Fixed Point Result in Menger Space with EA Property

This paper’s main objective is to define Menger space (PQM) and the concept of weakly compatible by using the notion of property (EA) & JSR maps to define new property to prove a common fixed point theorem for 4 self maps in Menger space (PQM). Key Words: Fixed Point, Probabilistic Metric Space, Menger space, JSR mappings, property EA Subject classification: 47H10, 54H2

Fixed Point Result in Probabilistic Metric Space

In this paper we prove common fixed point theorem for four mapping with weak compatibility in probabilistic metric space. Keywords: Menger space, Weak compatible mapping, Semi-compatible mapping, Weakly commuting mapping, common fixed point. AMS Subject Classification: 47H10, 54H25

Advanced Ensemble Modeling Method For Space Object State Prediction Accounting For Uncertainty In Atmospheric Density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed HASDM-ML, CHAMP-ML, and MSIS-UQ machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called consider covariance sigma point (CCSP) filter that can account for the density uncertainties during orbit propagation. As a testbed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions

Stochastic Modeling Of Physical Drag Coefficient – Its Impact On Orbit Prediction And Space Traffic Management

Ambitious satellite constellation projects by commercial entities and the ease of access to space in recent times have led to a dramatic proliferation of low-Earth space traffic. It jeopardizes space safety and long-term sustainability, necessitating better space domain awareness (SDA). Correct modeling of uncertainties in force models and orbital states, among other things, is an essential part of SDA. For objects in the low-Earth orbit (LEO) region, the uncertainty in the orbital dynamics mainly emanate from limited knowledge of the atmospheric drag-related parameters and variables. In this paper, which extends the work by Paul et al. (2021), we develop a feed-forward deep neural network model for the prediction of the satellite drag coefficient for the full range of satellite attitude (i.e., satellite pitch ∈ (-90°, +90°) and satellite yaw ∈ (0°, +360°)). The model simultaneously predicts the mean and the standard deviation and is well-calibrated. We use numerically simulated physical drag coefficient data for training our neural network. The numerical simulations are carried out using the test particle Monte Carlo method using the diffuse reflection with incomplete accommodation gas-surface interaction model. Modeling is carried out for the well-known Challenging Minisatellite Payload (CHAMP) satellite. Finally, we use the Monte Carlo approach to propagate CHAMP over a three-day period under various modeling scenarios to investigate the distribution of radial, along-track, and cross-track orbital errors caused by drag coefficient uncertainty. The key takeaways of this paper are - (a) a constant drag coefficient cannot be used for reliable SDA purposes, and (b) stochastic machine learning models allow for the computation of drag coefficients in a timely manner while providing reliable uncertainty estimates

Updates And Improvements To The Satellite Drag Coefficient Response Surface Modeling Toolkit

For satellites in the Low Earth Orbit (LEO) region, the drag coefficient is a primary source of uncertainty for orbit determination and prediction. Researchers at the Los Alamos National Laboratory (LANL) have created the so-called Response Surface Modeling (RSM) toolkit to provide the community with a resource for simulating and modeling satellite drag coefficients for satellites with complex geometries (modeled using triangulated facets) in the free molecular flow (FMF) regime. The toolkit fits an interpolation surface using non-parametric Gaussian Process Regression (GPR) over drag coefficient data computed using the numerical Test Particle Monte Carlo (TPMC) method. The fitted response surface provides a substantial computational benefit over numerical approaches for calculating drag coefficients. In this work, the RSM toolkit is further developed into a versatile software with extended capabilities. The capabilities are specifically expanded to include uncertainty quantification and adaptation for automatic development of regression models for satellites with non-stationary components (e.g., rotating solar panels). Furthermore, the toolkit uses Python 3.x and C programming languages to provide an open-source software package with a OSI approved GPL license. To assist the end user, the new RSM toolkit has been developed to have a user-friendly installation process and is provided with extensive documentation. The analysis of two different conceptual satellites is performed during this work: a simple cube and a CubeSat consisting of a simple cube body with 2 rotating solar panels. During the creation of the regression model for each satellite for different atmospheric species, it is found that the cube\u27s minimum Root Mean Squared Error (RMSE) is 0.00211 and the maximum RMSE is 0.00350. The CubeSat has a minimum RMSE of 0.00304 and the maximum is 0.00498. These results are overall conducive of a well performing regression model

Crystal Structure of the 6-Hydroxymethyl-7,8-Dihydropterin Pyrophosphokinase•Dihydropteroate Synthase Bifunctional Enzyme from Francisella tularensis

