Defensive alliances in graphs: a survey

A set $S$ of vertices of a graph $G$ is a defensive $k$-alliance in $G$ if every vertex of $S$ has at least $k$ more neighbors inside of $S$ than outside. This is primarily an expository article surveying the principal known results on defensive alliances in graph. Its seven sections are: Introduction, Computational complexity and realizability, Defensive $k$-alliance number, Boundary defensive $k$-alliances, Defensive alliances in Cartesian product graphs, Partitioning a graph into defensive $k$-alliances, and Defensive $k$-alliance free sets.Comment: 25 page

Inequality of opportunity and growth

Theoretical and empirical studies exploring the effects of income inequality upon growth reach a disappointing inconclusive result. This paper postulates that one reason for this ambiguity is that income inequality is actually a composite measure of at least two different sorts of inequality: inequality of opportunity and inequality of returns to effort. These two types of inequality affect growth through opposite channels, so the relationship between income inequality and growth is positive or negative depending on which component is larger. We test this proposal using inequality-of-opportunity measures computed from the PSID database for 23 states of the U.S. in 1980 and 1990. We find robust support for a negative relationship between inequality of opportunity and growth, and a positive relationship between inequality of returns to effort and growth.income inequality; inequality of opportunity; economic growth.

Inequality of opportunity in Europe: Economic and policy facts

In this paper we consider the main factors that have influenced inequality of opportunity (IO) in Europe. Based on the EU-SILC database, we find that the various levels of development, education and social protection expenditure in 23 European countries significantly affect IO. Dropping out from school, reaching at least secondary levels of education, social spending to promote social integration and child care are the most important variables of those analyzed. The functioning of the labor market and the tax structure, on the other hand, do not have a significant bearing on IO. Lastly, we note that IO and total inequality exhibit differentiated explanatory patterns, which signifies that means of redistribution that serve to reduce overall inequality do not necessarily reduce IO.inequality of opportunity; growth; education; public expenditure; labor market.

Exponential localization of singular vectors in spatiotemporal chaos

In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval $\tau$. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law $\tau^{-\gamma}$ for the localization of the SV. Moreover the same exponent $\gamma$ characterizes the finite-$\tau$ deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improving existing forecasting techniques.Comment: 5 page

TAIP: an anytime algorithm for allocating student teams to internship programs

In scenarios that require teamwork, we usually have at hand a variety of specific tasks, for which we need to form a team in order to carry out each one. Here we target the problem of matching teams with tasks within the context of education, and specifically in the context of forming teams of students and allocating them to internship programs. First we provide a formalization of the Team Allocation for Internship Programs Problem, and show the computational hardness of solving it optimally. Thereafter, we propose TAIP, a heuristic algorithm that generates an initial team allocation which later on attempts to improve in an iterative process. Moreover, we conduct a systematic evaluation to show that TAIP reaches optimality, and outperforms CPLEX in terms of time.Comment: 10 pages, 7 figure