Convex Combinatorial Optimization

We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.Comment: 26 pages including 12 figures. Accepted for publication in Ap

A theory on power in networks

The eigenvector centrality equation $\lambda x = A \, x$ is a successful compromise between simplicity and expressivity. It claims that central actors are those connected with central others. For at least 70 years, this equation has been explored in disparate contexts, including econometrics, sociometry, bibliometrics, Web information retrieval, and network science. We propose an equally elegant counterpart: the power equation $x = A x^{\div}$, where $x^{\div}$ is the vector whose entries are the reciprocal of those of $x$. It asserts that power is in the hands of those connected with powerless others. It is meaningful, for instance, in bargaining situations, where it is advantageous to be connected to those who have few options. We tell the parallel, mostly unexplored story of this intriguing equation

Bounded gaps between primes in number fields and function fields

The Hardy--Littlewood prime $k$-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress toward this problem. In this work, we extend the Maynard-Tao method to both number fields and the function field $\mathbb{F}_q(t)$

The Integration of Western Hemisphere Grain Markets in the Eighteenth Century: Early Progress and Decline of Globalization

In this work it is shown evidence supporting the idea that, if globalization is defined as the convergence of commodity prices between distant markets, the process started and advanced gradually in the eighteenth century instead of suddenly appearing after 1820, as claimed by the canonical version developed in a series of important works by O’Rourke and Williamson (1999, 2002, 2004). We use long time-series of grain prices for several markets in Western Europe and the Americas to explore the extent and dynamics of market integration across the Western Hemisphere throughout the eighteenth century. An innovative methodology, consisting in studying the standard deviations of the innovations in the ARMA model of pairwise relative prices between markets, is used. A general decrease in price dispersion is observed when the early eighteenth century is compared with the three decades preceding 1793. Neither Argentina nor Mexico participated in this general trend towards closer market integration across the Western Hemisphere. From 1793 to 1828 we observe a substantial increase in dispersion between markets. After this first backlash, globalization resumed at an unprecedented pace since it was favored by the transport revolution and other factors.En este trabajo se muestra que, si se acepta la definición de globalización como convergencia de los precios de mercancías de amplio consumo entre mercados distantes entre sí, el proceso comenzó y avanzó gradualmente in el siglo XVIII en vez de “explotar” después de 1820, como sostiene la versión canónica desarrollada en una serie de importantes trabajos de O’Rourke y Williamson (1999, 2002 y 2004). Usamos series históricas largas de precios de granos en varios mercados de Europa Occidental y América para determinar el alcance y la dinámica de la integración de mercados en el Hemisferio Occidental durante el siglo XVIII. Nuestra metodología es original, pues consiste en estudiar las desviaciones standard de las innovaciones en los modelos ARMA de las series de precios relativos entre pares de mercados. Un descenso general de la dispersión de precios se observa al comparar los inicios del siglo XVIII con las tres décadas que preceden a 1793. Ni Argentina ni México participan en esta tendencia general hacia una mayor integración de los mercados del Hemisferio Occidental. Entre 1793 y 1828 observamos un aumento sustancial de la dispersión entre mercados. Tras este primer retroceso, la globalización se relanzó a un ritmo antes desconocido gracias a la revolución de los transportes y otros factores.market integration, globalization, mercados de integración, globalización.