Mathematical modeling of water distribution networks makes use of simplifications aimed to optimize the development and use of the mathematical models involved. Simplified models are used systematically by water utilities, frequently with no awareness of the implications of the assumptions used. Some simplifications are derived from the various levels of granularity at which a network can be considered. This is the case of some demand simplifications, specifically, when consumptions associated with a line are equally allocated to the ends of the line. In this paper, we present examples of situations where this kind of simplification produces models that are very unrealistic. We also identify the main variables responsible for the errors. By performing some error analysis, we assess to what extent such a simplification is valid. Using this information, guidelines are provided that enable the user to establish if a given simplification is acceptable or, on the contrary, supplies information that differs substantially from reality. We also develop easy to implement formulae that enable the allocation of inner line demand to the line ends with minimal error; finally, we assess the errors associated with the simplification and locate the points of a line where maximum discrepancies occur.

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Over the last years, worldwide financial market instability has shaken confidence in global economies. Global financial crisis and changes in sovereign debts ratings have affected the Latin American financial markets and their economies. However, Latin American’s relative resilience to the more acute rise in risk seen in other regions like Europe during last years is offering investors new options for improving risk-return trade-offs. Therefore, forecasting the future of economic situation involves high levels of uncertainty. The Country Risk Score (CRS) represents a broadly used indicator to measure the current situation of a country regarding measures of economic, political, and financial risk in order to determine country risk ratings. In this contribution, we present a diffusion model to study the dynamics of the CRS in 18 Latin American countries which considers both the endogenous effect of each country policies and the contagion effect among them. The model predicts quite well the evolution of the CRS in the short term despite the economic and political instability. Furthermore, the model reproduces and forecasts a slight increasing trend, on average, in the CRS dynamics for almost all Latin American countries over the next months.

As the network technique is fast developing, the microblog has been a significant carrier representing the social public opinions. Therefore, it is important to investigate the propagation characteristics of the topics and to unearth the opinion leaders in Micro-blog network. The propagation status of the hot topics in the Micro-blog is influenced by the authority of the participating individuals. We build a time-varying model with the variational external field strength to simulate the topic propagation process. This model also fits for the multimodal events. The opinion leaders are important individuals who remarkably influence the topic discussions in its propagation process. They can help to guide the healthy development of public opinion. We build an AHP model based on the influence, the support, and the activity of a node, as well as a microblog-rank algorithm based on the weighted undirected network, to unearth and analyze the opinion leaders’ characteristics. The experiments in the data, collected from the Sina Micro-blog from October 2012 to November 2012 and from January 2013 to February 2013, show that our models predict the trend of hot topic efficiently and the opinion leaders we found are reasonable.

An SO₂ emission episode at coal-fired power station occurs when the series of bihourly average of SO₂ concentration, taken at 5-minute intervals, is greater than a specific value. Advance prediction of these episodes of pollution is very important for companies generating electricity by burning coal since it allows them to take appropriate preventive measures. In order to forecast SO₂ pollution episodes, three different methods were tested: Elman neural networks, autoregressive integrated moving average (ARIMA) models, and a hybrid method combining both. The three methods were applied to a time series of SO₂ concentrations registered in a control station in the vicinity of a coal-fired power station. The results obtained showed a better performance of the hybrid method over the Elman networks and the ARIMA models. The best prediction was obtained 115 minutes in advance by the hybrid model.

A modified classical method for preliminary orbit determination is presented. In our proposal, the spread of the observations is considerably wider than in the original method, as well as the order of convergence of the iterative scheme involved. The numerical approach is made by using matricial weight functions, which will lead us to a class of iterative methods with a sixth local order of convergence. This is a process widely used in the design of iterative methods for solving nonlinear scalar equations, but rarely employed in vectorial cases. The numerical tests confirm the theoretical results, and the analysis of the dynamics of the problem shows the stability of the proposed schemes.

We consider the perturbed dual risk model with constant interest and a threshold dividend strategy. Firstly, we investigate the moment-generation function of the present value of total dividends until ruin. Integrodifferential equations with certain boundary conditions are derived for the present value of total dividends. Furthermore, using techniques of sinc numerical methods, we obtain the approximation results to the expected present value of total dividends. Finally, numerical examples are presented to show the impact of interest on the expected present value of total dividends and the absolute ruin probability.

