Ensemble Space Research Articles

Development and Validation of NOAA’s 20-Year Global Wave Ensemble Reforecast

Abstract A new 20-yr wave reforecast was generated based on the NOAA Global Ensemble Forecast System, version 12 (GEFSv12). It was produced using the same wave model setup as the NCEP’s operational GEFSv12 wave component, which employs the numerical wave model WAVEWATCH III and utilizes three grids with spatial resolutions of 0.2° and 0.25°. The reforecast comprises five members with 1 cycle per day and a forecast range of 16 days. Once a week, it expands to 35 days and 11 members. This paper describes the development of the wave ensemble reforecast, focusing primarily on validation against buoys and altimeters. The statistical analyses demonstrated very good performance in the short range for significant wave height, with correlation coefficients of 0.95–0.96 on day 1 and between 0.86 and 0.88 within week 1, along with bias close to zero. After day 10, correlation coefficients fall below 0.70. We found that the degradation of predictability and the increase in scatter errors predominantly occur in the forecast lead time between days 4 and 10, in terms of the ensemble mean and individual members, including the control. For week 2 and beyond, a probabilistic spatiotemporal analysis of the ensemble space provides useful forecast guidance. Our results provide a framework for expanding the usefulness of wave ensemble data in operational forecasting applications.

Condensates of magnetoexcitations in quantum Hall dielectrics

The formation and spreading in real space of dense ensembles of photoexcitations in integer and fractional quantum Hall dielectrics with filling factors ν = 2 and ν = 1/3 is visualized using a high-aperture high-resolution optical system. A comparative analysis of the correlation between the transport properties and the spatial coherence of these ensembles is carried out.

Dynamical Gaussian, lognormal, and reverse lognormal maximum‐likelihood ensemble filter

AbstractWe present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve.

Condensates of the Magnetoexcitations in Quantum Hall Dielectrics

A high-resolution large-aperture optical system is used to visualize the formation and spreading in real space of dense photoexcitation ensembles in integer and fractional quantum Hall dielectrics at filling factors ν = 2 and ν = 1/3. A comparative analysis is performed of the correlation between the transport properties and spatial coherence of these ensembles.

The logic of recurrent circuits in the primary visual cortex

Recurrent cortical activity sculpts visual perception by refining, amplifying or suppressing visual input. However, the rules that govern the influence of recurrent activity remain enigmatic. We used ensemble-specific two-photon optogenetics in the mouse visual cortex to isolate the impact of recurrent activity from external visual input. We found that the spatial arrangement and the visual feature preference of the stimulated ensemble and the neighboring neurons jointly determine the net effect of recurrent activity. Photoactivation of these ensembles drives suppression in all cells beyond 30 µm but uniformly drives activation in closer similarly tuned cells. In nonsimilarly tuned cells, compact, cotuned ensembles drive net suppression, while diffuse, cotuned ensembles drive activation. Computational modeling suggests that highly local recurrent excitatory connectivity and selective convergence onto inhibitory neurons explain these effects. Our findings reveal a straightforward logic in which space and feature preference of cortical ensembles determine their impact on local recurrent activity.

Updating catastrophe models to today’s climate – An application of a large ensemble approach to extreme rainfall

As climate change unfolds, extreme weather events and natural hazards relevant for the insurance industry may change in frequency and intensity. In order to guarantee risk-adequate pricing, risk modelers have to ask themselves the question whether a certain ‘hazard’ parameter based on past observations and calibrated on past data is still valid or needs to be updated. Using the example of heavy rainfall between 3 h and 72 h as a proxy for flash flooding, we apply a unique high-resolution single model initial-condition large ensemble. We outline a methodology by which risk modelers can assess whether, where and by how much updating the hazard component of their risk model is needed. Therefore, we compare two time periods: 1980–1999 (as an example for a typical baseline period) and 2015–2034 (representing a 20-year period centered around today). We argue that assessing changes over the full ensemble space is vital for (i) the identification of homogeneous regions where a certain signal emerges, and (ii) the quantification of risk changes in the tail of the extreme value distribution that may still be hidden in the mean response to climate change. In the example case of 3-hourly 50-year rainfall return levels, we find a significant increase between 1980 and 1999 and 2015–2034 over 44 % of European land area. We also identify specific risk regions such as northwestern Spain where changes in the very tail (100-year rainfall return level) already emerge before more common extremes (1-year rainfall return level). Failing to detect and consider these tail changes or assuming equal changes for common and rare extremes may therefore lead to an under- or overestimation of the true level of risk today.

