Fast Dynamic System Identification with Karhunen-Lo\`eve Decomposed Gaussian Processes

A promising approach for scalable Gausian processes (GPs) is the Karhunen-Lo\`eve (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a `Susceptible, Infected, Recovered' (SIR) toy problem, with the transmissibility used as forcing function, along with the experimental `Cascaded Tanks' benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with a number of basis set / optimizer combinations within the SINDy package

Measurement of the active width in Sr-doped lanthanum manganate Sofc Cathodes using Nano-ct, impedance spectroscopy and Bayesian calibration

Bayesian model-based analysis (BMA) is a method for producing quantitative models of complex physical systems through the comparison between models and experimental data. A model of a porous LSM cathode (symmetrical cell) was applied to impedance data and its parameters estimated via Bayesian calibration. X-ray computed tomography provided microstructural information for the model. The combination of model calibration and microstructural characterization enabled an estimate of the active thickness for a porous LSM electrode. The active width extended only a few nanometers from the surface, strongly suggesting that future models should explicitly resolve the space-charge region

Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling

The density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard correction to treat strongly correlated electronic states. Unfortunately, the values of the Hubbard U and J parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the U and J parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest U correction. PBE has the smallest standard deviation and its U and J parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction

The Universal One-Loop Effective Action

We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has been checked against partial results available in the literature. The broad applicability of this approach simplifies one-loop matching from an ultraviolet model to a lower-energy effective field theory (EFT), a procedure which is now reduced to the evaluation of a combination of matrices in our universal expression, without any loop integrals to evaluate. We illustrate the relationship of our results to the Standard Model (SM) EFT, using as an example the supersymmetric stop and sbottom squark Lagrangian and extracting from our universal expression the Wilson coefficients of dimension-six operators composed of SM fields.Comment: 30 pages, v2 contains additional comments and corrects typos, version accepted for publication in JHE

Habitat Assessment of Non-Wadeable Rivers in Michigan

Habitat evaluation of wadeable streams based on accepted protocols provides a rapid and widely used adjunct to biological assessment. However, little effort has been devoted to habitat evaluation in non-wadeable rivers, where it is likely that protocols will differ and field logistics will be more challenging. We developed and tested a non-wadeable habitat index (NWHI) for rivers of Michigan, where non-wadeable rivers were defined as those of order ≥5, drainage area ≥1600 km 2 , mainstem lengths ≥100 km, and mean annual discharge ≥15 m 3 /s. This identified 22 candidate rivers that ranged in length from 103 to 825 km and in drainage area from 1620 to 16,860 km 2 . We measured 171 individual habitat variables over 2-km reaches at 35 locations on 14 rivers during 2000–2002, where mean wetted width was found to range from 32 to 185 m and mean thalweg depth from 0.8 to 8.3 m. We used correlation and principal components analysis to reduce the number of variables, and examined the spatial pattern of retained variables to exclude any that appeared to reflect spatial location rather than reach condition, resulting in 12 variables to be considered in the habitat index. The proposed NWHI included seven variables: riparian width, large woody debris, aquatic vegetation, bottom deposition, bank stability, thalweg substrate, and off-channel habitat. These variables were included because of their statistical association with independently derived measures of human disturbance in the riparian zone and the catchment, and because they are considered important in other habitat protocols or to the ecology of large rivers. Five variables were excluded because they were primarily related to river size rather than anthropogenic disturbance. This index correlated strongly with indices of disturbance based on the riparian (adjusted R 2 = 0.62) and the catchment (adjusted R 2 = 0.50), and distinguished the 35 river reaches into the categories of poor (2), fair (19), good (13), and excellent (1). Habitat variables retained in the NWHI differ from several used in wadeable streams, and place greater emphasis on known characteristic features of larger rivers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41269/1/267_2004_Article_141.pd

Ultra-rare genetic variation in common epilepsies: a case-control sequencing study

BACKGROUND:Despite progress in understanding the genetics of rare epilepsies, the more common epilepsies have proven less amenable to traditional gene-discovery analyses. We aimed to assess the contribution of ultra-rare genetic variation to common epilepsies. METHODS:We did a case-control sequencing study with exome sequence data from unrelated individuals clinically evaluated for one of the two most common epilepsy syndromes: familial genetic generalised epilepsy, or familial or sporadic non-acquired focal epilepsy. Individuals of any age were recruited between Nov 26, 2007, and Aug 2, 2013, through the multicentre Epilepsy Phenome/Genome Project and Epi4K collaborations, and samples were sequenced at the Institute for Genomic Medicine (New York, USA) between Feb 6, 2013, and Aug 18, 2015. To identify epilepsy risk signals, we tested all protein-coding genes for an excess of ultra-rare genetic variation among the cases, compared with control samples with no known epilepsy or epilepsy comorbidity sequenced through unrelated studies. FINDINGS:We separately compared the sequence data from 640 individuals with familial genetic generalised epilepsy and 525 individuals with familial non-acquired focal epilepsy to the same group of 3877 controls, and found significantly higher rates of ultra-rare deleterious variation in genes established as causative for dominant epilepsy disorders (familial genetic generalised epilepsy: odd ratio [OR] 2·3, 95% CI 1·7-3·2, p=9·1 × 10-8; familial non-acquired focal epilepsy 3·6, 2·7-4·9, p=1·1 × 10-17). Comparison of an additional cohort of 662 individuals with sporadic non-acquired focal epilepsy to controls did not identify study-wide significant signals. For the individuals with familial non-acquired focal epilepsy, we found that five known epilepsy genes ranked as the top five genes enriched for ultra-rare deleterious variation. After accounting for the control carrier rate, we estimate that these five genes contribute to the risk of epilepsy in approximately 8% of individuals with familial non-acquired focal epilepsy. Our analyses showed that no individual gene was significantly associated with familial genetic generalised epilepsy; however, known epilepsy genes had lower p values relative to the rest of the protein-coding genes (p=5·8 × 10-8) that were lower than expected from a random sampling of genes. INTERPRETATION:We identified excess ultra-rare variation in known epilepsy genes, which establishes a clear connection between the genetics of common and rare, severe epilepsies, and shows that the variants responsible for epilepsy risk are exceptionally rare in the general population. Our results suggest that the emerging paradigm of targeting of treatments to the genetic cause in rare devastating epilepsies might also extend to a proportion of common epilepsies. These findings might allow clinicians to broadly explain the cause of these syndromes to patients, and lay the foundation for possible precision treatments in the future. FUNDING:National Institute of Neurological Disorders and Stroke (NINDS), and Epilepsy Research UK