Prizing on Paths: A PTAS for the Highway Problem

In the highway problem, we are given an n-edge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the weight of the associated path, when it does not exceed the budget of the driver, and zero otherwise. The goal is choosing weights so as to maximize the profit. A lot of research has been devoted to this apparently simple problem. The highway problem was shown to be strongly NP-hard only recently [Elbassioni,Raman,Ray-'09]. The best-known approximation is O(\log n/\log\log n) [Gamzu,Segev-'10], which improves on the previous-best O(\log n) approximation [Balcan,Blum-'06]. In this paper we present a PTAS for the highway problem, hence closing the complexity status of the problem. Our result is based on a novel randomized dissection approach, which has some points in common with Arora's quadtree dissection for Euclidean network design [Arora-'98]. The basic idea is enclosing the highway in a bounding path, such that both the size of the bounding path and the position of the highway in it are random variables. Then we consider a recursive O(1)-ary dissection of the bounding path, in subpaths of uniform optimal weight. Since the optimal weights are unknown, we construct the dissection in a bottom-up fashion via dynamic programming, while computing the approximate solution at the same time. Our algorithm can be easily derandomized. We demonstrate the versatility of our technique by presenting PTASs for two variants of the highway problem: the tollbooth problem with a constant number of leaves and the maximum-feasibility subsystem problem on interval matrices. In both cases the previous best approximation factors are polylogarithmic [Gamzu,Segev-'10,Elbassioni,Raman,Ray,Sitters-'09]

Never been industrialized: a tale of African structural change

Africa is a case of structural change without industrialization and without diversification. Agriculture�s decline was matched by an increase in services and non-manufacturing industry, with manufacturing remaining low and stagnant throughout the post-colonial period. To what extent do these patterns of structural change account for the weak growth dynamics observed in the continent? We provide evidence that what is damaging for growth in Africa is not the expansion in services, but rather the reallocation of economic activity from agriculture to non-manufacturing industry. Because non-manufacturing industry is mainly mining, our results point to a form of resource curse.

On volume preserving complex structures on real tori

A basic problem in the classification theory of compact complex manifolds is to give simple characterizations of complex tori. It is well known that a compact K\"ahler manifold $X$ homotopically equivalent to a a complex torus is biholomorphic to a complex torus. The question whether a compact complex manifold $X$ diffeomorphic to a complex torus is biholomorphic to a complex torus has a negative answer due to a construction by Blanchard and Sommese. Their examples have however negative Kodaira dimension, thus it makes sense to ask the question whether a compact complex manifold $X$ with trivial canonical bundle which is homotopically equivalent to a complex torus is biholomorphic to a complex torus. In this paper we show that the answer is positive for complex threefolds satisfying some additional condition, such as the existence of a non constant meromorphic function.Comment: 20 pages, preliminary version of an article to be submitted to a memorial issue of the Journal of Mathematics of Kyoto University, in memory of Professor Nagat

Understanding the Jobs-Affordable Housing Balance in the Richmond Region

The mismatch between location of jobs and housing has a significant impact on the efficiency and quality of life within metropolitan areas. A well-planned region strives to be a “community of short distances.” A wide range of housing choices located close to employment centers could shorten commuting distances and substantially reduce government outlays for transportation facilities, reduce household transportation expenses, and increase feasibility of pedestrian movement. These needs are particularly important to families earning modest wages. CURA, with support from The Community Foundation Serving Richmond and Central Virginia and the Richmond Association of Realtors, has analyzed the spatial pattern of lower-wage jobs and lower-cost housing within the Richmond Metropolitan Statistical Area (MSA). The analysis reveals how low-cost housing and modest-wage jobs in the Richmond region are not well-balanced. Few areas in which modest-wage jobs cluster have comparable levels of low-cost housing. The established suburban areas north, west, and south of Richmond’s urban center have a large number of retail and service jobs that pay modest wages, yet these areas provide few affordable-dwelling units for these wage earners. The second part of this study addressed a major obstacle to the construction of new, affordable-housing units: fears. Many new, affordable dwelling units, by financial necessity, will be built at higher densities and smaller size to reduce cost. Homeowners in nearby neighborhoods often oppose construction of these units over fear of reduced property values, higher crime, and other factors. Six higher-density, 3 lower-cost housing projects were studied for their impact on the nearby middle-income neighborhoods. Documentation of home sale prices, assessment values, and crime rates before and after construction of the more affordable dwelling units did not reveal any notable long-term impact on crime rates, property values, or property sales

