Products of Farey graphs are totally geodesic in the pants graph

We show that for a surface S, the subgraph of the pants graph determined by fixing a collection of curves that cut S into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made by Aramayona, Parlier, and Shackleton and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex n-flat if and only if it contains an n-quasi-flat.Comment: v2: 25 pages, 16 figures. Completely rewritten, several figures added for clarit

Revolution and redistribution in Iran: poverty and inequality 25 years later

Despite nearly three decades of revolutionary government rule in Iran poverty and inequality remain the central issues of political debate in Iran. Public dissatisfaction, as demonstrated by the electoral success of the populist candidate in the 2005 presidential election, has been widely attributed to rising poverty and inequity. In this paper I use household survey data to describe the trends in poverty and inequality for the last three decades. The evidence shows that poverty, having substantially declined in recent years, is quite low by international standards and in comparison to pre-revolution years. Inequality improved significantly immediately after the Revolution but has remained relatively stable during the last 15 years. Significantly, poverty sharply declined and inequality decreased somewhat in the five years leading up to the election. Increased welfare of the poor over the period is also evident in access to basic services, such as electricity and safe water, as well as in ownership of household appliances. The wide gap between the evidence presented here, which shows improvement in the welfare of the poor, and popular sentiments in Iran, which indicate worsening poverty and inequality, raises important questions about the political economy of redistribution in Iran. I suggest that in the context of a distributive economy such as Iran's, in which wealth accumulation is seen to depend more on political access than individual productivity, more subjective feelings of envy and fairness may matter more than objective indicators of poverty and inequality.Iran, Poverty, Inequality, Redistribution

Polarization singularities in the clear sky

Ideas from singularity theory provide a simple account of the pattern of polarization directions in daylight. The singularities (two near the Sun and two near the anti-Sun) are points in the sky where the polarization line pattern has index +1/2 and the intensity of polarization is zero. The singularities are caused by multiple scattering that splits into two each of the unstable index +1 singularities at the Sun and anti-Sun, which occur in the single-dipole scattering (Rayleigh) theory. The polarization lines are contours of an elliptic integral. For the intensity of polarization (unnormalized degree), it is necessary to incorporate the strong depolarizing effect of multiple scattering near the horizon. Singularity theory is compared with new digital images of sky polarization, and gives an excellent description of the pattern of polarization directions. For the intensity of polarization, the theory can reproduce not only the zeros but also subtle variations in the polarization maxima

Decentralization and political institutions

Does fiscal decentralization lead to more efficient governance, better public goods, and higher economic growth? This paper tests hypotheses posed by theoretical literature that the results of decentralization depend on features of political institutions. Using data from up to 95 countries for 25 years, we show that the effect of decentralization on economic growth, quality of government, and public goods provision strongly depends on two aspects of political centralization: 1) strength of national party system (measured by the age of the main parties and fractionalization of the government parties) and 2) subordination (whether local and state executives are appointed or elected). We find solid support for Riker’s theory (1964) in developing countries: Strong parties significantly improve the results of fiscal decentralization in terms of economic growth, quality of government, and public goods provision. There is also some evidence that subordination of local to higher-level governments improves the effect of decentralization on growth and public goods provision (in developed and developing countries) and government quality (in developing countries)

Large-scale Multi-label Learning with Missing Labels

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of labels, and (b) the ability to handle data with missing labels. In this paper, we directly address both these problems by studying the multi-label problem in a generic empirical risk minimization (ERM) framework. Our framework, despite being simple, is surprisingly able to encompass several recent label-compression based methods which can be derived as special cases of our method. To optimize the ERM problem, we develop techniques that exploit the structure of specific loss functions - such as the squared loss function - to offer efficient algorithms. We further show that our learning framework admits formal excess risk bounds even in the presence of missing labels. Our risk bounds are tight and demonstrate better generalization performance for low-rank promoting trace-norm regularization when compared to (rank insensitive) Frobenius norm regularization. Finally, we present extensive empirical results on a variety of benchmark datasets and show that our methods perform significantly better than existing label compression based methods and can scale up to very large datasets such as the Wikipedia dataset

Designing with Users

1.1 The past 2-3 years has seen a resurgence of interest in the creation of pedestrian priority places. This interest has largely been stimulated by the advent of "traffic calming". There are two important differences however, compared to previous phases of interest in "pedestrian issues". Firstly, the emphasis is shifting beyond the town centre to residential and district centres. Secondly the interest is stimulated as much by `green issues' as by `pedestrian issues', meaning that people's interests are much broader than merely improving conditions for pedestrians. This new concern has led to fresh attention being focused on the design of pedestrian places and design processes. This attention is not only relevant to pedestrian places. All around us are transport systems, facilities and structures which at some point have been "designed". All too often these extensively researched projects still create dissatisfaction amongst the people who use them. The reasons for this dissatisfaction are numerous and need to be understood in order to provide better work and design in the future. In this paper we discuss how we might set about designing such places in order to produce satisfaction to these people who have to use them. We argue that the appropriate method should be a user-centred design. We define what this means and compare it with more conventional perspectives/approaches to design. For simplicity we have shown in Figure 1 the essence of the user-centred approach to design. 1.2 The term `design' is used to mean the exercise of a process to bring together all the requirements of the space and an endeavour to satisfy these requirements. Design as here used deals with the issues of function, cost, timing and effectiveness in use. The intangible functions of safety, comfort, attractiveness, visual appearance, respect for location are included, not just the usual interpretation of "Design" by non-designers, who think of it solely as the aesthetic aspects. Design is interpreted to mean an understanding of a continuing process - not just the first design of the project. But most importantly, here, design means design in terms of satisfaction of the user, not just satisfaction of the designer! The term `user' refers to those people who will have to live, work, shop, visit, walk around, drive through or look at the final project

Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

Higher ramification and varieties of secant divisors on the generic curve

For a smooth projective curve, the cycles of e-secant k-planes are among the most studied objects in classical enumerative geometry and there are well-known formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite various attempts, surprisingly little is known about the enumerative validity of such formulas. The aim of this paper is to completely clarify this problem in the case of the generic curve C of given genus. Using degeneration techniques and a few facts about the birational geometry of moduli spaces of stable pointed curves we determine precisely under which conditions the cycle of e-secant k-planes in non-empty and we compute its dimension. We also precisely determine the dimension of the variety of linear series on C carrying e-secant k-planes. In a different direction, in the last part of the paper we study the distribution of ramification points of the powers of a line bundle on C having prescribed ramification at a given point.Comment: 25 pages. Numerous changes suggested by the referee, several proofs explained in more detail. To appear in the Journal of the London Mathematical Societ