Differential evolution ensemble designer

A meta-evolutionary framework called Differential Evolution Ensemble Designer (DEED) has been proposed in this paper to automate the design of DE ensemble algorithms. Given the design components of DE ensembles and a set of optimization problems, DEED evolves effective and robust DE ensemble designs. The design components of DE ensemble algorithms include population management, constituent algorithms in the ensemble, information mixing amongst the sub-populations in the ensemble and the numerical parameters associated with various aspects of the ensemble. DEED employs Dynamic Structured Grammatical Evolution (DSGE) as the meta-evolutionary algorithm. A Backus–Naur form (BNF) grammar has been developed in this paper to represent the design space of DE ensembles and used by DSGE to evolve DE ensemble designs. DEED has been employed to evolve DE ensemble designs for solving 30-dimensional CEC’17 benchmark functions. The evolved designs (both the best design as well as all the final evolved designs) have been validated on CEC’14 and CEC’17 functions at 10, 30 and 50 dimensions and on real-world numerical optimization problems in CEC’11 benchmark suite. The DEED evolved designs have also been tested against the state-of-the-art algorithm configurator - irace. The performance of DEED evolved ensemble designs have been observed to be very competitive against that of manually designed and tuned state-of-the-art DE ensemble algorithms in the literature. DEED has also been demonstrated to evolve both co-operative and competitive style DE ensembles. The simulation experiments demonstrate the effectiveness as well as robustness of the evolved ensemble designs and the reliability of DEED framework in consistently evolving effective DE ensemble designs.

Using orthogonal vectors to improve the ensemble space of the ensemble Kalman filter and its effect on data assimilation and forecasting

Abstract. The space spanned by the background ensemble provides a basis for correcting forecast errors in the ensemble Kalman filter. However, the ensemble space may not fully capture the forecast errors due to the limited ensemble size and systematic model errors, which affect the assimilation performance. This study proposes a new algorithm to generate pseudomembers to properly expand the ensemble space during the analysis step. The pseudomembers adopt vectors orthogonal to the original ensemble and are included in the ensemble using the centered spherical simplex ensemble method. The new algorithm is investigated with a six-member ensemble Kalman filter implemented in the 40-variable Lorenz model. Our results suggest that the ensemble singular vector, the ensemble mean vector, and their orthogonal components can serve as effective pseudomembers for improving the analysis accuracy, especially when the background has large errors.

How sequence alterations enhance the stability and delay expansion of DNA triplet repeat domains

Abstract DNA sequence alterations within DNA repeat domains inexplicably enhance the stability and delay the expansion of interrupted repeat domains. Here we propose mechanisms that rationalise such unanticipated outcomes. Specifically, we describe how interruption of a DNA repeat domain restricts the ensemble space available to dynamic, slip out, repeat bulge loops by introducing energetic barriers to loop migration. We explain how such barriers arise because some possible loop isomers result in energetically costly mismatches in the duplex portion of the repeat domain. We propose that the reduced ensemble space is the causative feature for the observed delay in repeat DNA expansion. We further posit that the observed loss of the interrupting repeat in some expanded DNAs reflects the transient occupation of loop isomer positions that result in a mismatch in the duplex stem due to ‘leakiness’ in the energy barrier. We propose that if the lifetime of such a low probability event allows for recognition by the mismatch repair system, then ‘repair’ of the repeat interruption can occur; thereby rationalising the absence of the interruption in the final expanded DNA ‘product.’ Our proposed mechanistic pathways provide reasoned explanations for what have been described as ‘puzzling’ observations, while also yielding insights into a biomedically important set of coupled genotypic phenomena that map the linkage between DNA origami thermodynamics and phenotypic disease states.