On the probabilistic logical modelling of quantum and geometrically-inspired IR

Information Retrieval approaches can mostly be classed into probabilistic, geometric or logic-based. Recently, a new unifying framework for IR has emerged that integrates a probabilistic description within a geometric framework, namely vectors in Hilbert spaces. The geometric model leads naturally to a predicate logic over linear subspaces, also known as quantum logic. In this paper we show the relation between this model and classic concepts such as the Generalised Vector Space Model, highlighting similarities and differences. We also show how some fundamental components of quantum-based IR can be modelled in a descriptive way using a well-established tool, i.e. Probabilistic Datalog

Quieting the Sharholders\u27 Voice: Empirical Evidence of Pervasive Bundling in Proxy Solicitations

The integrity of shareholder voting is critical to the legitimacy of corporate law. One threat to this process is proxy “bundling,” or the joinder of more than one separate item into a single proxy proposal. Bundling deprives shareholders of the right to convey their views on each separate matter being put to a vote and forces them to either reject the entire proposal or approve items they might not otherwise want implemented. In this Paper, we provide the first comprehensive evaluation of the anti-bundling rules adopted by the Securities and Exchange Commission (“SEC”) in 1992. While we find that the courts have carefully developed a framework for the proper scope and application of the rules, the SEC and proxy advisory firms have been less vigilant in defending this instrumental shareholder right. In particular, we note that the most recent SEC interpretive guidance has undercut the effectiveness of the existing rules, and that, surprisingly, proxy advisory firms do not have well-defined heuristics to discourage bundling. Building on the theoretical framework, this Article provides the first large-scale empirical study of bundling of management proposals. We develop four possible definitions of impermissible bundling and, utilizing a data set of over 1,300 management proposals, show that the frequency of bundling in our sample ranges from 6.2 percent to 28.8 percent (depending on which of the four bundling definitions is used). It is apparent that bundling occurs far more frequently than indicated by prior studies. We further examine our data to report the items that are most frequently bundled and to analyze the proxy advisors’ recommendations and the voting patterns associated with bundled proposals. This Article concludes with important implications for the SEC, proxy advisors, and institutional investors as to how each party can more effectively deter impermissible bundling and thus better protect the shareholder franchise

Effective coverage and systems effectiveness for malaria case management in sub-saharan african countries

Scale-up of malaria preventive and control interventions over the last decade resulted in substantial declines in mortality and morbidity from the disease in sub-Saharan Africa and many other parts of the world. Sustaining these gains will depend on the health system performance. Treatment provides individual benefits by curing infection and preventing progression to severe disease as well as community-level benefits by reducing the infectious reservoir and averting emergence and spread of drug resistance. However many patients with malaria do not access care, providers do not comply with treatment guidelines, and hence, patients do not necessarily receive the correct regimen. Even when the correct regimen is administered some patients will not adhere and others will be treated with counterfeit or substandard medication leading to treatment failures and spread of drug resistance. We apply systems effectiveness concepts that explicitly consider implications of health system factors such as treatment seeking, provider compliance, adherence, and quality of medication to estimate treatment outcomes for malaria case management. We compile data for these indicators to derive estimates of effective coverage for 43 high-burden Sub-Saharan African countries. Parameters are populated from the Demographic and Health Surveys and other published sources. We assess the relative importance of these factors on the level of effective coverage and consider variation in these health systems indicators across countries. Our findings suggest that effective coverage for malaria case management ranges from 8% to 72% in the region. Different factors account for health system inefficiencies in different countries. Significant losses in effectiveness of treatment are estimated in all countries. The patterns of inter-country variation suggest that these are system failures that are amenable to change. Identifying the reasons for the poor health system performance and intervening to tac them become key priority areas for malaria control and elimination policies in the region