The 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) and dihydropteroate synthase (DHPS) enzymes catalyze sequential metabolic reactions in the folate biosynthetic pathway of bacteria and lower eukaryotes. Both enzymes represent validated targets for the development of novel anti-microbial therapies. We report herein that the genes which encode FtHPPK and FtDHPS from the biowarfare agent Francisella tularensis are fused into a single polypeptide. The potential of simultaneously targeting both modules with pterin binding inhibitors prompted us to characterize the molecular details of the multifunctional complex. Our high resolution crystallographic analyses reveal the structural organization between FtHPPK and FtDHPS which are tethered together by a short linker. Additional structural analyses of substrate complexes reveal that the active sites of each module are virtually indistinguishable from those of the monofunctional enzymes. The fused bifunctional enzyme therefore represents an excellent vehicle for finding inhibitors that engage the pterin binding pockets of both modules that have entirely different architectures. To demonstrate that this approach has the potential of producing novel two-hit inhibitors of the folate pathway, we identify and structurally characterize a fragment-like molecule that simultaneously engages both active sites. Our study provides a molecular framework to study the enzyme mechanisms of HPPK and DHPS, and to design novel and much needed therapeutic compounds to treat infectious diseases

High Levels of DEK Autoantibodies in Sera of Patients With Polyarticular Juvenile Idiopathic Arthritis and With Early Disease Flares Following Cessation of Antiâ Tumor Necrosis Factor Therapy

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142962/1/art40404_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142962/2/art40404-sup-0001-Supinfo.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142962/3/art40404.pd

Global, regional, and national sex differences in the global burden of tuberculosis by HIV status, 1990–2019: results from the Global Burden of Disease Study 2019

Background Tuberculosis is a major contributor to the global burden of disease, causing more than a million deaths annually. Given an emphasis on equity in access to diagnosis and treatment of tuberculosis in global health targets, evaluations of differences in tuberculosis burden by sex are crucial. We aimed to assess the levels and trends of the global burden of tuberculosis, with an emphasis on investigating differences in sex by HIV status for 204 countries and territories from 1990 to 2019. Methods We used a Bayesian hierarchical Cause of Death Ensemble model (CODEm) platform to analyse 21 505 site-years of vital registration data, 705 site-years of verbal autopsy data, 825 site-years of sample-based vital registration data, and 680 site-years of mortality surveillance data to estimate mortality due to tuberculosis among HIV-negative individuals. We used a population attributable fraction approach to estimate mortality related to HIV and tuberculosis coinfection. A compartmental meta-regression tool (DisMod-MR 2.1) was then used to synthesise all available data sources, including prevalence surveys, annual case notifications, population-based tuberculin surveys, and tuberculosis cause-specific mortality, to produce estimates of incidence, prevalence, and mortality that were internally consistent. We further estimated the fraction of tuberculosis mortality that is attributable to independent effects of risk factors, including smoking, alcohol use, and diabetes, for HIV-negative individuals. For individuals with HIV and tuberculosis coinfection, we assessed mortality attributable to HIV risk factors including unsafe sex, intimate partner violence (only estimated among females), and injection drug use. We present 95% uncertainty intervals for all estimates. Findings Globally, in 2019, among HIV-negative individuals, there were 1.18 million (95% uncertainty interval 1.08-1.29) deaths due to tuberculosis and 8.50 million (7.45-9.73) incident cases of tuberculosis. Among HIV-positive individuals, there were 217 000 (153 000-279 000) deaths due to tuberculosis and 1.15 million (1.01-1.32) incident cases in 2019. More deaths and incident cases occurred in males than in females among HIV-negative individuals globally in 2019, with 342 000 (234 000-425 000) more deaths and 1.01 million (0.82-1.23) more incident cases in males than in females. Among HIV-positive individuals, 6250 (1820-11 400) more deaths and 81 100 (63 300-100 000) more incident cases occurred among females than among males in 2019. Age-standardised mortality rates among HIV-negative males were more than two times greater in 105 countries and age-standardised incidence rates were more than 1.5 times greater in 74 countries than among HIV-negative females in 2019. The fraction of global tuberculosis deaths among HIV-negative individuals attributable to alcohol use, smoking, and diabetes was 4.27 (3.69-5.02), 6.17 (5.48-7.02), and 1.17 (1.07-1.28) times higher, respectively, among males than among females in 2019. Among individuals with HIV and tuberculosis coinfection, the fraction of mortality attributable to injection drug use was 2.23 (2.03-2.44) times greater among males than females, whereas the fraction due to unsafe sex was 1.06 (1.05-1.08) times greater among females than males. Interpretation As countries refine national tuberculosis programmes and strategies to end the tuberculosis epidemic, the excess burden experienced by males is important. Interventions are needed to actively communicate, especially to men, the importance of early diagnosis and treatment. These interventions should occur in parallel with efforts to minimise excess HIV burden among women in the highest HIV burden countries that are contributing to excess HIV and tuberculosis coinfection burden for females. Placing a focus on tuberculosis burden among HIV-negative males and HIV and tuberculosis coinfection among females might help to diminish the overall burden of tuberculosis. This strategy will be crucial in reaching both equity and burden targets outlined by global health milestone