Forecasting mortality rates with a coherent ensemble averaging approach

AbstractModeling and forecasting of mortality rates are closely related to a wide range of actuarial practices, such as the designing of pension schemes. To improve the forecasting accuracy, age coherence is incorporated in many recent mortality models, which suggests that the long-term forecasts will not diverge infinitely among age groups. Despite their usefulness, misspecification is likely to occur for individual mortality models when applied in empirical studies. The reliableness and accuracy of forecast rates are therefore negatively affected. In this study, an ensemble averaging or model averaging (MA) approach is proposed, which adopts age-specific weights and asymptotically achieves age coherence in mortality forecasting. The ensemble space contains both newly developed age-coherent and classic age-incoherent models to achieve the diversity. To realize the asymptotic age coherence, consider parameter errors, and avoid overfitting, the proposed method minimizes the variance of out-of-sample forecasting errors, with a uniquely designed coherent penalty and smoothness penalty. Our empirical data set include ten European countries with mortality rates of 0–100 age groups and spanning 1950–2016. The outstanding performance of MA is presented using the empirical sample for mortality forecasting. This finding robustly holds in a range of sensitivity analyses. A case study based on the Italian population is finally conducted to demonstrate the improved forecasting efficiency of MA and the validity of the proposed estimation of weights, as well as its usefulness in actuarial applications such as the annuity pricing.

Integral correction of initial and model errors in system of multigrid NLS‐4DVar data assimilation for numerical weather prediction (SNAP)

AbstractModel error has a marked influence on forecast error, and integral correction of the initial and model errors in a novel four‐dimensional variational data assimilation (4DVar) method (i4DVar) has recently been developed. Unlike traditional 4DVar, in which the analysis increment focuses only on the initial time point, i4DVar introduces an averaged integral correction term to correct the error evolution at multiple times with the same time interval in the assimilation window; that is, the assimilation window is divided into several sub‐windows. In this study, we incorporated i4DVar into the System of Multigrid Nonlinear Least‐squares‐4DVar Data Assimilation for Numerical Weather Prediction (NWP) (SNAP), hereafter referred to as SN‐i4DVar, and explored its impacts on NWP. The effectiveness and performance of SN‐i4DVar were evaluated using two extreme rainstorm cases assimilating conventional and satellite observations, respectively. The results indicated that integral correction of the initial and model errors reduced analysis error and forecast error growth rates. SN‐i4DVar performed better in precipitation forecasting than the original SNAP and exhibited generally better forecasting capability in terms of the horizontal wind speed (u and v), temperature, and humidity variables, indicating that SN‐i4DVar simultaneously countered initial model errors to improve NWP capability. Meanwhile, the 4DEnVar method, which considers the optimal analysis in the ensemble space, benefits from the improved ensemble space generated according to the formulas of i4DVar, and the observation information can be more effectively absorbed and a more accurate analysis can be obtained by SN‐i4DVar.

New impact diagnostics for cross‐validation of different observation types

AbstractNew cross‐validation diagnostics have been derived by further partitioning well‐established impact diagnostics. They are related to consistency relations, the most prominent of which indicates whether the first‐guess departures of a given observation type pull the model state into the direction of the verifying data (when processed with the ensemble estimated model error covariances). Alternatively, this can be regarded as cross‐validation between model error covariance estimates from the ensemble (which are used in the data assimilation system) and estimates diagnosed directly from the observations. A statistical cross‐validation tool has been developed that includes an indicator of statistical significance as well as a normalization that makes the statistical comparison largely independent from the total number of data and the closeness of their collocation. We also present a version of these diagnostics related to single‐observation experiments that exploits the same consistency relations but is easier to compute. Diagnostics computed within the Deutscher Wetterdienst's localized ensemble transform Kalman filter (LETKF) are presented for various kinds of bins. Results from well‐established in‐situ measurements are taken as a benchmark for more complex observations. Good agreement is found for radio‐occultation bending angle measurements, whereas atmospheric motion vectors are generally also beneficial but substantially less optimal than the corresponding in‐situ measurements. This is consistent with reported atmospheric motion vector height assignment problems. To illustrate its potential, a recent example is given where the method allowed identifying bias problems of a subgroup of aircraft measurements.Another diagnostic relationship compares the information content of the analysis increments with a theoretical optimum. From this, the information content of the LETKF increments is found to be considerably lower than those of the deterministic hybrid ensemble–variational system, which is consistent with the LETKF's limitation to the comparably low‐dimensional ensemble space for finding the optimal analysis.

