An axiomatic approach to image interpolation

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The absolute minimal Lipschitz extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range.     

The use of ghost variables and virtual programming in the documentation and verification of programs

Using ghost variables and virtual programming, a method for documenting programs which exhibit some common characteristics is presented. The annotations required are expressed in a powerful high level assertion language. The usefulness of these annotations is illustrated by the generation of verification conditions for some small example programs written in a dialect of Pascal. Demonstrations of the correctness of these programs are also given.     

Price competition between a macrocell and a small-cell service provider with limited resources and optimal bandwidth user subscription: a game-theoretical model

The ever-increasing demand for higher data rates in wireless commutations provides a rationale for small cells deployment. While the physical and technological aspects of small-cell networks have been extensively studied in recent years, the economic analysis has received much less attention. We focus on the economic rationale for a small-cell service provider (SSP) operating a market where an incumbent macrocell service provider (MSP) exists, and competition develops. We analyze such scenario for the case of fixed users by means of Game Theory, specifically through a two-stage game: in the first stage each service provider posts its price according to a Stackelberg game where the MSP is the leader and the SSP is the follower; and, in the second stage, each user chooses both which provider to subscribe to and the optimal amount of bandwidth. A subgame perfect Nash equilibrium is used as a solution concept, and it is derived analytically. We show that the SSP has an incentive to operate in the market and its profit gets higher as SSP’s resources increase. Furthermore, users benefit from SSP’s operation, which may provide a rationale for a regulatory authority to grant the SSP access to the market, despite the fact that MSP’s profit is harmed. Finally, we identify two modes of operation of the system, which depend on the SSP coverage: one where SSP’s deployment is limited and the MSP strategy is not affected by SSP competition and takes only the users outside the SSP coverage; and another, where the SSP covers a large area and the MSP competes against the SSP taking a fraction of the users inside the small cells.     

A Methodology for Modeling and Optimizing Social Systems

Abstract

A system methodology for modeling and optimizing social systems is presented. It allows constructing dynamical models formulated stochastically, i.e., their results are given by confidence intervals. The models provide optimal intervention ways to reach the stated objectives. Two optimization methods are used: (1) to test strategies and scenarios and (2) to optimize with a genetic algorithm. The application case presented is a small nonformal education Spanish business. First, the model is validated in the 2008–2012 period, and subsequently, the optimal way to obtain a maximum profit in the 2013–2025 period is obtained using the two methods.     

An EWMA control chart for the multivariate coefficient of variation

Monitoring the multivariate coefficient of variation over time is a natural choice when the focus is on stabilising the relative variability of a multivariate process, as is the case in a significant number of real situations in engineering, health sciences, and finance, to name but a few areas. However, not many tools are available to practitioners with this aim. This paper introduces a new control chart to monitor the multivariate coefficient of variation through an exponentially weighted moving average (EWMA) scheme. Concrete methodologies to calculate the limits and evaluate the performance of the chart proposed and determine the optimal values of the chart's parameters are derived based on a theoretical study of the statistic being monitored. Computational experiments reveal that our proposal clearly outperforms existing alternatives, in terms of the average run length to detect an out‐of‐control state. A numerical example is included to show the efficiency of our chart when operating in practice.     

An ecosystemic approach for assessing the urban water self-sufficiency potential: lessons from the Mediterranean

Frequent water stress episodes affecting urban hubs have caused a shift in urban water management towards integrated approaches and motivated a search for alternative water resources. Large-scale rainwater harvesting on the municipal scale can overcome the disadvantages of climate dependence and the volume restrictions associated with small-scale collection facilities. In this paper, two tools based on the urban metabolism concept are used to determine the water self-sufficiency potential of urban systems from urban runoff: a simple water self-sufficiency potential indicator and a socioeconomic water flow accounting scheme, which includes water losses. Both tools are applied to a densely populated coastal area that exemplifies urban centres in the Mediterranean. This approach is useful for regions with restricted data availability on water use and facilitates information dissemination to policy makers. The results indicate a significant water self-sufficiency potential for the area of study, even under projections of reduced precipitation in the area.     

Field induced vortex dynamics in magnetic Ni nanotriangles

The magnetization states in Ni triangular dots under an applied magnetic field have been studied using variable-field magnetic force microscopy (VF-MFM) imaging. In order to understand their dynamics we performed micromagnetic simulations which are in remarkable agreement with the experimental MFM results. The nanostructures present magnetic vortices as ground states which move under an external magnetic field. The combination of micromagnetic simulations and MFM imaging allows us to identify correctly the vortex chiralities and polarizations. The triangular geometry produces an improved contrast of the vortex core. Additionally, the vortices of different chiralities present clearly different MFM images under an?applied field.