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

Experimental calbration and implications of olivine-melt vanadium oxybarometry for hydrous magmas from Mutnovsky volcano (Kamchatka)

A promising method for the quantification of the redox conditions (oxygen fugacity, fO2) in basaltic systems, which might be applied to quenched melt inclusions in olivine, exploits the partitioning of vanadium between olivine and coexisting silicate melt (DV Ol‐M). Strong correlation of DV Ol‐M with fO2 was investigated in a number of experimental works on dry mafic and ultramafic melts in a wide range of fO2 conditions at pressures of 1 atm and 0.5–2 GPa, temperature range of 1150–1530°C (e.g., Canil&Fedortchouk, 2001; Mallmann&O’Neill, 2009; 2013). Only a few melt compositions equilibrated with olivine at T≤1250°C were studied so far. Although it was shown that melt composition, pressure and temperature have small effect on DV Ol‐M, more data are required to extend the calibration of the V oxybarometry to hydrous low‐temperature basalts representing island arc magmas

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

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

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

Improving Nursing Facility Care Through an Innovative Payment Demonstration Project: Optimizing Patient Transfers, Impacting Medical Quality, and Improving Symptoms: Transforming Institutional Care Phase 2

Optimizing Patient Transfers, Impacting Medical Quality, and Improving Symptoms: Transforming Institutional Care (OPTIMISTIC) is a 2‐phase Center for Medicare and Medicaid Innovations demonstration project now testing a novel Medicare Part B payment model for nursing facilities and practitioners in 40 Indiana nursing facilities. The new payment codes are intended to promote high‐quality care in place for acutely ill long‐stay residents. The focus of the initiative is to reduce hospitalizations through the diagnosis and on‐site management of 6 common acute clinical conditions (linked to a majority of potentially avoidable hospitalizations of nursing facility residents1): pneumonia, urinary tract infection, skin infection, heart failure, chronic obstructive pulmonary disease or asthma, and dehydration. This article describes the OPTIMISTIC Phase 2 model design, nursing facility and practitioner recruitment and training, and early experiences implementing new Medicare payment codes for nursing facilities and practitioners. Lessons learned from the OPTIMISTIC experience may be useful to others engaged in multicomponent quality improvement initiatives

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

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