Virologic Factors Contributing to the Genetic Diversification of Influenza Viruses Circulating in North American Swine

The purpose of this study was to determine mechanisms of reassortment of swine influenza viruses and determine if certain reassortant gene combinations can drive evolution and host adaptation in the context of the triple reassortant internal gene (TRIG) cassette. The TRIG contains a unique combination of a human polymerase basic 1 (PB1) gene with avian polymerase basic 2 (PB2) and polymerase acidic (PA) genes. The remaining internal genes, nucleoprotein (NP), matrix (M), and non-structural (NS) are of swine origin. This differs considerably from classical swine lineage viruses which are drifted variants of the 1918 pandemic with all swine origin genes. We hypothesized that the viruses containing the TRIG cassette reassort more frequently because the polymerase gene constellation is more promiscuous in its ability to replicate with novel HA and NA genes. Better understanding of these mechanisms that control reassortment can be applied to identifying high risk viruses that have an increased ability to reassort and potentially zoonotically transmit to humans. The segmented nature of influenza viruses provides an opportunity for gene segment reassortment in which a virus can exchange segments with another virus. Despite the ability to detect these reassortant viruses, there is little understanding of the mechanisms that control or drive this process. The first two aims addressed a barrier in the influenza field by determining what mechanisms restrict reassortment in particular viral genotypes. This can further be applied to predict the likelihood that other viruses may reassort or be restricted from reassorting. Based on epidemiologic data not all viruses have the same ability to reassort, thus giving some viruses particular advantages over others. However, our studies indicated that there are no virologic specific functions that restrict reassortment, but there are trends demonstrating that the TRIG cassette is more promiscuous than the classical swine viruses. Thus the propensity of the TRIG viruses to reassert, as seen in the field, was likely the result of a change in pig farming rather than one particular viral function. We next assessed the viral fitness of human HA and NA reassortants on both of the swine virus backbones. There were no observable differences with the human H3 and N2 on either of the swine backbones when compared to the parental swine backbones. However, we did see some viral fitness attenuation when the polymerase complex genes were reassorted between the TRIG and classical swine viruses, suggesting that viral growth efficiency is altered if the polymerase genes and presumable their interactions are changed. Influenza gene reassortment plays a major role in the evolution of new viruses, however, it may also drive these reassortant viruses to evolve more quickly and adapt to a new host. The final aim of the study is evaluated the role reassortment plays in driving host adaption and influenza evolution. This aim is designed to test a hypothesis derived from natural observations in which avian-like Eurasian swine virus HAs phylogenetically cluster with increased nucleotide changes in viruses containing the TRIG NS. We hypothesized that the TRIG and TRIG NS increase the number of nucleotide mutations in the HA gene resulting in increased viral diversity leading to more rapid host adaptation as observed by viral fitness in vitro. We found that this evolutionary burst was observed when the TRIG NS is rescued on the classical swine virus backbone; however it was not seen in a wholly TRIG virus. It is likely the introduction of a different gene segment that destabilizes the viral genome leading to the observed evolutionary burst rather than the inherent properties of the TRIG NS. However, this does raise the concern that reassortment can lead to more rapid host adaption through genetic diversity which could lead to novel subtypes entering pigs or humans. Of significant concern is that humans are immunologically naïve to most influenza subtypes. These revelations could help direct the influenza research community to focus on these particular rapidly evolving viruses that pose the most significant threat to public and agricultural health