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GNSS Reflectometry (GNSS-R) measurements are very sensitive to the presence of inland waters such as wetlands, floods, rivers and lakes. This paper reviews the basic characteristics of a GNSS-R ‘water detection’ product, including resolution and temporal sampling of wetlands, and discusses the main known sources of errors.
With the ongoing expansion of global observation networks, it is expected that we shall routinely analyze records of geophysical variables such as temperature from multiple collocated instruments. Validating datasets in this situation is not a trivial task because every observing system has its own bias and noise. Triple collocation is a general statistical framework to estimate the error characteristics in three or more observational-based datasets. In a triple colocation analysis, several metrics are routinely reported but traditional multiple-panel plots are not the most effective way to display information. A new formula of error variance is derived for connecting the key terms in the triple collocation theory. A diagram based on this formula is devised to facilitate triple collocation analysis of any data from observations, as illustrated using three aerosol optical depth datasets from the recent Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). An observational-based skill score is also derived to evaluate the quality of three datasets by taking into account both error variance and correlation coefficient. Several applications are discussed and sample plotting routines are provided.
Atomic force microscopy (AFM) is a versatile surface characterization method that can map a sample’s topography with high spatial resolution while simultaneously interrogating its surface chemistry through the site-specific high-resolution quantification of the forces acting between the sample and the probe tip. Thanks to considerable advances in AFM measurement technology, such local measurements of chemical properties have gained much popularity in recent years. To this end, dynamic AFM methodologies are implemented where either the oscillation frequency or the oscillation amplitude and phase of the vibrating cantilever are recorded as a function of tip-sample distance and subsequently converted to reflect tip-sample forces or interaction potentials. Such conversion has, however, been shown to produce non-negligible errors when applying the most commonly used mathematical conversion procedures if oscillation amplitudes are of the order of the decay length of the interaction. Extending on these earlier findings, the computational study presented in this paper reveals that the degree of divergence from actual values may also critically depend on both the overall strength of tip-sample interaction and the distance at which the interaction is obtained. These systematic errors can, however, be effectively eliminated by using oscillation amplitudes that are sufficiently larger than the decay length of the interaction potential.
An optimum adaptive delta modulator-demodulator configuration is derived. This device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov Gaussian source. The optimum system is compared using computer simulations with the linear delta modulator and an enhanced Abate delta modulator. In addition the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The results show that the output signal-to-noise ratio is independent of the input signal power and is subject only to the limitations of the hardware employed. In addition, voice was recorded using these systems. The demodulated voice indicates negligible degradation is caused by the optimum system and by the enhanced Abate system while the linear delta modulator suffers significant degradation at a sampling frequency of 56 kilobits/sec.
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.
High temperature solids and liquids are becoming increasingly important in next-generation energy and manufacturing systems that seek higher efficiencies and lower emissions. Accurate measurements of thermal conductivity at high temperatures are required for the modeling and design of these systems, but commonly employed time-domain measurements can have errors from convection, corrosion, and ambient temperature fluctuations. Here, we describe the development of a frequency-domain hot-wire technique capable of accurately measuring the thermal conductivity of solid and molten compounds from room temperature up to 800 °C. Therefore, by operating in the frequency-domain, we can lock into the harmonic thermal response of the material and reject the influence of ambient temperature fluctuations, and we can keep the probed volume below 1 µl to minimize convection. The design of the microfabricated hot-wire sensor, electrical systems, and insulating wire coating to protect against corrosion is covered in detail. Furthermore, we discuss the development of a full three-dimensional multilayer thermal model that accounts for both radial conduction into the sample and axial conduction along the wire and the effect of wire coatings. The 3D, multilayer model facilitates the measurement of small sample volumes important for material development. A sensitivity analysis and an error propagation calculation of the frequency-domain thermal model are performed to demonstrate what factors are most important for thermal conductivity measurements. Finally, we show thermal conductivity measurements including model data fitting on gas (argon), solid (sulfur), and molten substances over a range of temperatures.
