Lines in Euclidean Ramsey theory

Let $\ell_m$ be a sequence of $m$ points on a line with consecutive points of distance one. For every natural number $n$, we prove the existence of a red/blue-coloring of $\mathbb{E}^n$ containing no red copy of $\ell_2$ and no blue copy of $\ell_m$ for any $m \geq 2^{cn}$. This is best possible up to the constant $c$ in the exponent. It also answers a question of Erd\H{o}s, Graham, Montgomery, Rothschild, Spencer and Straus from 1973. They asked if, for every natural number $n$, there is a set $K \subset \mathbb{E}^1$ and a red/blue-coloring of $\mathbb{E}^n$ containing no red copy of $\ell_2$ and no blue copy of $K$.Comment: 7 page

Graph removal lemmas

The graph removal lemma states that any graph on n vertices with o(n^{v(H)}) copies of a fixed graph H may be made H-free by removing o(n^2) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory and computer science. In this survey we discuss these lemmas, focusing in particular on recent improvements to their quantitative aspects.Comment: 35 page

Understanding al-Shabaab : clan, Islam and insurgency in Kenya

Harakat al-Shabaab al-Mujahideen has proven itself to be a highly adaptable organisation. Their most recent evolution has seen them transform from an overt, military and governmental force in southern Somalia to a covert, insurgent and anarchic force in Kenya. This article indicates how al-Shabaab has reinvented itself in Kenya. Both ‘clan’ and ‘Islam’ are often thought of as immutable factors in al-Shabaab's make-up, but here we show that the organisation is pragmatic in its handling of clan relations and of Islamic theology. The movement is now able to exploit the social and economic exclusion of Kenyan Muslim communities in order to draw them into insurgency, recruiting Kenyans to its banner. Recent al-Shabaab attacks in Kenya, launched since June 2014, indicate how potent and dangerous their insurgency has become in the borderlands and coastal districts where Kenya's Islamic population predominates

The Minimal Modal Interpretation of Quantum Theory

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure---which we call subsystem space---that we believe merits further study. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure, updated references, generalized conditional probabilities with attendant changes to the sections on the EPR-Bohm thought experiment and Lorentz invariance; for a concise summary, see the companion letter at arXiv:1405.675

Electronic structure and transport properties of atomic NiO spinvalves

Ab-initio quantum transport calculations show that short NiO chains suspended in Ni nanocontacts present a very strong spin-polarization of the conductance. The generalized gradient approximation we use here predicts a similiar polarization of the conductance as the one previously computed with non-local exchange, confirming the robustness of the result. Their use as nanoscopic spinvalves is proposed.Comment: 2 pages, 1 figure; accepted in JMMM (Proceedings of ICM'06, Kyoto

The Scorecard on Development, 19602016: China and the Global Economic Rebound

This report looks at the rate of progress of economic, health, and social indicators, including per capita GDP, mortality, life expectancy, and education for all countries with available data. It examines the twenty-first century rebound for the majority of low- and middle-income countries after an unusual long-term decline in the rate of progress on most of these indicators in the last two decades of the twentieth century. It discuss the role of China in the twenty-first-century rebound, and the possible role of major policy changes that took place in many low- and middle-income countries, as well as other policy and institutional influences.The report is the latest edition of a series that began in 2001; the last version was published in 2011. The first two editions of the Scorecard (2001 and 2005) documented a then ongoing, historic long-term economic failure that occurred in the 1980s and '90s, before most low- and middle-income countries began to experience an economic rebound