Calculus from the past: multiple delay systems arising in cancer cell modelling

Non-local calculus is often overlooked in the mathematics curriculum. In this paper we present an interesting new class of non-local problems that arise from modelling the growth and division of cells, especially cancer cells, as they progress through the cell cycle. The cellular biomass is assumed to be unstructured in size or position, and its evolution governed by a time-dependent system of ordinary differential equations with multiple time delays. The system is linear and taken to be autonomous. As a result, it is possible to reduce its solution to that of a nonlinear matrix eigenvalue problem. This method is illustrated by considering case studies, including the model of the cell cycle developed in Simms K, Bean N, & Koeber A. [10]. The paper concludes by explaining how asymptotic expressions for the distribution of cells across the compartments can be determined and used to assess the impact of different chemotherapeutic agents

A cell growth model revisited

In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This probabilistic approach gives straightforward proof of the existence of the steady-size distribution and a simple derivation of the functional-differential equation for it. The latter one is the celebrated pantograph equation (of advanced type). This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework

A model for phenotype change in a stochastic framework

some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time

Is New Hampshire\u27s climate warming?

This Carsey brief looks at temperature anomalies across New Hampshire and shows that not only is the state warmer than it has been in the past, but it is also warming faster than much of the planet. Sociologist Lawrence Hamilton, research associate professor Cameron Wake, and former NH state climatologist Barry Keim analyzed over 100 years of temperatures across the state to produce this data for the Carsey Institute in August 2010

Optimal nutritional intake for fetal growth

View online at publisher's website: http://www.aimsciences.org/journals/displayArticles.jsp?paperID=6249The regular nutritional intake of an expectant mother clearly affects the weight development of the fetus. Assuming the growth of the fetus follows a deterministic growth law, like a logistic equation, albeit dependent on the nutritional intake, the ideal solution is usually determined by the birth-weight being pre-assigned, for example, as a percentage of the mother's average weight. This problem can then be specified as an optimal control problem with the daily intake as the control, which appears in a Michaelis-Menten relationship, for which there are well-developed procedures to follow. The best solution is determined by requiring minimum total intake under which the preassigned birth weight is reached. The algorithm has been generalized to the case where the fetal weight depends in a detailed way on the cumulative intake, suitably discounted according to the history. The optimality system is derived and then solved numerically using an iterative method for the specific values of parameter. The procedure is generic and can be adapted to any growth law and any parameterisation obtained by the detailed physiology

Hydrological Investigations at Biafo Glacier, Karakoram Range, Himalaya; an Important Source of Water For the Indus River

Over 80% of the flow of the Upper Indus River is derived from less than 20% of its area: essentially from zones of heavy snowfall and glacierized basins above 3500 m elevation. The trans-Himalaya n contribution comes largely from an area of some 20000 km2 of glacierized basins, mostly along the axis of the Greater Karakoram range and especially from 20-30 of the largest glacier basins. Very few glaciological investigations have so far been undertaken in this the major glacierized region of Central Asia. Biafo Glacier, one of the largest of the Karakoram glaciers, drains south-eastwards from the central Karakoram crest. Its basin covers a total area of 853 km2 , 628 km2 of which are permanent snow and ice, with 68% of the glacier area forming the accumulation zone. This paper describes investigations of snow accumulation, ablation , glacier movement, and glacier depth undertaken in the period 1985-87 , set against a background of investigations carried out over the last 130 yea rs. Biafo Glacier differs from most of the other Karakoram glaciers in being nourished mainly by direct snowfall rather than by avalanching; this has the advantage of allowing extensive investigation of accumulation over a broad range of altitude. Snow-accumulation studies in the Biafo Glacier basin have indicated that annual accumulation varies from 0.9 to 1.9 m of water equivalent between 4650 and 5450 m a .. s.l. This suggests an annual moisture input above the equilibrium line of approximately 0.6 km3. Monopulse radar measurements indicate the presence of ice thickness as great as 1400 m at the equilibrium line, although these results may not be completely reliable . Mean surface velocity during the summer of 0.8 m d -I has been measured near to the equilibrium line. Calculations of annual ice flux through the vertical cross-profile at the equilibrium line indicate a throughput of 0.7 km3 a-I Estimates from stake ablation measurements also suggest that ice loss on Biafo Glacier is about 0.7 km3 a-I. The close agreement between these three sets of measurements is reassuring, indicating that the ablation zone of Biafo Glacier, whose area covers 0.09% of the whole Upper Indus basin, produces approximately 0.9% of the total run-off. However. it should be mentioned that this estimate does not include water originating from seasonal snow melt, e either above or below the equilibrium line, or from rainfall. Net annual ice losses due to wastage of the glacier since 1910 are probably of the order of 0.4-{).5 m a-I; this would represent between 12 and 15% of annual water yield from melting ice

