Bad semidefinite programs: they all look the same

Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\em badly behaved} if the value of $\sup { | A x <= b }$ is finite but the dual program has no solution with the same value for {\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidefinite systems in the literature; we characterize such systems by certain {\em excluded matrices}, which are easy to spot in all published examples. We show how to transform semidefinite systems into a canonical form, which allows us to easily verify whether they are badly behaved. We prove several other structural results about badly behaved semidefinite systems; for example, we show that they are in $NP \cap co-NP$ in the real number model of computing. As a byproduct, we prove that all linear maps that act on symmetric matrices can be brought into a canonical form; this canonical form allows us to easily check whether the image of the semidefinite cone under the given linear map is closed.Comment: For some reason, the intended changes between versions 4 and 5 did not take effect, so versions 4 and 5 are the same. So version 6 is the final version. The only difference between version 4 and version 6 is that 2 typos were fixed: in the last displayed formula on page 6, "7" was replaced by "1"; and in the 4th displayed formula on page 12 "A_1 - A_2 - A_3" was replaced by "A_3 - A_2 - A_1

Visualizing the Structure of Large Trees

This study introduces a new method of visualizing complex tree structured objects. The usefulness of this method is illustrated in the context of detecting unexpected features in a data set of very large trees. The major contribution is a novel two-dimensional graphical representation of each tree, with a covariate coded by color. The motivating data set contains three dimensional representations of brain artery systems of 105 subjects. Due to inaccuracies inherent in the medical imaging techniques, issues with the reconstruction algo- rithms and inconsistencies introduced by manual adjustment, various discrepancies are present in the data. The proposed representation enables quick visual detection of the most common discrepancies. For our driving example, this tool led to the modification of 10% of the artery trees and deletion of 6.7%. The benefits of our cleaning method are demonstrated through a statistical hypothesis test on the effects of aging on vessel structure. The data cleaning resulted in improved significance levels.Comment: 17 pages, 8 figure

Modeling Past and Present in the Eastern Highlands of Papua New Guinea

The existence of “fringe societies” in Papua New Guinea has long been recognized by anthropologists. In the New Guinea Highlands, the term refers to peoples who occupy the fringes of more populous and better-known valleys. In many instances, these groups also subsist on staples other than Ipomoea batatas, more commonly known as sweet potato, a tuber introduced to the highlands within the last 300 years. The Awa at the far eastern edge of the Eastern Highlands are such a group, and the word fringe has often been used to describe them. Surprisingly, anthropologists and archaeologists have not seized on the possibility that their unusual subsistence represents a survival of a previous adaptation that has not completed its conversion to the new crop. The authors of this paper use the Awa economy to model a pre-ipomoean past for members of the Tairora language subfamily, namely, the South Tairora, Auyana, and Awa languages. Using archaeological, paleoenvironmental, demographic, and ethnohistorical data from our study area; data for Awa from ethnographer David Boyd’s research; and other sources and simulation modeling, we explore long-standing questions about the dispersal of early horticultural peoples, its determinants, the differentiation of languages, possible time frames for their migrations, and impacts on the resulting landscapes

MODELING PAST AND PRESENT IN THE EASTERN HIGHLANDS OF PAPUA NEW GUINEA: SUPPLEMENTAL MATERIAL

Supplement 1: Contact history in the project areaSupplement 2: Archaeological sequences in the study areaSupplement 3: Methodolog

Evaluating the effects of turf-replacement programs in Los Angeles

Water utilities incentivize turf replacement to promote water conservation, but the effects of such programs have received limited evaluations. In 2014, the Metropolitan Water District of Southern California (MWD) undertook an unprecedented investment to incentive turf replacement throughout Southern California in response to a serious Statewide drought. MWD devoted $350 million to the program, resulting in more than 46,000 rebate payments (25,000 in Los Angeles County) to remove 15.3 million square meters of turf. The program implementation provided a unique opportunity to address research gaps on turf replacement implementation. We analyzed socioeconomic and spatial trends of program participants and assessed landscape changes from turf replacement using a random sample of properties (4% of LA County participants in 2014–16). Specifically, we used a novel and cost-effective approach Google Earth Street View to characterize landscapes in front yards and created a typology of land cover types. Results showed: post-replacement landscapes had a diversity of land cover types – diverse yards with several land cover types, as well as more homogenous yards with a single land cover such as woodchips, bare soil, gravel, and artificial turf. Analysis also indicated some evidence of “neighborhood adoption” effects. We describe the need for longitudinal studies to understand long-term effects of turf replacement and associated water use, and suggest that water utilities should also evaluate results in backyards, which requires site visits. This study provides a novel contribution that can be replicated over space and time to further knowledge of turf replacement program implementations and evaluation

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

The Benefits and Limits of Urban Tree Planting for Environmental and Human Health

Many of the world's major cities have implemented tree planting programs based on assumed environmental and social benefits of urban forests. Recent studies have increasingly tested these assumptions and provide empirical evidence for the contributions of tree planting programs, as well as their feasibility and limits, for solving or mitigating urban environmental and social issues. We propose that current evidence supports local cooling, stormwater absorption, and health benefits of urban trees for local residents. However, the potential for urban trees to appreciably mitigate greenhouse gas emissions and air pollution over a wide array of sites and environmental conditions is limited. Consequently, urban trees appear to be more promising for climate and pollution adaptation strategies than mitigation strategies. In large part, this is due to space constraints limiting the extent of urban tree canopies relative to the current magnitude of emissions. The most promising environmental and health impacts of urban trees are those that can be realized with well-stewarded tree planting and localized design interventions at site to municipal scales. Tree planting at these scales has documented benefits on local climate and health, which can be maximized through targeted site design followed by monitoring, adaptive management, and studies of long-term eco-evolutionary dynamics.Peer reviewe