Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics

In this Dissertation, computational and analytic methods are presented to address nonlinear systems with applications in structural and celestial mechanics. Scalar Homotopy Methods (SHM) are first introduced for the solution of general systems of nonlinear algebraic equations. The methods are applied to the solution of postbuckling and limit load problems of solids and structures as exemplified by simple plane elastic frames, considering only geometrical nonlinearities. In many problems, instead of simply adopting a root solving method, it is useful to study the particular problem in more detail in order to establish an especially efficient and robust method. Such a problem arises in satellite geodesy coordinate transformation where a new highly efficient solution, providing global accuracy with a non-iterative sequence of calculations, is developed. Simulation results are presented to compare the solution accuracy and algorithm performance for applications spanning the LEOtoGEO range of missions. Analytic methods are introduced to address problems in structural mechanics and astrodynamics. Analytic transfer functions are developed to address the frequency domain control problem of flexible rotating aerospace structures. The transfer functions are used to design a Lyapunov stable controller that drives the spacecraft to a target position while suppressing vibrations in the flexible appendages. In astrodynamics, a Taylor series based analytic continuation technique is developed to address the classical two-body problem. A key algorithmic innovation for the trajectory propagation is that the classical averaged approximation strategy is replaced with a rigorous series based solution for exactly computing the acceleration derivatives. Evidence is provided to demonstrate that high precision solutions are easily obtained with the analytic continuation approach. For general nonlinear initial value problems (IVPs), the method of Radial Basis Functions time domain collocation (RBF-Coll ) is used to address strongly nonlinear dynamical systems and to analyze short as well as long-term responses. The algorithm is compared against, the second order central difference, the classical Runge-Kutta, the adaptive Runge-Kutta-Fehlberg, the Newmark-β, the Hilber-Hughes-Taylor and the modified Chebyshev-Picard iteration methods in terms of accuracy and computational cost for three types of problems; (1) the unforced highly nonlinear Duffing oscillator, (2) the Duffing oscillator with impact loading and (3) a nonlinear three degrees of freedom (3-DOF) dynamical system. The RBF-Collmethod is further extended for time domain inverse problems addressing fixed time optimal control problems and Lamberts orbital transfer problem. It is shown that this method is very simple, efficient and very accurate in obtaining the solutions. The proposed algorithm is advantageous and has promising applications in solving general nonlinear dynamical systems, optimal control problems and high accuracy orbit propagation in celestial mechanics

Dynamics of a 9-DOF Heterogeneous Robotic Platform for Spacecraft Motion Emulation

Increasing access to space has driven demand for low cost, portable, and highly specialized robotic platforms to accurately simulate multi-dimensional space missions. Presented is an effective heterogeneous robotic system that emulates orbital motion from given control algorithms. This robotic platform is composed of a three degrees of freedom (3-DOF) holonomic omni wheel ground vehicle carrying a 6-DOF robotic manipulator, which results in a 9-DOF coupled moving manipulator system. The dynamical models are derived and feedback linearization is studied to control the system. The integrated controls and hardware result in an a sophisticated in-lab system that will be scalable from orbital motion to execution of complex tasks, including spaceflight rendezvous and proximity operations, servicing missions, and surface exploration and sampling

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

A Simple and Accurate Apollo-Trained Neural Network Controller for Mars Atmospheric Entry

We present a new method to design the controller for Mars capsule atmospheric entry using deep neural networks and flight-proven Apollo entry data. The controller is trained to modulate the bank angle with data from the Apollo entry simulations. The neural network controller reproduces the classical Apollo results over a variation of entry state initial conditions. Compared to the Apollo controller as a baseline, the present approach achieves the same level of accuracy for both linear and nonlinear entry dynamics. The Apollo-trained controller is then applied to Mars entry missions. As in Earth environment, the controller achieves the desired level of accuracy for Mars missions using both linear and nonlinear entry dynamics with higher uncertainties in the entry states and the atmospheric density. The deep neural network is only trained with data from Apollo reentry simulation in an Earth model and works in both Earth and Mars environments. It achieves the desired landing accuracy for a Mars capsule. This method works with both linear and nonlinear integration and can generate the bank angle commands in real-time without a prestored trajectory

Novel Method In Uncertainty Quantification And Probability Of Collision For Space Objects

