In order to prove the Strong Perfect Graph Conjecture, the existence of a ”simple” property P holding for any minimal non-quasi-parity Berge graph G would really reduce the difficulty of the problem. We prove here that this property cannot be of type ”G is F-free”, where F is any fixed family of Berge graphs.

Our proof (with Robertson and Thomas) of the strong perfect graph conjecture ran to 179 pages of dense matter; and the most impenetrable part was the final 55 pages, on what we called “wheel systems”. In this paper we give a replacement for those 55 pages, much easier and shorter, using “even pairs”. This is based on an approach of Maffray and Trotignon.

We introduce M -tensors. This concept extends the concept ofM -matrices. We denote Z-tensors as the tensors with nonpositive off-diagonal entries. We show that M -tensors must be Ztensors and the maximal diagonal entry must be nonnegative. The diagonal elements of a symmetric M -tensor must be nonnegative. A symmetric M -tensor is copositive. Based on the spectral theory of nonnegative tensors,...

We consider discrete time Heath–Jarrow–Morton type interest rate models, where the interest rate curves are driven by a geometric spatial autoregression field. Strong consistency and asymptotic normality of the maximum likelihood estimators of the parameters are proved for stable no-arbitrage models containing a general stochastic discounting factor, where explicit form of the ML estimators is ...

In reliability or medical studies, we may only observe each ongoing renewal process for a certain period of time. When the underlying distribution F is arithmetic, Vardi (Ann. Statist. 10 (1982b), 772-785) developed the RT algorithm for nonparametric estimation. In this paper we extend the study to the nonarithmetic case and show that the choice of an arbitrary constant in the RT algorithm can ...

We consider the question of strong cosmic censorship in spatially compact, spatially locally homogeneous vacuum models. We show in particular that strong cosmic censorship holds in Bianchi IX vacuum space–times with spherical spatial topology.

An important recent finding is that testing improves learning and memory. In this article, the authors describe a demonstration that illustrates this principle and helps students incorporate more testing into their learning. The authors asked students to read one text using a Study–Study strategy and one text using a Study–Test strategy. One week later, the authors tested students’ memory for b...

De Vrijer has presented a proof of the finite developments theorem which, in addition to showing that all developments are finite, gives an effective reduction strategy computing longest developments as well as a simple formula computing their length. We show that by applying a rather simple and intuitive principle of duality to de Vrijer’s approach one arrives at a proof that some developments...

3 Adapting the Covariance Matrix 10 3.1 Estimating the Covariance Matrix From Scratch . . . . . . . . . . . . . . . . 10 3.2 Rank-μ-Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Rank-One-Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.1 A Different Viewpoint . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.2 Cumulation: Uti...