Global Gronwall Estimates for Integral Curves on Riemannian Manifolds

We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.Comment: 4 pages, 1 figure, correction of some misprint

"They Would Not Take Me There" People, Places, and Stories from Champlain's Travels in Canada 1603-1616

This is the publisher's version, also available electronically from http://www.cartographicperspectives.org/index.php/journal/article/view/96.No abstract is available for this item

Spectroscopy and Thermometry of Drumhead Modes in a Mesoscopic Trapped-Ion Crystal using Entanglement

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a $\sim$400 $\mu$m-diameter planar crystal of several hundred $^9$Be$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing ($\sim$20 \nolinebreak$\mu$m). Center-of-mass displacements below 1 nm are detected via entanglement of spin and motional degrees of freedom.Comment: 12 pages, 7 figures (includes Supplementary Material

Tracing Multiple Scattering Patterns in Absolute (e, 2e) Cross Sections for H₂ and He over a 4π Solid Angle

Absolutely normalized (e,2e) measurements for H2 and He covering the full solid angle of one ejected electron are presented for 16 eV sum energy of both final state continuum electrons. For both targets rich cross-section structures in addition to the binary and recoil lobes are identified and studied as a function of the fixed electron\u27s emission angle and the energy sharing among both electrons. For H2 their behavior is consistent with multiple scattering of the projectile as discussed before. For He the binary and recoil lobes are significantly larger than for H2 and partly cover the multiple scattering structures. To highlight these patterns we propose a alternative representation of the triply differential cross section. Nonperturbative calculations are in good agreement with the He results and show discrepancies for H2 in the recoil peak region. For H2 a perturbative approach reasonably reproduces the cross-section shape but deviates in absolute magnitude

The Quest for System-Theoretical Medicine in the COVID-19 Era

Precision medicine and molecular systems medicine (MSM) are highly utilized and successful approaches to improve understanding, diagnosis, and treatment of many diseases from bench-to-bedside. Especially in the COVID-19 pandemic, molecular techniques and biotechnological innovation have proven to be of utmost importance for rapid developments in disease diagnostics and treatment, including DNA and RNA sequencing technology, treatment with drugs and natural products and vaccine development. The COVID-19 crisis, however, has also demonstrated the need for systemic thinking and transdisciplinarity and the limits of MSM: the neglect of the bio-psycho-social systemic nature of humans and their context as the object of individual therapeutic and population-oriented interventions. COVID-19 illustrates how a medical problem requires a transdisciplinary approach in epidemiology, pathology, internal medicine, public health, environmental medicine, and socio-economic modeling. Regarding the need for conceptual integration of these different kinds of knowledge we suggest the application of general system theory (GST). This approach endorses an organism-centered view on health and disease, which according to Ludwig von Bertalanffy who was the founder of GST, we call Organismal Systems Medicine (OSM). We argue that systems science offers wider applications in the field of pathology and can contribute to an integrative systems medicine by (i) integration of evidence across functional and structural differentially scaled subsystems, (ii) conceptualization of complex multilevel systems, and (iii) suggesting mechanisms and non-linear relationships underlying the observed phenomena. We underline these points with a proposal on multi-level systems pathology including neurophysiology, endocrinology, immune system, genetics, and general metabolism. An integration of these areas is necessary to understand excess mortality rates and polypharmacological treatments. In the pandemic era this multi-level systems pathology is most important to assess potential vaccines, their effectiveness, short-, and long-time adverse effects. We further argue that these conceptual frameworks are not only valid in the COVID-19 era but also important to be integrated in a medicinal curriculum

ISO LWS Spectroscopy of M82: A Unified Evolutionary Model

We present the first complete far-infrared spectrum (43 to 197 um) of M82, the brightest infrared galaxy in the sky, taken with the Long Wavelength Spectrometer of the Infrared Space Observatory (ISO). We detected seven fine structure emission lines, [OI] 63 and 145 um, [OIII] 52 and 88 um, [NII] 122 um, [NIII] 57 um and [CII] 158 um, and fit their ratios to a combination starburst and photo-dissociation region (PDR) model. The best fit is obtained with HII regions with n = 250 cm^{-3} and an ionization parameter of 10^{-3.5} and PDRs with n = 10^{3.3} cm^{-3} and a far-ultraviolet flux of G_o = 10^{2.8}. We applied both continuous and instantaneous starburst models, with our best fit being a 3-5 Myr old instantaneous burst model with a 100 M_o cut-off. We also detected the ground state rotational line of OH in absorption at 119.4 um. No excited level OH transitions are apparent, indicating that the OH is almost entirely in its ground state with a column density ~ 4x10^{14} cm^{-2}. The spectral energy distribution over the LWS wavelength range is well fit with a 48 K dust temperature and an optical depth, tau_{Dust} proportional to lambda^{-1}.Comment: 23 pages, 4 figures, accepted by ApJ, Feb. 1, 199

Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0<a<3; d_ij is the distance between spin pairs. These power-laws correspond physically to infinite-range (a=0), Coulomb-like (a=1), monopole-dipole (a=2) and dipole-dipole (a=3) couplings. Experimentally, we demonstrate excellent agreement with theory for 0.05<a<1.4. This demonstration coupled with the high spin-count, excellent quantum control and low technical complexity of the Penning trap brings within reach simulation of interesting and otherwise computationally intractable problems in quantum magnetism.Comment: 10 pages, 10 figures; article plus Supplementary Material

Model Evaluation Guidelines for Geomagnetic Index Predictions

Geomagnetic indices are convenient quantities that distill the complicated physics of some region or aspect of near‐Earth space into a single parameter. Most of the best‐known indices are calculated from ground‐based magnetometer data sets, such as Dst, SYM‐H, Kp, AE, AL, and PC. Many models have been created that predict the values of these indices, often using solar wind measurements upstream from Earth as the input variables to the calculation. This document reviews the current state of models that predict geomagnetic indices and the methods used to assess their ability to reproduce the target index time series. These existing methods are synthesized into a baseline collection of metrics for benchmarking a new or updated geomagnetic index prediction model. These methods fall into two categories: (1) fit performance metrics such as root‐mean‐square error and mean absolute error that are applied to a time series comparison of model output and observations and (2) event detection performance metrics such as Heidke Skill Score and probability of detection that are derived from a contingency table that compares model and observation values exceeding (or not) a threshold value. A few examples of codes being used with this set of metrics are presented, and other aspects of metrics assessment best practices, limitations, and uncertainties are discussed, including several caveats to consider when using geomagnetic indices.Plain Language SummaryOne aspect of space weather is a magnetic signature across the surface of the Earth. The creation of this signal involves nonlinear interactions of electromagnetic forces on charged particles and can therefore be difficult to predict. The perturbations that space storms and other activity causes in some observation sets, however, are fairly regular in their pattern. Some of these measurements have been compiled together into a single value, a geomagnetic index. Several such indices exist, providing a global estimate of the activity in different parts of geospace. Models have been developed to predict the time series of these indices, and various statistical methods are used to assess their performance at reproducing the original index. Existing studies of geomagnetic indices, however, use different approaches to quantify the performance of the model. This document defines a standardized set of statistical analyses as a baseline set of comparison tools that are recommended to assess geomagnetic index prediction models. It also discusses best practices, limitations, uncertainties, and caveats to consider when conducting a model assessment.Key PointsWe review existing practices for assessing geomagnetic index prediction models and recommend a “standard set” of metricsAlong with fit performance metrics that use all data‐model pairs in their formulas, event detection performance metrics are recommendedOther aspects of metrics assessment best practices, limitations, uncertainties, and geomagnetic index caveats are also discussedPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147764/1/swe20790_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147764/2/swe20790.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147764/3/swe20790-sup-0001-2018SW002067-SI.pd

Benchmarking High-Field Few-Electron Correlation and QED Contributions in Hg⁷⁵⁺ to Hg⁷⁸⁺ Ions. I. Experiment

The photorecombination of highly charged few-electron mercury ions Hg75+ to Hg78+ has been explored with the Heidelberg electron beam ion trap. By monitoring the emitted x rays (65-76 keV) and scanning the electron beam energy (45-54 keV) over the KLL dielectronic recombination (DR) region, the energies of state-selected DR resonances were determined to within ±4 eV (relative) and ±14 eV (absolute). At this level of experimental accuracy, it becomes possible to make a detailed comparison to various theoretical approaches and methods, all of which include quantum electrodynamic (QED) effects and finite nuclear size contributions (for a 1s electron, these effects can be as large as 160 and 50 eV, respectively). In He-like Hg78+, a good agreement between the experimental results and the calculations has been found. However, for the capture into Li-, Be-, and B-like ions, significant discrepancies have been observed for specific levels. The discrepancies suggest the need for further theoretical and experimental studies with other heavy ions along these isoelectronic sequences