Entropic and gradient flow formulations for nonlinear diffusion

Nonlinear diffusion $\partial_t \rho = \Delta(\Phi(\rho))$ is considered for a class of nonlinearities $\Phi$. It is shown that for suitable choices of $\Phi$, an associated Lyapunov functional can be interpreted as thermodynamics entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role

Large deviations principle for Curie-Weiss models with random fields

In this article we consider an extension of the classical Curie-Weiss model in which the global and deterministic external magnetic field is replaced by local and random external fields which interact with each spin of the system. We prove a Large Deviations Principle for the so-called {\it magnetization per spin} $S_n/n$ with respect to the associated Gibbs measure, where $S_n/n$ is the scaled partial sum of spins. In particular, we obtain an explicit expression for the LDP rate function, which enables an extensive study of the phase diagram in some examples. It is worth mentioning that the model considered in this article covers, in particular, both the case of i.\,i.\,d.\ random external fields (also known under the name of random field Curie-Weiss models) and the case of dependent random external fields generated by e.\,g.\ Markov chains or dynamical systems.Comment: 11 page

The Elusive Ideal: Civic Learning and Higher Education

General book description: From curriculum standards and testing to school choice and civic learning, issues in American education are some of the most debated in the United States. The Institutions of American Democracy , a collection of essays by the nation\u27s leading education scholars and professionals, is designed to inform the debate and stimulate change. In association with the Annenberg Foundation Trust at Sunnylands and the Annenberg Public Policy Center at the University of Pennsylvania, The Institutions of American Democracy is the first in a series of books commissioned to enhance public understanding of the nature and function of democratic institutions. A national advisory board--including, among others, Nancy Kassebaum Baker, David Boren, John Brademas, Ellen Condliffe Lagemann, David Gergen, and Lee Hamilton--will guide the vision of the project, which includes future volumes on the press and the three branches of government. Each essay in The Institutions of American Democracy addresses essential questions for policymakers, educators, and anyone committed to public education. What role should public education play in a democracy? How has that role changed through American history? Have the schools lost sight of their responsibility to teach civics and citizenship? How are current debates about education shaping the future of this democratic institution

The development of structural adhesive systems suitable for use with liquid oxygen Annual summary report, 1 Jul. 1964 - 30 Jun. 1965

Preparation and testing of adhesive polyurethanes, polycarbonates, and other highy halogenated polymers for liquid oxygen compatibilit

Law of large numbers for a class of random walks in dynamic random environments

In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the right/left. We adapt a regeneration-time argument originally developed by Comets and Zeitouni [2] for static random environments to prove that, under a space-time mixing property for the dynamic random environment called conemixing, the random walk has an a.s. constant global speed. In addition, we show that if the dynamic random environment is exponentially mixing in space-time and the local drifts are small, then the global speed can be written as a power series in the size of the local drifts. From the first term in this series the sign of the global speed can be read off. The results can be easily extended to higher dimension

Large deviation principle for one-dimensional random walk in dynamic random environment : attractive spin-flips and simple symmetric exclusion

Consider a one-dimensional shift-invariant attractive spin-ip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In [2] we proved a law of large numbers for dynamic random environments satisfying a space-time mixing property called cone-mixing. If an attractive spin-ip system has a finite average coupling time at the origin for two copies starting from the all-occupied and the all-vacant configuration, respectively, then it is cone-mixing. In the present paper we prove a large deviation principle for the empirical speed of the random walk, both quenched and annealed, and exhibit some properties of the associated rate functions. Under an exponential space-time mixing condition for the spin-ip system, which is stronger than cone-mixing, the two rate functions have a unique zero, i.e., the slow-down phenomenon known to be possible in a static random environment does not survive in a fast mixing dynamic random environment. In contrast, we show that for the simple symmetric exclusion dynamics, which is not cone-mixing (and which is not a spin-ip system either), slow-down does occur

Rimonabant improves cardiometabolic risk factors in overweight/obese patients with poorly controlled type 2 diabetes (HbA(1c)>= 8%) on monotherapy with metformin or sulfonylureas

peer reviewe

Firm-Level Exposure to Epidemic Diseases: Covid-19, SARS, and H1N1

Using tools described in our earlier work (Hassan et al., 2019, 2020), we develop text-based measures of the costs, benefits, and risks listed firms in the US and over 80 other countries associate with the spread of Covid-19 and other epidemic diseases. We identify which firms expect to gain or lose from an epidemic disease and which are most affected by the associated uncertainty as a disease spreads in a region or around the world. As Covid-19 spreads globally in the first quarter of 2020, we find that firms’ primary concerns relate to the collapse of demand, increased uncertainty, and disruption in supply chains. Other important concerns relate to capacity reductions, closures, and employee welfare. By contrast, financing concerns are mentioned relatively rarely. We also identify some firms that foresee opportunities in new or disrupted markets due to the spread of the disease. Finally, we find some evidence that firms that have experience with SARS or H1N1 have more positive expectations about their ability to deal with the coronavirus outbreak

N-Terminal Pro–B-Type Natriuretic Peptide in the Emergency Department: The ICON-RELOADED Study

Background Contemporary reconsideration of diagnostic N-terminal pro–B-type natriuretic peptide (NT-proBNP) cutoffs for diagnosis of heart failure (HF) is needed. Objectives This study sought to evaluate the diagnostic performance of NT-proBNP for acute HF in patients with dyspnea in the emergency department (ED) setting. Methods Dyspneic patients presenting to 19 EDs in North America were enrolled and had blood drawn for subsequent NT-proBNP measurement. Primary endpoints were positive predictive values of age-stratified cutoffs (450, 900, and 1,800 pg/ml) for diagnosis of acute HF and negative predictive value of the rule-out cutoff to exclude acute HF. Secondary endpoints included sensitivity, specificity, and positive (+) and negative (−) likelihood ratios (LRs) for acute HF. Results Of 1,461 subjects, 277 (19%) were adjudicated as having acute HF. The area under the receiver-operating characteristic curve for diagnosis of acute HF was 0.91 (95% confidence interval [CI]: 0.90 to 0.93; p < 0.001). Sensitivity for age stratified cutoffs of 450, 900, and 1,800 pg/ml was 85.7%, 79.3%, and 75.9%, respectively; specificity was 93.9%, 84.0%, and 75.0%, respectively. Positive predictive values were 53.6%, 58.4%, and 62.0%, respectively. Overall LR+ across age-dependent cutoffs was 5.99 (95% CI: 5.05 to 6.93); individual LR+ for age-dependent cutoffs was 14.08, 4.95, and 3.03, respectively. The sensitivity and negative predictive value for the rule-out cutoff of 300 pg/ml were 93.9% and 98.0%, respectively; LR− was 0.09 (95% CI: 0.05 to 0.13). Conclusions In acutely dyspneic patients seen in the ED setting, age-stratified NT-proBNP cutpoints may aid in the diagnosis of acute HF. An NT-proBNP <300 pg/ml strongly excludes the presence of acute HF