Functional and Banach Space Stochastic Calculi: Path-Dependent Kolmogorov Equations Associated with the Frame of a Brownian Motion

First, we revisit basic theory of functional It\uf4/path-dependent calculus, using the formulation of calculus via regularization. Relations with the corresponding Banach space valued calculus are explored. The second part of the paper is devoted to the study of the Kolmogorov type equation associated with the so called window Brownian motion, called path-dependent heat equation, for which well-posedness at the level of strict solutions is established. Then, a notion of strong approximating solution, called strong-viscosity solution, is introduced which is supposed to be a substitution tool to the viscosity solution. For that kind of solution, we also prove existence and uniqueness

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]

Concurrent La and A-site Vacancy Doping Modulates the Thermoelectric Response of SrTiO3. Experimental and Computational Evidence

To help understand the factors controlling the performance of one of the most promising n-type oxide thermoelectric SrTiO3, we need to explore structural control at the atomic level. In Sr1–xLa2x/3TiO3 ceramics (0.0 ≤ x ≤ 0.9), we determined that the thermal conductivity can be reduced and controlled through an interplay of La-substitution and A-site vacancies and the formation of a layered structure. The decrease in thermal conductivity with La and A-site vacancy substitution dominates the trend in the overall thermoelectric response. The maximum dimensionless figure of merit is 0.27 at 1070 K for composition x = 0.50 where half of the A-sites are occupied with La and vacancies. Atomic resolution Z-contrast imaging and atomic scale chemical analysis show that as the La content increases, A-site vacancies initially distribute randomly (x < 0.3), then cluster (x ≈ 0.5), and finally form layers (x = 0.9). The layering is accompanied by a structural phase transformation from cubic to orthorhombic and the formation of 90° rotational twins and antiphase boundaries, leading to the formation of localized supercells. The distribution of La and A-site vacancies contributes to a nonuniform distribution of atomic scale features. This combination induces temperature stable behavior in the material and reduces thermal conductivity, an important route to enhancement of the thermoelectric performance. A computational study confirmed that the thermal conductivity of SrTiO3 is lowered by the introduction of La and A-site vacancies as shown by the experiments. The modeling supports that a critical mass of A-site vacancies is needed to reduce thermal conductivity and that the arrangement of La, Sr, and A-site vacancies has a significant impact on thermal conductivity only at high La concentration

Clinical and organizational factors associated with mortality during the peak of first COVID-19 wave: the global UNITE-COVID study

Purpose: To accommodate the unprecedented number of critically ill patients with pneumonia caused by coronavirus disease 2019 (COVID-19) expansion of the capacity of intensive care unit (ICU) to clinical areas not previously used for critical care was necessary. We describe the global burden of COVID-19 admissions and the clinical and organizational characteristics associated with outcomes in critically ill COVID-19 patients. Methods: Multicenter, international, point prevalence study, including adult patients with SARS-CoV-2 infection confirmed by polymerase chain reaction (PCR) and a diagnosis of COVID-19 admitted to ICU between February 15th and May 15th, 2020. Results: 4994 patients from 280 ICUs in 46 countries were included. Included ICUs increased their total capacity from 4931 to 7630 beds, deploying personnel from other areas. Overall, 1986 (39.8%) patients were admitted to surge capacity beds. Invasive ventilation at admission was present in 2325 (46.5%) patients and was required during ICU stay in 85.8% of patients. 60-day mortality was 33.9% (IQR across units: 20%–50%) and ICU mortality 32.7%. Older age, invasive mechanical ventilation, and acute kidney injury (AKI) were associated with increased mortality. These associations were also confirmed specifically in mechanically ventilated patients. Admission to surge capacity beds was not associated with mortality, even after controlling for other factors. Conclusions: ICUs responded to the increase in COVID-19 patients by increasing bed availability and staff, admitting up to 40% of patients in surge capacity beds. Although mortality in this population was high, admission to a surge capacity bed was not associated with increased mortality. Older age, invasive mechanical ventilation, and AKI were identified as the strongest predictors of mortality

