Physics-Informed Neural Networks for 2nd order ODEs with sharp gradients

In this work, four different methods based on Physics-Informed Neural Networks (PINNs) for solving Differential Equations (DE) are compared: Classic-PINN that makes use of Deep Neural Networks (DNNs) to approximate the DE solution;Deep-TFC improves the efficiency of classic-PINN by employing the constrained expression from the Theory of Functional Connections (TFC) so to analytically satisfy the DE constraints;PIELM that improves the accuracy of classic-PINN by employing a single-layer NN trained via Extreme Learning Machine (ELM) algorithm;X-TFC, which makes use of both constrained expression and ELM. The last has been recently introduced to solve challenging problems affected by discontinuity, learning solutions in cases where the other three methods fail. The four methods are compared by solving the boundary value problem arising from the 1D Steady-State Advection–Diffusion Equation for different values of the diffusion coefficient. The solutions of the DEs exhibit steep gradients as the value of the diffusion coefficient decreases, increasing the challenge of the problem

Composite xenohybrid bovine bone-derived scaffold as bone substitute for the treatment of tibial plateau fractures

Introduction: Tibial plateau fractures represent a common challenge for orthopaedic surgeons, sometimes representing complex cases to manage, where augmentation using bone grafts is required for stabilisation. Autologous iliac bone graft (AIBG) is the current gold standard for bone grafting. In order to overcome limitations related to the procedure, alternative strategies, like allogenic and xenogeneic bone substitutes have been investigated. Here, within the framework of an observational clinical study, we report clinical and radiological outcomes of patients treated for tibial plateau fractures with a composite xenohybrid bone graft, aiming at assessing clinical and radiological outcomes. Materials and Methods: We performed a cohort retrospective study of patients treated for tibial plateau fractures from May 2017 to January 2018. Thirty-four patients, i.e. 100% of those having received the bone graft under investigation for tibial plateaux fracture treatment, met the inclusion criteria and were enrolled in the study. Patients were assessed at 2 weeks, and then at a 1-, 3-, and 6-months, and 1-year follow-up. At each evaluation patients filled a visual analogue scale (VAS) for the level of pain during the day life activities and underwent physical exam and anteroposterior and lateral projection radiographs of the knee. At 1 year the Tegner Lysholm Scoring Scale, International Knee Document Committee 2000 (IKDC 2000), and Short Form (36) Health Survey (SF-36) were administered. Results: At 1-year, mean VAS decreased from 6.33 \ub1 1.40 to 1 \ub1 0.79 (P < 0.0001); Tegner Lysholm Scoring Scale was 89 \ub1 4.10 and mean IKDC 2000 was 78.67 \ub1 3.31. No infections, neurovascular complications or adverse effects related to implants werereported during the clinical exams at follow-up. Mean ROM was 124 \ub1 6\ub0. Radiographs did not show defects of consolidation or progressive post-surgical subsidence and demonstrated a good grade of integration of the implant. Conclusions: Clinical and radiological outcomes, and scores of questionnaires, were good. The xenograft has demonstrated to be a safe biomaterial, with satisfactory mechanical and biological performances in the mid-term period. It also showed a high grade of osteointegration and remodelling

Analysis and Performance Evaluation of the ZEM/ZEV Guidance and its Sliding Robustification for Autonomous Rendezvous in Relative Motion

Devising closed-loop guidance algorithms for autonomous relative motion is an important problem within the field of orbital dynamics. In this paper, we study the guided relative motion of two spacecraft for which one of them is executing an autonomous rendezvous via the ZEM/ZEV feedback guidance and its robustified Optimal Sliding Guidance (OSG) counterpart. Starting from the classical Clohessy-Wiltshire (CW) model, we systematically analyze the ability of the ZEM/ZEV feedback guidance to generate closed loop trajectories that drive the deputy spacecraft to the chief satellite and evaluate its performance in terms of target accuracy and propellant consumption. It is shown that the guidance gains and the time of flight predicted by the theoretical solution generates a class of feedback trajectories that are accurate but suboptimal with respect to the open-loop fuel-optimal solution. Indeed, a parametric study shows that a different set of gains may generate relative guided trajectories that yields fuel consumption closer to the ideal optimal. The guidance algorithms are also demonstrated to be accurate in guiding the relative motion of the deputy toward a chief spacecraft in highly elliptical orbit where the Linearized Equations of Relative Motions (LERM) are employed to compute the Zero-Effort-Miss (ZEM) and Zero-Effort-Velocity (ZEV) necessary to compute the acceleration command as prescribed by the theory

Automated Global Feature Analyzer - A Driver for Tier-Scalable Reconnaissance

For the purposes of space flight, reconnaissance field geologists have trained to become astronauts. However, the initial forays to Mars and other planetary bodies have been done by purely robotic craft. Therefore, training and equipping a robotic craft with the sensory and cognitive capabilities of a field geologist to form a science craft is a necessary prerequisite. Numerous steps are necessary in order for a science craft to be able to map, analyze, and characterize a geologic field site, as well as effectively formulate working hypotheses. We report on the continued development of the integrated software system AGFA: automated global feature analyzerreg, originated by Fink at Caltech and his collaborators in 2001. AGFA is an automatic and feature-driven target characterization system that operates in an imaged operational area, such as a geologic field site on a remote planetary surface. AGFA performs automated target identification and detection through segmentation, providing for feature extraction, classification, and prioritization within mapped or imaged operational areas at different length scales and resolutions, depending on the vantage point (e.g., spaceborne, airborne, or ground). AGFA extracts features such as target size, color, albedo, vesicularity, and angularity. Based on the extracted features, AGFA summarizes the mapped operational area numerically and flags targets of "interest", i.e., targets that exhibit sufficient anomaly within the feature space. AGFA enables automated science analysis aboard robotic spacecraft, and, embedded in tier-scalable reconnaissance mission architectures, is a driver of future intelligent and autonomous robotic planetary exploration