This paper deals with the construction of a discrete population mathematical model for the short-term forecast until January 2016 of the electoral support of extreme ideology parties in Spain. Firstly, the nontrivial concept of extreme ideology is stated. Then, the electoral register is split in three subpopulations: supporters of extremist parties, abstentions/blank voters, and supporters of establishment parties. The model takes into account the following variables: economy measured throughout the Spanish unemployment rate; demography quantified in terms of birth and death rates and emigration; sociopolitical situation measured by the Spanish poverty indicator, trust on the Government labor indicator (GLI), and the indicator of political trust. By considering the dynamic subpopulations transits built throughout data obtained from public and private prestigious institutions and sociopolitical analysis, a system of difference equations models the electoral population behavior in Spain allowing us to compute the expected electoral support in the time horizon of January 2016. Sensitivity analysis versus uncertain parameters is performed in order to improve the reliability of the model results.

For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. According to these regions, we further demonstrate dispersion relations and spatial patterns. Our results indicate that self-diffusion plays an important role in the spatial patterns.

Plastic surgery practice grows continuously among the women in Western countries due to their body image dissatisfaction, aging anxiety, and an ideal body image propagated by the media. The consumption growth is so important that plastic surgery is becoming a normal practice among women, like any other cosmetic product, with the risk of suffering psychopathology disorders in the sense that plastic surgery could be employed as an instrument to recover personal self-esteem or even happiness. Plastic surgery practice depends on economic, demographic, and social contagion factors. In this paper, a mathematical epidemiological model to forecast female plastic surgery consumption in Spain is fully constructed. Overconsumer subpopulation is predicted and simulated. Robustness of the model versus uncertain parameters is studied throughout a sensitivity analysis.

The consideration of uncertainty in differential equations leads to the emergent area of random differential equations. Under this approach, inputs become random variables and/or stochastic processes. Often one assumes that inputs are independent, a hypothesis that simplifies the mathematical treatment although it could not be met in applications. In this paper, we analyse, through the Airy equation, the influence of statistical dependence of inputs on the output, computing its expectation and standard deviation by Fröbenius and Polynomial Chaos methods. The results are compared with Monte Carlo sampling. The analysis is conducted by the Airy equation since, as in the deterministic scenario its solutions are highly oscillatory, it is expected that differences will be better highlighted. To illustrate our study, and motivated by the ubiquity of Gaussian random variables in numerous practical problems, we assume that inputs follow a multivariate Gaussian distribution throughout the paper. The application of Fröbenius method to solve Airy equation is based on an extension of the method to the case where inputs are dependent. The numerical results show that the existence of statistical dependence among the inputs and its magnitude entails changes on the variability of the output.

We discuss a computational system following the paradigm of distributed computing, which will allow us to simulate the epidemic propagation in random networks with large number of nodes up to one million. This paradigm consists of a server that delivers tasks to be carried out by client computers. When the task is finished, the client sends the obtained results to the server to be stored until all tasks are finished and then ready to be analysed. Finally, we show that this technique allows us to disclose the emergence of seasonal patterns in the respiratory syncytial virus transmission dynamics which do not appear neither in smaller systems nor in continuous systems.

This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.

Many different factors are taken into account by students when choosing a degree and university. Some of these are general considerations, such as the quality of the degree course (ratio of available places/places in first choice, cut-off mark, etc.), while others are subjective factors (e.g., friends doing the same course). This paper presents a partial multivariate model that considers the weight of the different variables linked to this decision, as identified in the bibliography. We analyzed four samples of first-year students (total $n=1790$) from different engineering degree courses at the Universitat Politècnica de València (UPV) in the 2010-2011 and 2011-2012 academic years. All the students involved in the study had chosen this university and their courses as their first option. The overall effect shows that the structural model adjusts reasonably well to the different engineering courses analyzed. Similarly, the individual models for each engineering degree manage to identify the different effects involved. In the case of the engineering degree based on new technologies (ICT), the statistical effects are much greater and more statistically significant than in the other three branches of engineering considered. Social and individual factors were seen to have more impact on the choice of ICT degrees at the UPV.

The contamination through the geological formation cannot move and disperse with the same speed and dispersion coefficient, respectively, due to the variability of the geological formation. This paper is therefore first devoted to the description of the hydrodynamic advection dispersion equation with the seepage velocity and dispersion coefficient as function of space and time. Secondly the equation is solved via two analytical techniques: the homotopy decomposition method and the differential transform method. The numerical simulations of the approximated solutions are presented.