Estableciendo diálogos entre diferentes marcos teóricos: de los procesos narrativos a la teoría antropológica de lo didáctico

El punto de partida de este artículo es el fenómeno de la co-existencia de diferentes marcos teóricos en didáctica de las matemáticas. Proponemos reformular este fenómeno en términos de un problema científico: el problema del establecimiento de diálogos entre praxeologías de investigación. Iniciamos un diálogo entre dos praxeología de investigación partiendo de una secuencia de clase de una profesora inglesa. El problema de investigación inicial, comprender la acción didáctica de la profesora, fue formulado y abordado, desde la tradición anglosajona, usando el marco de los procesos narrativos. Exploramos aquí los mismos hechos empíricos desde la Teoría Antropológica de lo Didáctico, mostrando que cada praxeología de investigación construye sus propios problemas de investigación y ofreciendo resultados nuevos y complementarios

Granite Staters Weigh in on Renewable Energy Versus Drilling: Environmental Quality of Life Ranks High Across Party Lines

Since the fall of 2001, the Granite State Poll has been conducting telephone interviews with random samples of New Hampshire residents about four times each year. State and national political topics, such as how people view candidates or elected officials, have been staples of this poll. During campaign seasons, the poll draws national attention in forecasting election results. During quieter times, it asks many nonpolitical questions as well.Trained personnel at the University of New Hampshire Survey Center conduct the 10- to 15-minute interviews

The Spatial Variation of Asian Dust and Marine Aerosol Contributions to Glaciochemical Signals in Central Asia

Short-term (6 months to 17 years) glaciochemical records have been collected from several glacier basins in the mountains of central Asia. The spatial distribution of snow chemistry in central Asia is controlled by the influx of dust from the large expanse of arid and semiarid regions in central Asia. Glaciers in the Northern and Western Tibetan Plateau show elevated concentrations and elevated annual fluxes of calcium, sodium, chloride, sulphate and nitrate due to the influx of desert dust from nearby arid and semi-arid regions. Glaciers in the Southeastern Tibetan Plateau show lower concentrations and lower annual fluxes of major ions due to longer transport distances of dust from the arid and semi-arid regions of Western China. Snow from the Karakoram and Western Himalaya show ion concentrations similar to those in Southeastern Tibetan Plateau, but much higher annual fluxes suggesting that much of the aerosol and moisture transported with the westerly jet stream is removed as it ascends the Southwest margin of the Tibetan Plateau. Snow from the Southern slopes of the Eastern Himalayas shows very low concentrations and very low annual fluxes of major ions, indicating that this region is relatively free from the chemical influence of Asian dust. The glaciochemical data suggest that glaciers which are removed from large source areas of mineral aerosol, such as those in the Himalaya, the Karakoram, and the Southeastern Tibetan Plateau, are the ones most likely to contain longer-term glaciochemical records which detail annual to decadal variation in the strength of the Asian monsoon and long-range transport of Asian dust

Climate Change in Northern New Hampshire: Past, Present and Future

EARTH’S CLIMATE CHANGES. It always has and always will. However, an extensive and growing body of scientific evidence indicates that human activities—including the burning of fossil fuel (coal, oil, and natural gas) for energy, clearing of forested lands for agriculture, and raising livestock—are now the primary force driving change in the Earth’s climate system. This report describes how the climate of northern New Hampshire has changed over the past century and how the future climate of the region will be affected by a warmer planet due to human activities