The state of a dynamical system and its uncertainty, as defined by its probability density function (PDF), are valuable for numerous fields in science and engineering. There have been numerous methods proposed to estimate and quantify this uncertainty. In as-trodynamics, space situational awareness (SSA) is a major area that relies on uncertainty quantification to estimate a space object’s state and its associated uncertainty. This data is invaluable for making informed decisions regarding probability of collision, tracking, and catalog maintenance. A new method for uncertainty quantification based on orthogonal polynomials and the application of Liouville’s theorem is developed. The method identifies the region of extreme probability at the time of interest and populates that region with structured points. The associated PDF is computed based on the a-priori PDF of the initial conditions and/or the nominal values of the system parameters (e.g. drag coefficient). High dimension orthogonal polynomials are used to approximate the PDF at the target time. Having an analytical expression for the propagated PDF enables rigorous probabilistic analysis. The present method is applied to several problems to compute the probability of collision between two objects. Numerical experiments show an order of magnitude improvement in computational cost versus classical Monte Carlo Methods. The new approach is easy to implement, extensible to higher dimensions, computationally efficient and provides a rigorous approach to address probability of collision problems in SSA

Investigating the Structure-Activity Relationship of Marine Polycyclic Batzelladine Alkaloids as Promising Inhibitors for SARS-CoV-2 Main Protease (Mpro)

Over a span of two years ago, since the emergence of the first case of the novel coronavirus (SARS-CoV-2) in China, the pandemic has crossed borders causing serious health emergencies, immense economic crisis and impacting the daily life worldwide. Despite the discovery of numerous forms of precautionary vaccines along with other recently approved orally available drugs, yet effective antiviral therapeutics are necessarily needed to hunt this virus and its variants. Historically, naturally occurring chemicals have always been considered the primary source of beneficial medications. Considering the SARS-CoV-2 main protease (Mpro) as the duplicate key element of the viral cycle and its main target, in this paper, an extensive virtual screening for a focused chemical library of 15 batzelladine marine alkaloids, was virtually examined against SARS-CoV-2 main protease (Mpro) using an integrated set of modern computational tools including molecular docking (MDock), molecule dynamic (MD) simulations and structure-activity relationships (SARs) as well. The molecular docking predictions had disclosed four promising compounds including batzelladines H-I (8-9) and batzelladines F-G (6-7), respectively according to their prominent ligand-protein energy scores and relevant binding affinities with the (Mpro) pocket residues. The best two chemical hits, batzelladines H-I (8-9) were further investigated thermodynamically though studying their MD simulations at 100 ns, where they showed excellent stability within the accommodated (Mpro) pocket. Moreover, SARs studies imply the crucial roles of the fused tricyclic guanidinic moieties, its degree of unsaturation, position of the N-OH functionality and the length of the side chain as a spacer linking between two active sites, which disclosed fundamental structural and pharmacophoric features for efficient protein-ligand interaction. Such interesting findings are greatly highlighting further in vitro/vivo examinations regarding those marine natural products (MNPs) and their synthetic equivalents as promising antivirals

The Beneficial Impact of Intraoperative Ultrasound on Resection Margin Status during Breast Conserving Surgery

Background. Surgical resection with clear surgical cut margins is the mainstay of managing malignant breast neoplasms. Multiple techniques have been suggested to enhance resection status during breast-conserving surgery (BCS), including intraoperative ultrasonography (IOUS). Herein, we conducted the current investigation to reveal the benefit of IOUS on the achievement of R0 resection. Patients and Methods. This retrospective investigation included 140 patients who underwent BCS. They were divided into two groups: the IOUS group (40 cases) and the control group (100 cases). Our primary objective was to determine the free resection margin status (R0). Results. Both study groups expressed statistically comparable demographic and clinical data. Additionally, histopathological examination revealed no significant difference between the two groups regarding the tumor type, stage, or grade. Nonetheless, the R0 resection margin was more frequently encountered in association with IOUS application (97.5% compared to 79% in the control group), and that difference was statistically significant (p=0.007). Conclusion. The application of IOUS has a significant beneficial impact on the outcomes of BCS. It is associated with a marked decline in positive resection margins, and its application should be encouraged in the breast oncological practice