Bayesian Mass Averaging in Rigs and Engines

This paper introduces the Bayesian mass average and details its computation. Owing to the complexity of flow in an engine and the limited instrumentation and the precision of the sensor apparatus used, it is difficult to rigorously calculate mass averages. Building upon related work, this paper views any thermodynamic quantity's spatial variation at an axial plane in an engine (or a rig) as a Gaussian random field. In cases where the mass flow rate is constant in the circumferential direction but can be expressed via a polynomial or spline radially, this paper presents an analytical calculation of the Bayesian mass average. In cases where the mass flow rate itself can be expressed as a Gaussian random field, a sampling procedure is presented to calculate the Bayesian mass average. Examples of the calculation of the Bayesian mass average for temperature are presented, including with a real engine case study where velocity profiles are inferred from stagnation pressure measurements.

Investigating non-Gaussianity in Cosmic Microwave Background temperature maps using spherical harmonic phases

In the era of precision cosmology, accurate estimation of cosmological parameters is based upon the implicit assumption of the Gaussian nature of Cosmic Microwave Background (CMB) radiation. Therefore, an important scientific question to ask is whether the observed CMB map is consistent with Gaussian prediction. In this work, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2π] [1,2]. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP for a given ℓ mode and independence of nearby ℓ mode SHP. We performed our analysis on the scales limited by spherical harmonic modes ≤ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 α levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method, performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that SHP corresponding to some of the m-modes are non-uniform, some of the ℓ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps.

Altered Microstructure of Cerebral Gray Matter in Neuromyelitis Optica Spectrum Disorder-Optic Neuritis: A DKI Study

The purpose of this study was to analyze microstructural alterations in cerebral gray matter using non-Gaussian diffusion kurtosis imaging (DKI) in neuromyelitis optica spectrum disorder (NMOSD) patients with optic neuritis (NMOSD-ON). DKI was performed in 14 NMOSD-ON patients and 22 normal controls (NCs). DKI-derived metrics, including mean kurtosis (MK), radial kurtosis (RK), axial kurtosis (AK), fractional anisotropy (FA), and mean diffusivity (MD), were voxel-wisely compared by two-sample t-tests with gaussian random field (GRF) correction between the two groups. The correlations between altered DKI metrics and clinical features were analyzed. Compared with NCs, NMOSD-ON patients showed significantly decreased MK and RK both in the left inferior temporal gyrus (ITG), and decreased AK in the bilateral calcarine (CAL). While increased MD in the left fusiform gyrus (FFG), right CAL, and right hippocampus (HIP)/parahippocampal gyrus (PHG) were found. Furthermore, correlation analysis showed that mean deviation was negatively correlated with AK values of bilateral CAL and positively correlated with MD values of right CAL (q < 0.05, false discovery rate (FDR) corrected). For NMOSD-ON patients, microstructural abnormalities in the occipital visual cortex are correlated with clinical disability. These findings may provide complementary information to understand the neuropathological mechanisms underlying the impairments of cerebral gray matter in NMOSD-ON.

Supervised linear classification of Gaussian spatio-temporal data

In this article we focus on the problem of supervised classifying of the spatio-temporal Gaussian random field observation into one of two classes, specified by different mean parameters. The main distinctive feature of the proposed approach is allowing the class label to depend on spatial location as well as on time moment. It is assumed that the spatio-temporal covariance structure factors into a purely spatial component and a purely temporal component following AR(p) model. In numerical illustrations with simulated data, the influence of the values of spatial and temporal covariance parameters to the derived error rates for several prior probabilities models are studied.

