Asymptotic bounds on the combinatorial diameter of random polytopes

The combinatorial diameter $\operatorname{diam}(P)$ of a polytope $P$ is the maximum shortest path distance between any pair of vertices. In this paper, we provide upper and lower bounds on the combinatorial diameter of a random "spherical" polytope, which is tight to within one factor of dimension when the number of inequalities is large compared to the dimension. More precisely, for an $n$-dimensional polytope $P$ defined by the intersection of $m$ i.i.d.\ half-spaces whose normals are chosen uniformly from the sphere, we show that $\operatorname{diam}(P)$ is $\Omega(n m^{\frac{1}{n-1}})$ and $O(n^2 m^{\frac{1}{n-1}} + n^5 4^n)$ with high probability when $m \geq 2^{\Omega(n)}$. For the upper bound, we first prove that the number of vertices in any fixed two dimensional projection sharply concentrates around its expectation when $m$ is large, where we rely on the $\Theta(n^2 m^{\frac{1}{n-1}})$ bound on the expectation due to Borgwardt [Math. Oper. Res., 1999]. To obtain the diameter upper bound, we stitch these ``shadows paths'' together over a suitable net using worst-case diameter bounds to connect vertices to the nearest shadow. For the lower bound, we first reduce to lower bounding the diameter of the dual polytope $P^\circ$, corresponding to a random convex hull, by showing the relation $\operatorname{diam}(P) \geq (n-1)(\operatorname{diam}(P^\circ)-2)$. We then prove that the shortest path between any ``nearly'' antipodal pair vertices of $P^\circ$ has length $\Omega(m^{\frac{1}{n-1}})$

Using Capabilities to Project Growth, 2010-30

We forecast average annual GDP growth for 147 countries for 2010-30. We use a cross-country regression model where the long-run fundamentals are determined by countries' accumulated capabilities and the capacity to undergo structural transformation

Development Imperatives for the Asian Century

Evidence-based economic policies - pragmatic policies that work - played a major role in Asia's success in raising its living standards in the last half century. However, growth prospects are now threatened by rising income inequality and environmental degradation if Asia continues on its established growth path. Evidence strongly argues for Asia to broaden its development priorities into a triple bottom line: that is, a focus on growth, social inclusion, and environmental sustainability. The paper focuses on how Asia can manage this ambitious goal. Possible resistance from vested interests is to be anticipated, but pursuing this path could bring large overall gains. The paper looks at how Asian governments and their development partners can make a difference in promoting the three policy objectives. Innovations in governance for better accountability, transparency, and feedback will be necessary for achieving these priorities. Societies in Asia and the international community will also need rigorous evidence and analysis to establish the benefits of this strategy and to make informed policy choices. International financial institutions and the donor community can provide financial lubricants for cooperation, as well as knowledge to help governments counter vested interests and champion regional perspectives on transborder issues. Reversing the negative social and environmental trends has to become a real development priority rather than a mere aspiration. Progress is possible on the three bottom-line goals, but it will require focusing Asia's vaunted methods of learning and innovation to meet the new challenges

Towards EU-MENA Shared Prosperity

With a strong conviction that fruitful policy dialogue should be primarily anchored in sound policy research, Bruegel and PCNS researchers have tackled issues of utmost importance to all shores of the Mediterranean basin through their papers. In the first paper, Uri Dadush and Yana Myachenkova explain how trade agreements that the European Union has with North African countries are often seen as having delivered disappointing results, and how the agreements have been judged too harshly, as they helped generate large amounts of trade. In this regard, the paper gives relevant recommendations of policies for a greater trade performance. The second paper highlights the role of structural economic transformation as a necessary gateway for nations wishing to move up along the development path. It focuses on the case of Morocco, shedding light on its manufacturing sector\u2019s transformation, its integration in Global Value Chains (GVC) and its economic challenges. In \u201cThe EU-Southern Mediterranean Energy Relationship: A Fresh Perspective\u201d, Simone Tagliapietra analyses how regional energy cooperation should strongly focus on fostering large-scale deployment of renewable energy, allowing southern Mediterranean countries to meet their increasing energy demand in a more sustainable way, and having positive economic and political benefits for Europe