possibility of determining the solar heavy-element abundance without reference to spectroscopy by using helioseismic data. Using the dimensionless sound-speed derivative in the solar convection zone, we find that the heavy element abundance, Z, of 0.0172 +/- 0.002, which is closer to the older, higher value of the abundances.Comment: To appear in Ap