Coordinate shadows of semi-definite and Euclidean distance matrices

We consider the projected semi-definite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semi-definite and Euclidean distance completion problems. We classify when these sets are closed, and use the boundary structure of these two sets to elucidate the Krislock-Wolkowicz facial reduction algorithm. In particular, we show that under a chordality assumption, the "minimal cones" of these problems admit combinatorial characterizations. As a byproduct, we record a striking relationship between the complexity of the general facial reduction algorithm (singularity degree) and facial exposedness of conic images under a linear mapping.Comment: 21 page

Ecohydrology in a Colorado River riparian forest: implications for the decline of Populus fremontii

Journal ArticlePopulus fremontii (Fremont cottonwood) was once a dominant species in desert riparian forests but has been increasingly replaced by the exotic invasive Tamarix ramosissima (saltcedar). Interspecific competition, reduced flooding frequency, and increased salinity have been implicated in the widespread decline of P. fremontii. To elucidate some of the multiple and interacting mechanisms of this decline, we examined ecological processes in a control stand of P. fremontii along the Colorado River in Utah, USA, as well as a disturbed stand characterized by high groundwater salinity and invasion of T. ramosissima. Sap flux data showed that P. fremontii at the saline site experienced large reductions in afternoon canopy stomatal conductance relative to the control. Thus, average daily stand transpiration was 4.8 6 0.1 mm/d at the saline site in comparison to 9.3 6 0.2 mm/d at the control site over a two-month period. Light-saturated photosynthesis and apparent quantum yield were also reduced in saline P. fremontii. Stable isotope analysis indicated that trees at the saline site utilized evaporatively enriched groundwater that was likely derived from a nearby pond of irrigation runoff; this was also the probable source of high salinity. Interspecific competition for water at the saline site is unlikely, as T. ramosissima is still a minor species that is present only in the understory. However, reduced tissue N content in P. fremontii at the saline site suggested that physiological stress during salinity and halophyte invasion may be exacerbated by altered N relations

Effect of Cutting Date on Quality of Red Clover Forage

Development stage or plant age is an important factor determining the chemical composition and quality of red clover forage (Ignjatovic et al., 2001). In early spring, young red clover plants have large leaf mass, high contents of moisture, protein and minerals and a low fibre content. In the course of the growing season, under the effects of long days and high temperatures, the plant undergoes morphological changes: leaves grow more slowly, the stem elongates, dry matter yield increases and quality drops, especially digestibility and the contents of protein and minerals

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

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

Triplet-blockaded Josephson supercurrent in double quantum dots

Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this Rapid Communication, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demonstrate a direct spin to supercurrent conversion, the superconducting equivalent of the Pauli spin blockade. This effect can be exploited in hybrid quantum architectures coupling the quantum states of spin systems and superconducting circuits

Protecting climate with forests

Policies for climate mitigation on land rarely acknowledge biophysical factors, such as reflectivity, evaporation, and surface roughness. Yet such factors can alter temperatures much more than carbon sequestration does, and often in a conflicting way. We outline a framework for examining biophysical factors in mitigation policies and provide some best-practice recommendations based on that framework. Tropical projects-avoided deforestation, forest restoration, and afforestation-provide the greatest climate value, because carbon storage and biophysics align to cool the Earth. In contrast, the climate benefits of carbon storage are often counteracted in boreal and other snow-covered regions, where darker trees trap more heat than snow does. Managers can increase the climate benefit of some forest projects by using more reflective and deciduous species and through urban forestry projects that reduce energy use. Ignoring biophysical interactions could result in millions of dollars being invested in some mitigation projects that provide little climate benefit or, worse, are counter-productive