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

We use caustic beam shaping on 100 fs pulses to experimentally generate non-paraxial accelerating beams along a 60 degree circular arc, moving laterally by 14 \mum over a 28 \mum propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of non-paraxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic

Mass Loss From Calving in Himalayan Proglacial Lakes

The formation and expansion of Himalayan glacial lakes has implications for glacier dynamics, mass balance and glacial lake outburst floods (GLOFs). Subaerial and subaqueous calving is an important component of glacier mass loss but they have been difficult to track due to spatiotemporal resolution limitations in remote sensing data and few field observations. In this study, we used near-daily 3 m resolution PlanetScope imagery in conjunction with an uncrewed aerial vehicle (UAV) survey to quantify calving events and derive an empirical area–volume relationship to estimate calved glacier volume from planimetric iceberg areas. A calving event at Thulagi Glacier in 2017 was observed by satellite from before and during the event to nearly complete melting of the icebergs, and was observed in situ midway through the melting period, thus giving insights into the melting processes. In situ measurements of Thulagi Lake’s surface and water column indicate that daytime sunlight absorption heats mainly just the top metre of water, but this heat is efficiently mixed downwards through the top tens of metres due to forced convection by wind-blown icebergs; this heat then is retained by the lake and is available to melt the icebergs. Using satellite data, we assess seasonal glacier velocities, lake thermal regime and glacier surface elevation change for Thulagi, Lower Barun and Lhotse Shar glaciers and their associated lakes. The data reveal widely varying trends, likely signifying divergent future evolution. Glacier velocities derived from 1960/70s declassified Corona satellite imagery revealed evidence of glacier deceleration for Thulagi and Lhotse Shar glaciers, but acceleration at Lower Barun Glacier following lake development. We used published modelled ice thickness data to show that upon reaching their maximum extents, Imja, Lower Barun and Thulagi lakes will contain, respectively, about 90 × 106 , 62 × 106 and 5 × 106 m3 of additional water compared to their 2018 volumes. Understanding lake–glacier interactions is essential to predict future glacier mass loss, lake formation and associated hazards

Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light

We report the observation of arbitrary accelerating beams designed using a non-paraxial description of optical caustics. We use a spatial light modulator-based setup and techniques of Fourier optics to generate circular and Weber beams subtending over 95 degrees of arc. Applying a complementary binary mask also allows the generation of periodic accelerating beams taking the forms of snake-like trajectories, and the application of a rotation to the caustic allows the first experimental synthesis of optical accelerating beams upon the surface of a sphere in three dimensions.Comment: 4 pages, 4 figures articl

Realistic On-the-fly Outcomes of Planetary Collisions: Machine Learning Applied to Simulations of Giant Impacts

Planet formation simulations are capable of directly integrating the evolution of hundreds to thousands of planetary embryos and planetesimals as they accrete pairwise to become planets. In principle, these investigations allow us to better understand the final configuration and geochemistry of the terrestrial planets, and also to place our solar system in the context of other exosolar systems. While these simulations classically prescribe collisions to result in perfect mergers, recent computational advances have begun to allow for more complex outcomes to be implemented. Here we apply machine learning to a large but sparse database of giant impact studies, which allows us to streamline the simulations into a classifier of collision outcomes and a regressor of accretion efficiency. The classifier maps a four-dimensional (4D) parameter space (target mass, projectile-to-target mass ratio, impact velocity, impact angle) into the four major collision types: merger, graze-and-merge, hit-and-run, and disruption. The definition of the four regimes and their boundary is fully data-driven. The results do not suffer from any model assumption in the fitting. The classifier maps the structure of the parameter space and it provides insights into the outcome regimes. The regressor is a neural network that is trained to closely mimic the functional relationship between the 4D space of collision parameters, and a real-variable outcome, the mass of the largest remnant. This work is a prototype of a more complete surrogate model, that will be based on extended sets of simulations (big data), that will quickly and reliably predict specific collision outcomes for use in realistic N-body dynamical studies of planetary formation.NASA Planetary Science Division; University of ArizonaThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Performance of the galactomannan antigen detection test in the diagnosis of invasive aspergillosis in children with cancer or undergoing haemopoietic stem cell transplantation

AbstractSerum galactomannan (GM) antigen detection is not recommended for defining invasive aspergillosis (IA) in children undergoing aggressive chemotherapy or allogeneic haemopoietic stem cell transplantation (HSCT). The ability of the GM test to identify IA in children was retrospectively evaluated in a cohort of children. Test performance was evaluated on samples that were collected during 195 periods at risk of IA. Proven IA was diagnosed in seven periods, all with positive GM test results (true positives, 4%), and possible IA was diagnosed in 15 periods, all with negative GM test results (false negatives, 8%). The test result was positive with negative microbiological, histological and clinical features in three periods (false positives, 1%), and in 170 periods it was negative with negative microbiological, histological and clinical features (true negatives, 87%). The sensitivity was 0.32 and the specificity was 0.98; the positive predictive value was 0.70 and the negative predictive value was 0.92. The efficiency of the test was 0.91, the positive likelihood ratio was 18.3, and the negative likelihood ratio was 1.4. The probability of missing an IA because of a negative test result was 0.03. Test performance proved to be better during at-risk periods following chemotherapy than in periods following allogeneic HSCT. The GM assay is useful for identifying periods of IA in children undergoing aggressive chemotherapy or allogeneic HSCT