We consider the numerical integration of a size-structured cell population model. We propose a new second-order numerical method to attain its solution. The scheme is analyzed and the optimal rate of convergence is derived. We show experimentally the predicted accuracy of the scheme.

We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.

Fluorescence recovery after photobleaching (FRAP) is a widely used measurement technique to determine the mobility of fluorescent molecules within living cells. While the experimental setup and protocol for FRAP experiments are usually fixed, data (pre)processing represents an important issue. The aim of this paper is twofold. First, we formulate and solve the problem of relevant FRAP data selection. The theoretical findings are illustrated by the comparison of the results of parameter identification when the full data set was used and the case when the irrelevant data set (data with negligible impact on the confidence interval of the estimated parameters) was removed from the data space. Second, we analyze and compare two approaches of FRAP data processing. Our proposition, surprisingly for the FRAP community, claims that the data set represented by the FRAP recovery curves in form of a time series (integrated data approach commonly used by the FRAP community) leads to a larger confidence interval compared to the full (spatiotemporal) data approach.

We develop a family of predator-prey models with age structure and cannibalism in the prey population. It consists of systems of $m$ ordinary differential equations, where $m$ is a parameter associated with new proposed prey birth rates. We discuss how these new birth rates give the required flexibility to produce differential systems with well-behaved solutions. The main feature required in these models is the coexistence among the involved species, which translates mathematically into stable equilibria and periodic solutions. The search for such characteristics is based on heuristic predation functions that account for cannibalism in the prey.

The bomb attacks in Madrid three days before the general elections of March 14, 2004, and their possible influence on the victory of PSOE (Spanish Workers Socialist Party), defeating PP (Popular Party), have been a matter of study from several points of view (i.e., sociological, political, or statistical). In this paper, we present a dynamic model based on a system of differential equations such that it, using data from Spanish CIS (National Center of Sociological Research), describes the evolution of voting intention of the Spanish people over time. Using this model, we conclude that the probability is very low that the PSOE would have won had the attack not happened. Moreover, after the attack, the PSOE increased an average of 5.6% in voting on March 14 and an average of 11.2% of the Spanish people changed their vote between March 11 and March 14. These figures are in accordance with other studies.

Traumatic brain injury (TBI) is a critical public health and socioeconomic problem throughout the world. Cognitive rehabilitation (CR) has become the treatment of choice for cognitive impairments after TBI. It consists of hierarchically organized tasks that require repetitive use of impaired cognitive functions. One important focus for CR professionals is the number of repetitions and the type of task performed throughout treatment leading to functional recovery. However, very little research is available that quantifies the amount and type of practice. The Neurorehabilitation Range (NRR) and the Sectorized and Annotated Plane (SAP) have been introduced as a means of identifying formal operational models in order to provide therapists with decision support information for assigning the most appropriate CR plan. In this paper we present a novel methodology based on combining SAP and NRR to solve what we call the Neurorehabilitation Range Maximal Regions (NRRMR) problem and to generate analytical and visual tools enabling the automatic identification of NRR. A new SAP representation is introduced and applied to overcome the drawbacks identified with existing methods. The results obtained show patterns of response to treatment that might lead to reconsideration of some of the current clinical hypotheses.

We obtain a result that relates the risk-neutral jump size of interest rates with yield curve data. This function is unobservable; therefore, this result opens a way to estimate the jump size directly from data in the markets together with the risk-neutral drift and jump intensity estimations. Then, we investigate the finite sample performance of this approach with a test problem. Moreover, we analyze the effect of estimating the risk-neutral jump size instead of assuming that it is artificially absorbed by the jump intensity, as usual in the interest rate literature. Finally, an application to US Treasury Bill data is also illustrated.