Multi-stage Neural Networks: Function Approximator of Machine Precision

Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction errors below $O(10^{-5})$ even with large network size and extended training iterations. To address this issue, we developed the multi-stage neural networks that divides the training process into different stages, with each stage using a new network that is optimized to fit the residue from the previous stage. Across successive stages, the residue magnitudes decreases substantially and follows an inverse power-law relationship with the residue frequencies. The multi-stage neural networks effectively mitigate the spectral biases associated with regular neural networks, enabling them to capture the high frequency feature of target functions. We demonstrate that the prediction error from the multi-stage training for both regression problems and physics-informed neural networks can nearly reach the machine-precision $O(10^{-16})$ of double-floating point within a finite number of iterations. Such levels of accuracy are rarely attainable using single neural networks alone.Comment: 38 pages, 17 page

(4Z)-4-[(2,6-Diisopropyl­anilino)(phen­yl)methyl­idene]-3-methyl-1-phenyl-1H-pyrazol-5(4H)-one

In the title compound, C29H31N3O, the three terminal benzene rings are oriented at dihedral angles of 20.7 (3), 65.8 (3) and 72.6 (3)° with respect to the central pyrazolone ring. Intra­molecular N—H⋯O hydrogen bonding occurs between the imine and carbonyl groups. Inter­molecular C—H⋯π inter­actions are present in the crystal structure

Impact of Heavy Metals in Ambient Air in Insulin Resistance of Shipyard Welders in Northern Taiwan

Exposure to metals poses potential health risks, including insulin resistance (IR), to those exposed to them in excess. Limited studies have examined such risks in occupational workers, including welders, and these have yielded inconsistent results. Thus, we examined the associations between exposure to welding metals and IR in welders. We recruited 78 welders and 75 administrative staff from a shipyard located in northern Taiwan. Personal exposure to heavy metals, including chromium (Cr), manganese (Mn), iron (Fe), nickel (Ni), copper (Cu), zinc (Zn), and cadmium (Cd), was monitored through particulate matter with an aerodynamic diameter of less than 2.5 μm (PM2.5) and urine analysis by inductively coupled plasma mass spectrometry (ICP–MS). After each participant fasted overnight, blood samples were collected and analyzed for IR assessment through updated homeostasis model assessment (HOMA2) modeling. Air sampling in the personal breathing zone was performed during a Monday shift prior to the blood and urine sample collection the following morning. The welders’ median personal Cr, Mn, Fe, Ni, Cu, and Zn airborne PM2.5 levels and urinary Cd levels were significantly higher than those of the administrative staff. After adjustment for covariates, logarithmic PM2.5-Mn, PM2.5-Fe, PM2.5-Cu, and PM2.5-Zn levels were positively correlated with logarithmic fasting plasma glucose (P-FGAC) levels (PM2.5-Mn: β = 0.0105, 95% C.I.: 0.0027–0.0183; PM2.5-Fe: β = 0.0127, 95% C.I.: 0.0027–0.0227; PM2.5-Cu: β = 0.0193, 95% C.I.: 0.0032–0.0355; PM2.5-Zn: β = 0.0132, 95% C.I.: 0.0005–0.0260). Logarithmic urinary Zn was positively correlated with logarithmic serum insulin and HOMA2-IR levels and negatively correlated with logarithmic HOMA2-insulin sensitivity (%S; βinsulin = 0.2171, 95% C.I.: 0.0025–0.4318; βIR = 0.2179, 95% C.I.: 0.0027–0.4330; β%S = −0.2180, 95% C.I.: −0.4334 to −0.0026). We observed that glucose homeostasis was disrupted by Mn, Fe, Cu, and Zn exposure through increasing P-FGAC and IR levels in shipyard welders

Impact of body-mass factors on setup displacement in patients with head and neck cancer treated with radiotherapy using daily on-line image guidance

BACKGROUND: To determine the impact of body-mass factors (BMF) before radiotherapy and changes during radiotherapy on the magnitude of setup displacement in patients with head and neck cancer (HNC). METHODS: The clinical data of 30 patients with HNC was analyzed using the alignment data from daily on-line on-board imaging from image-guided radiotherapy. BMFs included body weight, body height, and the circumference and bilateral thickness of the neck. Changes in the BMFs during treatment were retrieved from cone beam computed tomography at the 10th and 20th fractions. Setup errors for each patient were assessed by systematic error (SE) and random error (RE) through the superior-inferior (SI), anterior-posterior (AP), and medial-lateral (ML) directions, and couch rotation (CR). Using the median values of the BMFs as a cutoff, the impact of the factors on the magnitude of displacement was assessed by the Mann–Whitney U test. RESULTS: A higher body weight before radiotherapy correlated with a greater AP-SE (p = 0.045), SI-RE (p = 0.023), and CR-SE (p = 0.033). A longer body height was associated with a greater SI-RE (p = 0.002). A performance status score of 1 or 2 was related to a greater AP-SE (p = 0.043), AP-RE (p = 0.015), and SI-RE (p = 0.043). Among the ratios of the BMFs during radiotherapy, the values at the level of mastoid tip at the 20(th) fraction were associated with greater setup errors. CONCLUSIONS: To reduce setup errors in patients with HNC receiving RT, the use of on-line image-guided radiotherapy is recommended for patients with a large body weight or height, and a performance status score of 1–2. In addition, adaptive planning should be considered for those who have a large reduction ratio in the circumference (<1) and thickness (<0.94) over the level of the mastoid tip during the 20(th) fraction of treatment