We propose an algorithm for solving the problem of local error correction of the surface shape by a low-dimensional ion beam. The algorithm presumes successive sampling running over protrusions relative to the average height aimed at searching for the optimal etching point satisfying the criterion for the reduction of the sum of derivative moduli on the etching spot. It is shown that the new approach makes it possible to considerably extend the range of spatial frequencies accessible to the action for a given dimension of an ion beam.
ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.
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An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.
Ligand binding free energy simulations (LB-FES) that involve sampling of protein functional conformations have been longstanding challenges in research on molecular recognition. Particularly, modeling of the conformational transition pathway and design of the heuristic biasing mechanism are severe bottlenecks for the existing enhanced configurational sampling (ECS) methods. Inspired by the key role of hydration in regulating conformational dynamics of macromolecules, this report proposes a novel ECS approach that facilitates binding-associated structural dynamics by accelerated hydration transitions in combination with the lambda-exchange of free energy perturbation (FEP). Further, two challenging protein-ligand binding processes involving large configurational transitions of the receptor are studied, with hydration transitions at binding sites accelerated by Hamiltonian-simulated annealing of the hydration layer. Without the need for pathway analysis or ad hoc barrier flattening potential, LB-FES were performed with FEP/lambda-exchange molecular dynamics simulation at a minor overhead for annealing of the hydration layer. The LB-FES studies showed that the accelerated rehydration significantly enhances the collective conformational transitions of the receptor, and convergence of binding affinity calculations is obtained at a sweet-spot simulation time scale. Alchemical LB-FES with the proposed ECS strategy is free from the effort of trial and error for the setup and realizes efficient on-the-fly sampling for the collective functional response of the receptor and bound water and therefore presents a practical approach to high-throughput screening in drug discovery.
An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory. SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.
During the four years of this grant (including the one year extension), we have explored many aspects of the visualization of large CFD (Computational Fluid Dynamics) datasets. These have included new direct volume rendering approaches, hierarchical methods, volume decimation, error metrics, parallelization, hardware texture mapping, and methods for analyzing and comparing images. First, we implemented an extremely general direct volume rendering approach that can be used to render rectilinear, curvilinear, or tetrahedral grids, including overlapping multiple zone grids, and time-varying grids. Next, we developed techniques for associating the sample data with a k-d tree, a simple hierarchial data model to approximate samples in the regions covered by each node of the tree, and an error metric for the accuracy of the model. We also explored a new method for determining the accuracy of approximate models based on the light field method described at ACM SIGGRAPH (Association for Computing Machinery Special Interest Group on Computer Graphics) '96. In our initial implementation, we automatically image the volume from 32 approximately evenly distributed positions on the surface of an enclosing tessellated sphere. We then calculate differences between these images under different conditions of volume approximation or decimation.
We discuss the possibility of constraining cosmological parameters using the Sunyaev-Zel'dovich (SZ) effect and thermal bremsstrahlung caused by intra-cluster gas in clusters of galaxies. The new generation of X-ray satellites and ground based interferometers dedicated to SZ observations will enable one to reduce uncertainties in these measurements, and thus make this method potentially quite promising in the near future. The importance of this method is that, unlike most other methods, it is based on physical principles, no 'standard candles' or 'rulers' needed. We estimate the accuracy achievable in the determination of the matter density, OMEGA(sub m), the cosmological constant, OMEGA(sub LAMBDA), and the Hubble constant, h, using the redshift dependence of the angular diameter distance derived from observations in the near future. We demonstrate that constraints from the angular diameter distance are orthogonal to those from Cosmic Microwave Background (CMB) fluctuations in the parameter space defined by OMEGA(sub m), OMEGA(sub LAMBDA), and h. Assuming a statistical error of five percent in the angular diameter distance for each cluster in a sample of five hundred clusters, we show that the redshift dependence of the angular diameter distance combined with constraints from CMB fluctuations can put stringent constraints on OMEGA(sub m) (+/- 0.03), OMEGA(sub LAMBDA) (+/- 0.03) and h (+/- 0.03, 3(sigma) errors). We also show that, with as few as 50 clusters between redshifts 0.01 and 1.5 with an assumed 10% statistical error in the angular diameter distance determination, one can distinguish between models with zero cosmological constant and spatially flat models with a cosmological constant with high confidence level (independently from the supernova results) and put meaningful constraints on OMEGA(sub m) (+/- 0.01), OMEGA(sub LAMBDA) (+/- 0.01) and h (+/- 0.01, 3(sigma) errors). With the expected advances in observational technology, we will be limited by systematic errors. We discuss the sources of systematic errors and how they can be reduced.
