Estimation of subgraph density in noisy networks

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version of some underlying network as data. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. Accordingly, we develop method-of-moment estimators of network subgraph densities and error rates for the case where a minimal number of network replicates are available. These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates based on the asymptotic normality. To construct the confidence intervals, a new and non-standard bootstrap method is proposed to compute asymptotic variances, which is infeasible otherwise. We illustrate the proposed methods in the context of gene coexpression networks

Papers prepared for the Colloquium "Working for Europe: Perspectives on the EU 50 Years after the Treaties of Rome"

The Chamber of Representatives of the Belgian Parliament asked the permanent professors of the College of Europe to write brief papers for a conference organized in honour of the 50th anniversary of the Treaty of Rome. The objective of these papers was to highlight the main challenges facing the European Union in four different issue areas (Lisbon Strategy, enlargement, Neighbourhood Policy and institutional reform) and to generate a debate among Belgian academics, politicians and members of civil society. The papers produced used to promote this discussion are reprinted here

The Zika outbreak of the 21st century.

The Zika virus outbreak has captivated the attention of the global audience and information has spread rapidly and wildly through the internet and other media channels. This virus was first identified in 1947, when it was isolated from a sentinel rhesus monkey placed by British scientists working at the Yellow Fever Research Laboratory located in the Zika forest area of Uganda, hence its name, and is transmitted primarily by the mosquito vector, Aedes aegypti. The fact that the rhesus macaque is an Asian species being placed in an African forest brings to mind the possibility of rapid adaptation of the virus from an African to Asian species, an issue that has not been considered. Whether such adaptation has played any role in acquiring pathogenicity due to cross species transmission remains to be identified. The first human infection was described in Nigeria in 1954, with only scattered reports of about a dozen human infections identified over a 50-year period. It was not until 2007 that Zika virus raised its ugly head with infections noted in three-quarters of the population on the tiny island of Yap located between the Philippines and Papua New Guinea in the western Pacific Ocean, followed by a major outbreak in French Polynesia in 2013. The virus remained confined to a narrow equatorial band in Africa and Asia until 2014 when it began to spread eastward, first toward Oceania and then to South America. Since then, millions of infected individuals have been identified in Brazil, Colombia, Venezuela, including 25 additional countries in the Americas. While the symptoms associated with Zika virus infection are generally mild, consisting of fever, maculopapular rash, arthralgia and conjunctivitis, there have been reports of more severe reactions that are associated with neurological complications. In pregnant women, fetal neurological complications include brain damage and microcephaly, while in adults there have been several cases of virus-associated Guillain-Barre syndrome. The virus was until recently believed to only be transmitted via mosquitoes. But when the Zika virus was isolated from the semen specimens from a patient in Texas, this provided the basis for the recent report of possible sexual transmission of the Zika virus. Due to the neurological complications, various vectors for infection as well as the rapid spread throughout the globe, it has prompted the World Health Organization to issue a global health emergency. Various governmental organizations have recommended that pregnant women do not travel to countries where the virus is epidemic, and within the countries affected by the virus, recommendations were provided for women of childbearing age to delay pregnancy. The overall public health impact of these above findings highlights the need for a rapid but specific diagnostic test for blood banks worldwide to identify those infected and for the counseling of women who are pregnant or contemplating pregnancy. As of this date, there are neither commercially licensed diagnostic tests nor a vaccine. Because cross-reactivity of the Zika virus with dengue and Chikungunya virus is common, it may pose difficulty in being able to quickly develop such tests and vaccines. So far the most effective public health measures include controlling the mosquito populations via insecticides and preventing humans from direct exposure to mosquitoes

Coupling of Nonlocal Potentials to Electromagnetic Fields

Nonlocal Hamiltonians are used widely in first-principles quantum calculations; the nonlocality stems from eliminating undesired degrees of freedom, e.g. core electrons. To date, attempts to couple nonlocal systems to external electromagnetic (EM) fields have been heuristic or limited to weak or long wavelength fields. Using Feynman path integrals, we derive an exact, closed-form coupling of arbitrary EM fields to nonlocal systems. Our results justify and clarify the couplings used to date and are essential for systematic computation of linear and especially nonlinear response.Comment: 1 figure, 1 tabl

A Sierpinski Mandelbrot spiral for rational maps of the form Zᴺ + λ / Zᴰ

We identify three structures that lie in the parameter plane of the rational map F(z) = zⁿ + λ / zᵈ, for which z is a complex number, λ a complex parameter, n ≥ 4 is even, and d ≥ 3 is odd. There exists a Sierpindelbrot arc, an infinite sequence of pairs of Mandelbrot sets and Sierpinski holes, that limits to the parameter at the end of the arc. There exists as well a qualitatively different Sierpindelbrot arc, an infinite sequence of pairs of Mandelbrot sets and Sierpinski holes, that limits to the parameter at the center of the arc. Furthermore, there exist infinitely many arcs of each type. A parameter can travel along a continuous path from the Cantor set locus, along infinitely many arcs of the first type in a successively smaller region of the parameter plane, while passing through an arc of the second type, to the parameter at the center of the latter arc. This infinite sequence of Sierpindelbrot arcs is a Sierpinski Mandelbrot spiral