Investigation of a Photoelectrochemical Passivated ZnO-Based Glucose Biosensor

A vapor cooling condensation system was used to deposit high quality intrinsic ZnO thin films and intrinsic ZnO nanorods as the sensing membrane of extended-gate field-effect-transistor (EGFET) glucose biosensors. The sensing sensitivity of the resulting glucose biosensors operated in the linear range was 13.4 μA mM−1 cm−2. To improve the sensing sensitivity of the ZnO-based glucose biosensors, the photoelectrochemical method was utilized to passivate the sidewall surfaces of the ZnO nanorods. The sensing sensitivity of the ZnO-based glucose biosensors with passivated ZnO nanorods was significantly improved to 20.33 μA mM−1 cm−2 under the same measurement conditions. The experimental results verified that the sensing sensitivity improvement was the result of the mitigation of the Fermi level pinning effect caused by the dangling bonds and the surface states induced on the sidewall surface of the ZnO nanorods

Elastic stress coupling between supraglacial lakes

Supraglacial lakes have been observed to drain within hours of each other, leading to the hypothesis that stress transmission following one drainage may be sufficient to induce hydro-fracture-driven drainages of other nearby lakes. However, available observations characterizing drainage-induced stress perturbations have been insufficient to evaluate this hypothesis. Here, we use ice-sheet surface displacement observations from a dense global positioning system array deployed in the Greenland Ice Sheet ablation zone to investigate elastic stress transmission between three neighboring supraglacial lake basins. We find that drainage of a central lake can place neighboring basins in either tensional or compressional stress relative to their hydro-fracture scarp orientations, either promoting or inhibiting hydro-fracture initiation beneath those lakes. For two lakes located within our array that drain close in time, we identify tensional surface stresses caused by ice-sheet uplift due to basal-cavity opening as the physical explanation for these lakes’ temporally clustered, hydro-fracture-driven drainages and frequent triggering behavior. However, lake-drainage-induced stresses in the up-flowline direction remain low beyond the margins of the drained lakes. This short stress-coupling length scale is consistent with idealized lake-drainage scenarios for a range of lake volumes and ice-sheet thicknesses. Thus, on elastic timescales, our observations and idealized-model results support a stress-transmission hypothesis for inducing hydro-fracture-driven drainage of lakes located within the region of basal cavity opening produced by the initial drainage, but refute this hypothesis for distal lakes

Hydraulic transmissivity inferred from ice-sheet relaxation following Greenland supraglacial lake drainages

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Lai, C.-Y., Stevens, L. A., Chase, D. L., Creyts, T. T., Behn, M. D., Das, S. B., & Stone, H. A. Hydraulic transmissivity inferred from ice-sheet relaxation following Greenland supraglacial lake drainages. Nature Communications, 12(1), (2021): 3955, https://doi.org/10.1038/s41467-021-24186-6.Surface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye and gas-tracing studies conducted in the western margin sector of the ice sheet have directly observed drainage efficiency to evolve seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we infer drainage system transmissivity based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of-magnitude increase in subglacial transmissivity (from 0.8 ± 0.3 mm3 to 215 ± 90.2 mm3) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input.C.-Y.L. and L.A.S thank Lamont-Doherty Earth Observatory for funding through the Lamont Postdoctoral Fellowships. D.L.C acknowledges support from the National Science Foundation (NSF) Graduate Research Fellowship. T.T.C. was supported by NSF’s Office of Polar Programs (NSF-OPP) through OPP-1643970, the National Aeronautics and Space Administration (NASA) through NNX16AJ95G, and a grant from the Vetlesen Foundation. S.B.D. and M.D.B. acknowledge funding from NSF-OPP and NASA’s Cryospheric Sciences Program through OPP-1838410, ARC-1023364, ARC-0520077, and NNX10AI30G. H.A.S. thanks the High Meadows Environmental Institute and the Carbon Mitigation Initiative at Princeton University. This publication was supported by the Princeton University Library Open Access Fund