Constrained Differential Optimization

Many optimization models of neural networks need constraints to restrict the space of outputs to a subspace which satisfies external criteria. Optimizations using energy methods yield "forces" which act upon the state of the neural network. The penalty method, in which quadratic energy constraints are added to an existing optimization energy, has become popular recently, but is not guaranteed to satisfy the constraint conditions when there are other forces on the neural model or when there are multiple constraints. In this paper, we present the basic differential multiplier method (BDMM), which satisfies constraints exactly; we create forces which gradually apply the constraints over time, using "neurons" that estimate Lagrange multipliers. The basic differential multiplier method is a differential version of the method of multipliers from Numerical Analysis. We prove that the differential equations locally converge to a constrained minimum. Examples of applications of the differential method of multipliers include enforcing permutation codewords in the analog decoding problem and enforcing valid tours in the traveling salesman problem

Comparison of Risk of Recrudescent Fever in Children With Kawasaki Disease Treated With Intravenous Immunoglobulin and Low-Dose vs High-Dose Aspirin

Importance: Timely initiation of intravenous immunoglobulin plus aspirin is necessary for decreasing the risk of recrudescent fever and coronary artery abnormalities in children with Kawasaki disease (KD). The optimal dose of aspirin, however, remains unclear. Objective: To evaluate whether initial treatment with low-dose compared with high-dose aspirin in children with KD is associated with an increase in fever recrudescence. Design, Setting, and Participants: A retrospective cohort study of 260 children with KD at Riley Hospital for Children, Indianapolis, Indiana, between January 1, 2007, and December 31, 2018, was conducted. Children aged 0 to 18 years with a first episode of KD, identified by International Classification of Diseases, Ninth Revision and International Statistical Classification of Diseases and Related Health Problems, Tenth Revision diagnosis codes treated within 10 days of symptom onset with high-dose intravenous immunoglobulin plus aspirin were eligible. Patients who received an alternative diagnosis, experienced a second episode of KD, did not receive intravenous immunoglobulin plus aspirin for initial treatment, were not treated within 10 days of symptoms, or had incomplete records were excluded. Exposures: High-dose (≥10 mg/kg/d) or low-dose (<10 mg/kg/d) aspirin therapy. Main Outcomes and Measures: The primary outcome was recrudescent fever necessitating retreatment of KD. The secondary outcomes were coronary artery abnormalities and hospital length of stay. Results: Among the 260 patients included, the median (interquartile range) age was 2.5 (1.6-4.3) years, 103 (39.6%) were girls, 166 (63.8%) were non-Hispanic white, 57 (21.9%) were African American, 22 (8.5%) were Asian, 11 (4.2%) were Hispanic, and 4 (1.5%) were of unknown race/ethnicity. One hundred-forty-two patients (54.6%) were treated with low-dose aspirin. There was no association between recrudescent fever and aspirin dose, with 39 children (27.5%) having recrudescent fever in the low-dose group compared with 26 children (22.0%) in the high-dose group (odds ratio [OR], 1.34; 95% CI, 0.76-2.37; P = .31), with similar results after adjusting for potential confounding variables (OR, 1.63; 95% CI, 0.89-2.97; P = .11). In a subset analysis of 167 children with complete KD, however, there was nearly a 2-fold difference in the odds of recrudescent fever with low-dose aspirin (OR, 1.87; 95% CI, 0.82-4.23; P = .14), although this difference did not reach statistical significance. In addition, no association was identified between treatment group and coronary artery abnormalities (low-dose, 7.4% vs high-dose, 9.4%; OR, 0.86; 95% CI, 0.48-1.55; P = .62) or median (interquartile range) length of stay (3 [3-5] days for both groups; P = .27). Conclusions and Relevance: In this study, low-dose aspirin for the initial treatment of children with KD was not associated with fever recrudescence or coronary artery abnormalities. Given the potential benefits, further study of low-dose aspirin to detect potentially clinically relevant outcome differences is warranted to inform treatment decisions and guideline development

