Deterministic mathematical modelling for cancer chronotherapeutics: cell population dynamics and treatment optimisation

Chronotherapeutics has been designed and used for more than twenty years as an effective treatment against cancer by a few teams around the world, among whom one of the first is Francis Lévi's at Paul-Brousse hospital (Villejuif, France), in application of circadian clock physiology to determine best infusion times within the 24-hour span for anticancer drug delivery. Mathematical models have been called in the last ten years to give a rational basis to such optimised treatments, for use in the laboratory and ultimately in the clinic. While actual clinical applications of the theoretical optimisation principles found have remained elusive so far to improve chronotherapeutic treatments in use, mathematical models provide proofs of concepts and tracks to be explored experimentally, to progress from theory to bedside. Starting from a simple ordinary differential equation model that allowed setting and numerically solving a drug delivery optimisation problem with toxicity constraints, this modelling enterprise has been extended to represent the division cycle in proliferating cell populations with different molecular targets, to allow for the representation of anticancer drug combinations that are used in clinical oncology. The main point to be made precise in such a therapeutic optimisation problem is to establish, here in the frame of circadian chronobiology, physiologically based differences between healthy and cancer cell populations in their responses to drugs. To this aim, clear biological evidence at the molecular level is still lacking, so that, starting from indirect observations at the experimental and clinical levels and from theoretical considerations on the model, speculations have been made, that will be exposed in this review of cancer chronotherapeutics models with the corresponding optimisation problems and their numerical solutions, to represent these differences between the two cell populations, with regard to circadian clock control

Numerical Inversion Methods for Computing Approximate p-Values

The paper considers the problem of computing p-values of non-standard distributions for which the characteristic function is available in closed form. When the characteristic function is a multivalued complex function, the standard numerical inversion method needs to be used with care as the integrand may become discontinous due to branch cuts. An alternative inversion method based on the Gaver-Wynn-Rho algorithm is shown to be a general and effective solution to the discontinuity problem as it works with real-valued functions. The method is illustrated with two well-known time series tests with non-standard distributions. Copyright Springer Science+Business Media, Inc. 2005characteristic function, numerical transform inversion, tail probability,

Modelos de cointegração com um ou dois limiares: uma aplicação para o preço do frango inteiro resfriado em mercados atacadistas no Brasil

A maioria dos estudos de integração de mercados que utiliza a técnica de cointegração com threshold não se preocupa em testar qual o número de regimes de ajustamento de preços é o mais adequado. Neste estudo, utiliza-se um procedimento para determinar o número de regimes estatisticamente indicado para diferentes mercados regionais de carne de frango no Brasil, no período de janeiro de 1998 a junho de 2007. Os resultados mostram que, para um grupo de mercados, o modelo com dois regimes é o mais indicado, enquanto para os demais mercados, o modelo com três regimes é o que melhor se ajusta. Constata-se a presença de significativas barreiras à transmissão de choques de preços entre os mercados, o que provavelmente resulta de custos de transação não desprezíveis na comercialização da carne de frango.<br>Most studies about market integration that use threshold cointegration do not usually test the number of regimes of price adjustment. In this study, we use a testing procedure to determine the number of statistically significant regimes for regional markets of poultry in Brazil in the period of January 1998 to June 2007. Results show that, for some markets, two regimes are adequate, whereas for others, the model should have three regimes. We also conclude that there are important barriers to price transmission among the markets which may come from the existence of high transaction costs regarding trades involving poultry

Predator-prey interactions between Dugesia gonocephala and free-living nematodes

Beier S, Bolley M, Traunspurger W. Predator-prey interactions between Dugesia gonocephala and free-living nematodes. FRESHWATER BIOLOGY. 2004;49(1):77-86.1. Three groups of laboratory experiments clarified the role of nematodes as a potential food resource for the triclad Dugesia gonocephala. The first group measured the functional response of adult D. gonocephala feeding on juvenile or adult Caenorhabditis elegans. The feeding rates of D. gonocephala on adult and juvenile C. elegans followed a type II functional response. The maximum number of adult nematodes and juvenile nematodes eaten by a single D. gonocephala individual within 3 h was 94 and 197 nematodes, respectively. 2. A second group of microcosm experiments investigated the effect of D. gonocephala on the density and the vertical distribution of a nematode community in fine sand. The following treatments were performed: (i) microcosms with 400 nematodes and (ii) microcosms with 400 nematodes and one D. gonocephala. After 5 days, nematodes as a group, as well as the dominant species Tobrilus pellucidus and Trischistoma monohystera, showed no significant difference in vertical patterns between the treatments with and without D. gonocephala. 3. The third group of experiments determined whether grain size of the sediment (sand, fine gravel and coarse gravel) altered the ability of D. gonocephala to consume adult C. elegans. Sand and fine gravel reduced the predation effectiveness of D. gonocephala by 100%, whereas the predator consumed nematodes in coarse gravel (19 nematodes within 3 h)