Modelling the probability of capture for New Zealand's longfin eels ('Anguilla dieffenbachii') and shortfin eels ('Anguilla australis')

<p>Longfin eel and shortfin eel probability of capture models can be used to build probability of capture maps. These maps can help identify eel encounter hotspots in New Zealand and are useful for managing and conserving the species. This research models longfin eel and shortfin eel presence/absence data using regularized random forest (RRF) models, vectorautoregressive spatial-temporal (VAST) models and Bayesian Gaussian random field (GRaF) models. Probability of capture maps built under VAST and GRaF remain approximately consistent with the maps built under RRF models. That is, longfin eels have high probabilities of capture around the coast of New Zealand’s North Island and have low probabilities of capture throughout the centre of New Zealand’s South Island. Shortfin eels have high probabilities of capture in small isolated regions of New Zealand’s North Island and have very low probabilities of capture throughout most of New Zealand’s South Island. Cross validation and spatial cross validation was used to compare the models. Cross validation results show that, compared to RRF models, VAST models improve predictive accuracy for the longfin eel and shortfin eel. Whereas, GRaF only improves predictive performance for the longfin eel. However, spatial cross validation shows no significant difference between VAST and RRF models. Hence, VAST models have higher predictive accuracy than RRF models for the longfin eel and shortfin eel when the training set is spatially correlated to the test set.</p>

Modelling the probability of capture for New Zealand's longfin eels ('Anguilla dieffenbachii') and shortfin eels ('Anguilla australis')

<p>Longfin eel and shortfin eel probability of capture models can be used to build probability of capture maps. These maps can help identify eel encounter hotspots in New Zealand and are useful for managing and conserving the species. This research models longfin eel and shortfin eel presence/absence data using regularized random forest (RRF) models, vectorautoregressive spatial-temporal (VAST) models and Bayesian Gaussian random field (GRaF) models. Probability of capture maps built under VAST and GRaF remain approximately consistent with the maps built under RRF models. That is, longfin eels have high probabilities of capture around the coast of New Zealand’s North Island and have low probabilities of capture throughout the centre of New Zealand’s South Island. Shortfin eels have high probabilities of capture in small isolated regions of New Zealand’s North Island and have very low probabilities of capture throughout most of New Zealand’s South Island. Cross validation and spatial cross validation was used to compare the models. Cross validation results show that, compared to RRF models, VAST models improve predictive accuracy for the longfin eel and shortfin eel. Whereas, GRaF only improves predictive performance for the longfin eel. However, spatial cross validation shows no significant difference between VAST and RRF models. Hence, VAST models have higher predictive accuracy than RRF models for the longfin eel and shortfin eel when the training set is spatially correlated to the test set.</p>

Probabilistic Forecasts of Arctic Sea Ice Thickness

In recent decades, warming temperatures have caused sharp reductions in the volume of sea ice in the Arctic Ocean. Predicting changes in Arctic sea ice thickness is vital in a changing Arctic for making decisions about shipping and resource management in the region. We propose a statistical spatio-temporal two-stage model for sea ice thickness and use it to generate probabilistic forecasts up to three months into the future. Our approach combines a contour model to predict the ice-covered region with a Gaussian random field to model ice thickness conditional on the ice-covered region. Using the most complete estimates of sea ice thickness currently available, we apply our method to forecast Arctic sea ice thickness. Point predictions and prediction intervals from our model offer comparable accuracy and improved calibration compared with existing forecasts. We show that existing forecasts produced by ensembles of deterministic dynamic models can have large errors and poor calibration. We also show that our statistical model can generate good forecasts of aggregate quantities such as overall and regional sea ice volume. Supplementary materials accompanying this paper appear on-line.

Construction of elliptic stochastic partial differential equations solver in groundwater flow with convolutional neural networks

Elliptic stochastic partial differential equations (SPDEs) play an indispensable role in mathematics, engineering and other fields, and its solution methods emerge in endlessly with the progress of science and technology. In this paper, we make use of the convolutional neural networks (CNNs), which are widely used in machine learning, to construct a solver for SPDEs. The SPDEs with Neumann boundary conditions are considered, and two CNNs are employed. One is used to deal with the essential equation, and the other satisfies the boundary conditions. With the help of the length factor, the integrated neural network model can predict the solution of the equations accurately. We show an example of groundwater flow to evaluate the model proposed with Gaussian random field (GRF). The experimental results show that the proposed neural network solver can approximate the traditional numerical algorithm, and has high computational efficiency.