Optical properties of Southern Hemisphere aerosols: Report of the joint CSIRO/NASA study

This study was made in support of the LAWS and GLOBE programs, which aim to design a suitable Doppler lidar system for measuring global winds from a satellite. Observations were taken from 5 deg S to 45 deg S along and off the E and SE Australian coast, thus obtaining representative samples over a large latitude range. Observations were made between 0 and 6 km altitude of aerosol physical and chemical properties in situ from the CSIRO F-27 aircraft; of lidar backscatter coefficients at 10.6 micron wavelength from the F-27 aircraft; of lidar backscatter profiles at 0.694 microns at Sale, SE Australia; and of lidar backscatter profiles at 0.532 microns at Cowley Beach, NE Australia. Both calculations and observations in the free troposphere gave a backscatter coefficient of 1-2 x 10 to the -11/m/sr at 10.6 microns, although the accuracies of the instruments were marginal at this level. Equivalent figures were 2-8 x 10 to the -9/m/sr (aerosol) and 9 x 10 to the -9 to 2 x 10 to the -8/m/sr (lidar) at 0.694 microns wavelength at Sale; and 3.7 x 10 to the -9/m/sr (aerosol) and 10 to the -8 to 10 to the -7/m/sr (lidar) at 0.532 microns wavelength at Cowley Beach. The measured backscatter coefficients at 0.694 and 0.532 microns were consistently higher than the values calculated from aerosol size distributions by factors of typically 2 to 10

Analog Circuits for Constrained Optimization

This paper explores whether analog circuitry can adequately perform constrained optimization. Constrained optimization circuits are designed using the differential multiplier method. These circuits fulfill time-varying constraints correctly. Example circuits include a quadratic programming circuit and a constrained flip-flop

Sequential Threshold Circuits

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Time Scale for Rapid Draining of a Surficial Lake Into the Greenland Ice Sheet

A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial lake, of approximately 44×10^6 m^3, into the Greenland ice sheet over a time scale moderately longer than 1 hr. The lake had been instrumented to record the time-dependent fall of water level and the uplift of the ice nearby. Liquid water, denser than ice, was presumed to have descended through the sheet along a crevasse system and spread along the bed as a hydraulic facture. The event led two of the present authors to initiate modeling studies on such natural hydraulic fractures. Building on results of those studies, we attempt to better explain the time evolution of such a drainage event. We find that the estimated time has a strong dependence on how much a pre-existing crack/crevasse system, acting as a feeder channel to the bed, has opened by slow creep prior to the time at which a basal hydraulic fracture nucleates. We quantify the process and identify appropriate parameter ranges, particularly of the average temperature of the ice beneath the lake (important for the slow creep opening of the crevasse). We show that average ice temperatures 5–7  °C below melting allow such rapid drainage on a time scale which agrees well with the 2006 observations

HRTF Magnitude Synthesis via Sparse Representation of Anthropometric Features

International audienceWe propose a method for the synthesis of the magnitudes of Head-related Transfer Functions (HRTFs) using a sparse representation of anthropometric features.Our approach treats the HRTF synthesis problem as finding a sparse representation of the subject's anthropometric features w.r.t. the anthropometric features in the training set.The fundamental assumption is that the magnitudes of a given HRTF set can be described by the same sparse combination as the anthropometric data.Thus, we learn a sparse vector that represents the subject's anthropometric features as a linear superposition of the anthropometric features of a small subset of subjects from the training data.Then, we apply the same sparse vector directly on the HRTF tensor data.For evaluation purpose we use a new dataset, containing both anthropometric features and HRTFs.We compare the proposed sparse representation based approach with ridge regression and with the data of a manikin (which was designed based on average anthropometric data), and we simulate the best and the worst possible classifiers to select one of the HRTFs from the dataset.For instrumental evaluation we use log-spectral distortion.Experiments show that our sparse representation outperforms all other evaluated techniques, and that the synthesized HRTFs are almost as good as the best possible HRTF classifier