Clique-Stable Set separation in perfect graphs with no balanced skew-partitions

Inspired by a question of Yannakakis on the Vertex Packing polytope of perfect graphs, we study the Clique-Stable Set Separation in a non-hereditary subclass of perfect graphs. A cut (B,W) of G (a bipartition of V(G)) separates a clique K and a stable set S if $K\subseteq B$ and $S\subseteq W$. A Clique-Stable Set Separator is a family of cuts such that for every clique K, and for every stable set S disjoint from K, there exists a cut in the family that separates K and S. Given a class of graphs, the question is to know whether every graph of the class admits a Clique-Stable Set Separator containing only polynomially many cuts. It is open for the class of all graphs, and also for perfect graphs, which was Yannakakis' original question. Here we investigate on perfect graphs with no balanced skew-partition; the balanced skew-partition was introduced in the proof of the Strong Perfect Graph Theorem. Recently, Chudnovsky, Trotignon, Trunck and Vuskovic proved that forbidding this unfriendly decomposition permits to recursively decompose Berge graphs using 2-join and complement 2-join until reaching a basic graph, and they found an efficient combinatorial algorithm to color those graphs. We apply their decomposition result to prove that perfect graphs with no balanced skew-partition admit a quadratic-size Clique-Stable Set Separator, by taking advantage of the good behavior of 2-join with respect to this property. We then generalize this result and prove that the Strong Erdos-Hajnal property holds in this class, which means that every such graph has a linear-size biclique or complement biclique. This property does not hold for all perfect graphs (Fox 2006), and moreover when the Strong Erdos-Hajnal property holds in a hereditary class of graphs, then both the Erdos-Hajnal property and the polynomial Clique-Stable Set Separation hold.Comment: arXiv admin note: text overlap with arXiv:1308.644

Age Dynamics and Economic Growth: Revisiting the Nexus in a Nonparametric Setting.

This paper explores the relationship between the growth rates of per capita income and age- structured population in a non-parametric setting. Analysis in this framework provides us with new insights about the interaction structure: significant non-linear relation between the two and interesting ’direct’ and ’feedback’ effects on growth. Nonlinearity is found to be a major source of growth fluctuations in OECD and non-OECD countries.Age dynamics, Economic growth, Non-parametric panel.

A consistent nonparametric estimation of spatial autocovariances

We examine some aspects of estimating sample autocovariances for spatial processes. Especially, we note that for such processes, it is not possible to approximate the expectation by the sample mean, like in the case of time series data. Then, we propose a consistent nonparametric estimation of sample autocovariances for an irregularly scattered spatial process, derived from a transformation of the initial process. We also suggest an L_2-consistent weighting matrix. Monte Carlo simulations are used to evaluate the performance of the proposed estimators in finite samples.

Economic Growth and CO2 Emissions: a Nonparametric Approach

This paper examines the empirical interplay between economic growth and greenhouse gas emissions using panel data.Relying on nonparametric methods, we find evidence supporting specifications which assume the constancy of the relationship between per capita CO2 emissions and per capita GDP during the period of the study. Moreover, the usually adopted polynomial functional form is rejected against our nonparametric modelling. It is shown that the relationship between gas emissions and GDP displays more complex patterns, despite its monotonous shape, than the well-known Kuznets curve obtained from ad hoc parametric specifications. The economic development process has a negative effect on gas emissions, especially for the early and the advanced stages of development. As a result, developed countries as well as developing countries should make efforts to reduce CO2 emissions.CO2 emissions; Economic development; Environmental Kuznets curve; Nonparametric estimation; Panel data

Multigraphs without large bonds are wqo by contraction

We show that the class of multigraphs with at most $p$ connected components and bonds of size at most $k$ is well-quasi-ordered by edge contraction for all positive integers $p,k$. (A bond is a minimal non-empty edge cut.) We also characterize canonical antichains for this relation and show that they are fundamental

An observer-based referential that is consistent with cosmological observations

In a universe of arbitrary spacetime geometry, we introduce a referential centered at the observer that constitutes a consistent representation of its environment and in which he performs measurements. We postulate some natural rules applying in this representation referential, that match our everyday experience of the physical world. We show that these assumptions turn out to be consistent with cosmological observations, provided we consider a particularly simple cosmological solution of the equations of general relativity: the static de Sitter space