Structures Related to the Emplacement of Shallow-Level Intrusions

A systematic view of the vast nomenclature used to describe the structures of shallow-level intrusions is presented here. Structures are organised in four main groups, according to logical breaks in the timing of magma emplacement, independent of the scales of features: (1) Intrusion-related structures, formed as the magma is making space and then develops into its intrusion shape; (2) Magmatic flow-related structures, developed as magma moves with suspended crystals that are free to rotate; (3) Solid-state, flow-related structures that formed in portions of the intrusions affected by continuing flow of nearby magma, therefore considered to have a syn-magmatic, non-tectonic origin; (4) Thermal and fragmental structures, related to creation of space and impact on host materials. This scheme appears as a rational organisation, helpful in describing and interpreting the large variety of structures observed in shallow-level intrusions

Co-infection and ICU-acquired infection in COIVD-19 ICU patients: a secondary analysis of the UNITE-COVID data set

Background: The COVID-19 pandemic presented major challenges for critical care facilities worldwide. Infections which develop alongside or subsequent to viral pneumonitis are a challenge under sporadic and pandemic conditions; however, data have suggested that patterns of these differ between COVID-19 and other viral pneumonitides. This secondary analysis aimed to explore patterns of co-infection and intensive care unit-acquired infections (ICU-AI) and the relationship to use of corticosteroids in a large, international cohort of critically ill COVID-19 patients.Methods: This is a multicenter, international, observational study, including adult patients with PCR-confirmed COVID-19 diagnosis admitted to ICUs at the peak of wave one of COVID-19 (February 15th to May 15th, 2020). Data collected included investigator-assessed co-infection at ICU admission, infection acquired in ICU, infection with multi-drug resistant organisms (MDRO) and antibiotic use. Frequencies were compared by Pearson's Chi-squared and continuous variables by Mann-Whitney U test. Propensity score matching for variables associated with ICU-acquired infection was undertaken using R library MatchIT using the "full" matching method.Results: Data were available from 4994 patients. Bacterial co-infection at admission was detected in 716 patients (14%), whilst 85% of patients received antibiotics at that stage. ICU-AI developed in 2715 (54%). The most common ICU-AI was bacterial pneumonia (44% of infections), whilst 9% of patients developed fungal pneumonia; 25% of infections involved MDRO. Patients developing infections in ICU had greater antimicrobial exposure than those without such infections. Incident density (ICU-AI per 1000 ICU days) was in considerable excess of reports from pre-pandemic surveillance. Corticosteroid use was heterogenous between ICUs. In univariate analysis, 58% of patients receiving corticosteroids and 43% of those not receiving steroids developed ICU-AI. Adjusting for potential confounders in the propensity-matched cohort, 71% of patients receiving corticosteroids developed ICU-AI vs 52% of those not receiving corticosteroids. Duration of corticosteroid therapy was also associated with development of ICU-AI and infection with an MDRO.Conclusions: In patients with severe COVID-19 in the first wave, co-infection at admission to ICU was relatively rare but antibiotic use was in substantial excess to that indication. ICU-AI were common and were significantly associated with use of corticosteroids

Floodwater farming, discontinuous ephemeral streams, and Puebloan abandonment in southwestern Colorado

Geoarchaeological study on the southern piedmont of Sleeping Ute Mountain in southwestern Colorado indicates the presence of discontinuous ephemeral streams that were the foci of episodic Puebloan occupation between A.D. 600s and 1280. Characterized by arroyos, discontinuous ephemeral streams contain alternating aggrading and degrading reaches and are well suited for ak chin floodwater agriculture. Episodic Puebloan abandonment of the southern piedmont correlates with periods of drought but does not appear to be linked to stream entrenchment. We question a priori assumptions of droughts correlated to stream entrenchment and urge caution in the use of drought-arroyo models for settlement shifts in alluvial flood plains without supporting stratigraphic or geomorphic evidence