Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

Electron Accumulation and Emergent Magnetism in LaMnO3/SrTiO3 Heterostructures

Emergent phenomena at polar-nonpolar oxide interfaces have been studied intensely in pursuit of next-generation oxide electronics and spintronics. Here we report the disentanglement of critical thicknesses for electron reconstruction and the emergence of ferromagnetism in polar-mismatched LaMnO3/SrTiO3 (001) heterostructures. Using a combination of element-specific X-ray absorption spectroscopy and dichroism, and first-principles calculations, interfacial electron accumulation and ferromagnetism have been observed within the polar, antiferromagnetic insulator LaMnO3. Our results show that the critical thickness for the onset of electron accumulation is as thin as 2 unit cells (UC), significantly thinner than the observed critical thickness for ferromagnetism of 5 UC. The absence of ferromagnetism below 5 UC is likely induced by electron over-accumulation. In turn, by controlling the doping of the LaMnO3, we are able to neutralize the excessive electrons from the polar mismatch in ultrathin LaMnO3 films and thus enable ferromagnetism in films as thin as 3 UC, extending the limits of our ability to synthesize and tailor emergent phenomena at interfaces and demonstrating manipulation of the electronic and magnetic structures of materials at the shortest length scales.Comment: Accepted by Phys. Rev. Let

Predicted effectiveness of daily and non-daily PrEP for MSM based on sex and pill-taking patterns from HPTN 067/ADAPT

Background: HPTN 067/ADAPT evaluated the feasibility of daily and non-daily HIV pre-exposure prophylaxis (PrEP) regimens among high-risk populations, including men who have sex with men (MSM) and transgender women, in Bangkok, Thailand and Harlem, New York, U.S. We used a mathematical model to predict the efficacy and effectiveness of different dosing regimens. Methods: An individual-based mathematical model was used to simulate annual HIV incidence among MSM cohorts. PrEP efficacy for covered sex acts, as defined in the HPTN 067/ADAPT protocol, was estimated using subgroup efficacy estimates from the iPrEx trial. Effectiveness was estimated by comparison of the HIV incidence with and without PrEP use. Results: We estimated that PrEP was highly protective (85%–96% efficacy across regimens and sites) for fully covered acts. PrEP was more protective for partially covered acts in Bangkok (71%–88% efficacy) than in Harlem (62%–81% efficacy). Our model projects 80%, 62%, and 68% effectiveness of daily, time-driven, and event-driven PrEP for MSM in Harlem compared with 90%, 85% and 79% for MSM in Bangkok. Halving the efficacy for partially covered acts decreases effectiveness by 8–9 percentage points in Harlem and by 5–9 percentage points in Bangkok across regimens. Conclusions: Our analysis suggests that PrEP was more effective among MSM in Thailand than in the U.S. as a result of more fully covered sex acts and more pills taken around partially covered acts. Overall, non-daily PrEP was less effective than daily PrEP, especially in the U.S. where the sex act coverage associated with daily use was substantially higher

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Intra-guild competition and its implications for one of the biggest terrestrial predators, Tyrannosaurus rex

Identifying tradeoffs between hunting and scavenging in an ecological context is important for understanding predatory guilds. In the past century, the feeding strategy of one of the largest and best-known terrestrial carnivores, Tyrannosaurus rex, has been the subject of much debate: was it an active predator or an obligate scavenger? Here we look at the feasibility of an adult T. rex being an obligate scavenger in the environmental conditions of Late Cretaceous North America, given the size distributions of sympatric herbivorous dinosaurs and likely competition with more abundant small-bodied theropods. We predict that nearly 50 per cent of herbivores would have been within a 55–85 kg range, and calculate based on expected encounter rates that carcasses from these individuals would have been quickly consumed by smaller theropods. Larger carcasses would have been very rare and heavily competed for, making them an unreliable food source. The potential carcass search rates of smaller theropods are predicted to be 14–60 times that of an adult T. rex. Our results suggest that T. rex and other extremely large carnivorous dinosaurs would have been unable to compete as obligate scavengers and would have primarily hunted large vertebrate prey, similar to many large mammalian carnivores in modern-day ecosystems

Ergosterol Effect on the Desaturation of 14C-Cis-Vaccenate in Tetrahymena

Supplement of ergosterol to the growth medium of the ciliated protozoan Tetrahymena pyriformis W leads to incorporation of the foreign sterol within cell membranes and suppression of synthesis of the native sterol-like compound tetrahymanol, as well as to changes in the fatty acid compositions of several major classes of membrane lipid. Alteration of fatty acid composition is thought to represent a regulatory mechanism whereby optimum membrane fluidity is maintained when the slightly dissimilar foreign sterol is added into the phospholipid bilayer of the membranes. The present study, using several different conditions of growth temperature, substrate concentrations and incubation time, and ergosterol concentrations and exposure time, is an attempt to provide evidence supporting a hypothetical regulatory mechanism. This mechanism proposes that there is a feedback regulation by membrane-bound sterol on an enzyme or enzymes involved in synthesis of the long chain fatty acids contained in membrane phospholipid. Such a mechanism could account for the balance between sterol and fatty acid content of membrane. The data presented here show that a statistically significant increase in desaturation of 14C-cis-vaccenate can be demonstrated in Tetrahymena cell cultures whose membranes contain the foreign sterol, when growth temperature is maintained at 20° or 29.5°. Tetrahymena desaturated 14C-cis-vaccenate substrate in both ergosterol supplemented and normal cultures. The 14C labeled product, 6,11-18:2 was recovered and separated by silver nitrate-Unisil column chromatography

Ferromagnetism and conductivity in atomically thin SrRuO3

Atomically thin ferromagnetic and conducting electron systems are highly desired for spintronics, because they can be controlled with both magnetic and electric fields. We present (SrRuO3)1-(SrTiO3)5 superlattices and single-unit-cell-thick SrRuO3 samples that are capped with SrTiO3. We achieve samples of exceptional quality. In these samples, the electron systems comprise only a single RuO2 plane. We observe conductivity down to 50 mK, a ferromagnetic state with a Curie temperature of 25 K, and signals of magnetism persisting up to approximately 100 K.Comment: The version published at Phys. Rev. X (open access) contains a large amount of additional material compared to the version published her

The relationship between the perception of distributed leadership in secondary schools and teachers' and teacher leaders' job satisfaction and organizational commitment

This study investigates the relation between distributed leadership, the cohesion of the leadership team, participative decision-making, context variables, and the organizational commitment and job satisfaction of teachers and teacher leaders. A questionnaire was administered to teachers and teacher leaders (n=1770) from 46 large secondary schools. Multiple regression analyses and path analyses revealed that the study variables explained significant variance in organizational commitment. The degree of explained variance for job satisfaction was considerably lower compared to organizational commitment. Most striking was that the cohesion of the leadership team and the amount of leadership support was strongly related to organizational commitment, and indirectly to job satisfaction. Decentralization of leadership functions was weakly related to organizational commitment and job satisfaction