With increasing demands for ocean color (OC) products with improved accuracy and well characterized, per-retrieval uncertainty budgets, it is vital to decompose overall estimated errors into their primary components. Amongst various contributing elements (e.g., instrument calibration, atmospheric correction, inversion algorithms) in the uncertainty of an OC observation, less attention has been paid to uncertainties associated with spatial sampling. In this paper, we simulate MODIS (aboard both Aqua and Terra) and VIIRS OC products using 30 m resolution OC products derived from the Operational Land Imager (OLI) aboard Landsat-8, to examine impacts of spatial sampling on both cross-sensor product intercomparisons and in-situ validations of R(sub rs) products in coastal waters. Various OLI OC products representing different productivity levels and in-water spatial features were scanned for one full orbital-repeat cycle of each ocean color satellite. While some view-angle dependent differences in simulated Aqua-MODIS and VIIRS were observed, the average uncertainties (absolute) in product intercomparisons (due to differences in spatial sampling) at regional scales are found to be 1.8%, 1.9%, 2.4%, 4.3%, 2.7%, 1.8%, and 4% for the R(sub rs)(443), R(sub rs)(482), R(sub rs)(561), R(sub rs)(655), Chla, K(sub d)(482), and b(sub bp)(655) products, respectively. It is also found that, depending on in-water spatial variability and the sensor's footprint size, the errors for an in-situ validation station in coastal areas can reach as high as +/- 18%. We conclude that a) expected biases induced by the spatial sampling in product intercomparisons are mitigated when products are averaged over at least 7 km × 7 km areas, b) VIIRS observations, with improved consistency in cross-track spatial sampling, yield more precise calibration/validation statistics than that of MODIS, and c) use of a single pixel centered on in-situ coastal stations provides an optimal sampling size for validation efforts. These findings will have implications for enhancing our understanding of uncertainties in ocean color retrievals and for planning of future ocean color missions and the associated calibration/validation exercises.
Three fragments of holocrystalline igneous rocks of the gabbro type, weighing 30 to 50 mg each, were investigated. The density of the fragments was established with a mercury pycnometer and was found to be 3.05 to 3.12 g/cu cm, with a relative error not more than 2 percent. The porosity was found for the difference between the volumes determined with the mercury and with the gas techniques; for all three samples together it was 13 percent, and the error of determination was 70 percent owing to the small volumes. It can be anticipated that the porosity of the rock in bulk will be higher than the value obtained based on small fragments. The porosity of lunar rocks can markedly affect the isostatic distribution of rocks and must be taken into account when developing models of lunar structure.
Second-order photon correlation measurements [g (2) (τ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of g (2) (τ = 0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g (2) (τ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g (2) (τ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g (2) (τ = 0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g (2) (τ) functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g (2) (τ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. Furthermore, this work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.
The subcarrier demodulation digital loop is part of the baseband assembly. The subcarrier demodulator is a fourth-order Costas-type loop corresponding to a type 2 analog loop in terms of steady state response. The expected value and the variance of the error signal are determined as functions of the input SNR. A Nyquist sampling rate of the input signal is assumed. From the integro-difference equations a mixed s/z domain block diagram is obtained. From the loop's transfer function a set of gains for the loop filter is obtained. Also, a set of state equations is presented for future reference. Finally, the noise-equivalent bandwidths are calculated for normalized computation times of 0, 0.25 and 0.5. The subcarrier demodulator analyzed tracks a parabolic phase input with finite steady state error. Since at each update instant the loop gains are adjusted to compensate for the variations in SNR of the input signal, the noise-equivalent bandwidth is maintained constant.