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

Climate tolerances and trait choices shape continental patterns of urban tree biodiversity

Aim: We propose and test a climate tolerance and trait choice hypothesis of urban macroecological variation in which strong filtering associated with low winter temperatures restricts urban biodiversity while weak filtering associated with warmer temperatures and irrigation allows dispersal of species from a global source pool, thereby increasing urban biodiversity. Location: Twenty cities across the USA and Canada. Methods: We examined variation in tree community taxonomic diversity, origins and production of an aesthetic ecosystem service trait in a cross-section of urban field surveys. We correlated urban tree community composition indicators with a key climate restriction, namely mean minimum winter temperature, and evaluated alternative possible drivers: precipitation, summer maximum temperature, population size and the percentage of adults with a college education. Results: Species accumulation curves differed substantially among cities, with observed richness varying from 22 to 122 species. Similarities in tree communities decreased exponentially with increases in climatic differences. Ordination of tree communities showed strong separation among cities with component axes correlated with minimum winter temperature and annual precipitation. Variation among urban tree communities in richness, origins and the provisioning of an aesthetic ecosystem service were all correlated with minimum winter temperature. Main conclusions: The urban climate tolerance and trait choice hypothesis provides a coherent mechanism to explain the large variation among urban tree communities resulting from an interacting environment, species and human decisions. Reconciling the feedbacks between human decision making and biophysical limitations provides a foundation for an urban ecological theory that can better understand and predict the dynamics of other linked biotic communities, associated ecosystem dynamics and resulting services provided to urban residents

Compact convex sets with prescribed facial dimensions

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the faces of general closed convex sets. We show that for any finite sequence of positive integers there exist compact convex sets which only have extreme points and faces with dimensions from this prescribed sequence. We also discuss another approach to dimensionality, considering the dimension of the union of all faces of the same dimension. We show that the questions arising from this approach are highly nontrivial and give examples of convex sets for which the sets of extreme points have fractal dimension

Compact convex sets with prescribed facial dimensions

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the faces of general closed convex sets. We show that for any finite sequence of positive integers there exist compact convex sets which only have extreme points and faces with dimensions from this prescribed sequence. We also discuss another approach to dimensionality, considering the dimension of the union of all faces of the same dimension. We show that the questions arising from this approach are highly nontrivial and give examples of convex sets for which the sets of extreme points have fractal dimension

Successful surgical intervention in a case of spontaneous chylothorax in an infant unresponsive to conservative therapy

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Monitoring Space Weather: Using Automated, Accurate Neural Network Based Whistler Segmentation for Whistler Inversion

It is challenging, yet important, to measure the - ever-changing - cold electron density in the plasmasphere. The cold electron density inside and outside of the plasmapause is a key parameter for radiation belt dynamics. One indirect measurement is through finding the velocity dispersion relation exhibited by lightning induced whistlers. The main difficulty of the method comes from low signal-to-noise ratios for most of the ground-based whistler components. To provide accurate electron density and L-shell measurements, whistler components need to be detectable in the noisy background, and their characteristics need to be reliably determined. For this reason precise segmentation is needed on a spectrogram image. Here we present a fully automated way to perform such an image segmentation by leveraging the power of convolutional neural networks, a state-of-the-art method for computer vision tasks. Testing the proposed method against a manually, and semi-manually segmented whistler dataset achieved <10% relative electron density prediction error for 80% of the segmented whistler traces, while for the L-shell, the relative error is <5% for 90% of the cases. By segmenting more than 1 million additional real whistler traces from Rothera station Antarctica, logged over 9 years, seasonal changes in the average electron density were found. The variations match previously published findings, and confirm the capabilities of the image segmentation technique

A novel forest state assessment methodology to support conservation and forest management planning

A new forest state assessment methodology to complement existing conservation and forestry data has been developed. The aim is to provide tools for strategic planning including spatial distribution of conservation priorities. The method is point-based using a dense systematic sampling grid and provides more detailed information than vegetation maps or forest subcompartment descriptions, but requires less effort than forest inventories. Indicators include canopy composition and structure, deadwood, herbs, microhabitats, disturbances, shrubs and regeneration. The results can inform managers about the structural and compositional diversity of forest stands in the form of thematic maps and can provide the basis for analysis of habitat suitability for forest-dwelling organisms. A smartphone application has been developed to enable electronic data collection. PostGIS and Python scripts were used in the data flow. In this paper, we outline the development of the assessment protocol, and present the sampling design and the variables recorded. The main advantages of the survey methodology are also shown by case-studies based on data collected during the first field season in 2014. The protocol has been designed for low mountain forests in Hungary, but it can be modified to fit other forest types