Allosteric Binding of MDMA to the Human Serotonin Transporter (hSERT) via Ensemble Binding Space Analysis with ΔG Calculations, Induced Fit Docking and Monte Carlo Simulations.

Despite the recent promising results of MDMA (3,4-methylenedioxy-methamphetamine) as a psychotherapeutic agent and its history of misuse, little is known about its molecular mode of action. MDMA enhances monoaminergic neurotransmission in the brain and its valuable psychoactive effects are associated to a dual action on the 5-HT transporter (SERT). This drug inhibits the reuptake of 5-HT (serotonin) and reverses its flow, acting as a substrate for the SERT, which possesses a central binding site (S1) for antidepressants as well as an allosteric (S2) one. Previously, we characterized the spatial binding requirements for MDMA at S1. Here, we propose a structure-based mechanistic model of MDMA occupation and translocation across both binding sites, applying ensemble binding space analyses, electrostatic complementarity, and Monte Carlo energy perturbation theory. Computed results were correlated with experimental data (r = 0.93 and 0.86 for S1 and S2, respectively). Simulations on all hSERT available structures with Gibbs free energy estimations (ΔG) revealed a favourable and pervasive dual binding mode for MDMA at S2, i.e., adopting either a 5-HT or an escitalopram-like orientation. Intermediate ligand conformations were identified within the allosteric site and between the two sites, outlining an internalization pathway for MDMA. Among the strongest and more frequent interactions were salt bridges with Glu494 and Asp328, a H-bond with Thr497, a π-π with Phe556, and a cation-π with Arg104. Similitudes and differences with the allosteric binding of 5-HT and antidepressants suggest that MDMA may have a distinctive chemotype. Thus, our models may provide a framework for future virtual screening studies and pharmaceutical design and to develop hSERT allosteric compounds with a unique psychoactive MDMA-like profile.

Rotational Spectroscopy of 2-Furoic Acid and Its Dimer: Conformational Distribution and Double Proton Tunneling.

Structural and tunneling properties of the 2-furoic acid (FA) monomer and dimer were investigated using rotational spectroscopy and DFT calculations. CREST, a conformational ensemble space exploration tool, was used to identify all possible low-energy conformations of the FA monomer and dimer, followed by the DFT geometry optimization and harmonic frequency calculations. Broadband rotational spectra in the 2-6 and 8-12 GHz regions were recorded in a supersonic jet expansion. The monomeric FA was found to exist dominantly as three different conformers: I, II, and III in a jet, with I and II taking on the cis-COOH configuration while III having the trans-COOH configuration. For the FA dimer, only the I-II conformer was observed experimentally, whereas the symmetric I-I and II-II conformers were not observed because of their zero dipole moments. The analysis of the splittings in the rotational transitions of I-II allowed one to extract the tunneling splitting to be 1056.0(12) MHz. The barrier height was determined to be ∼442 cm-1 using the scaled potential energy scans at several different levels of theory.

Stochastic Collocation Introduction Into Correlation Functions Method Applied for Underground Objects Detection

A method of space ensemble (SE) and time ensemble (TEs) correlation function technique applied on ground penetration radar (GPR) B-scan raw data proves to result in detailed information for tracking buried objects. These computations help in site allocations by time ensemble correlation functions (TESCs) and time stamps of objects scattering by space ensemble correlation functions (SECFs) which are precisely consistent with the simulation results. While these results are applied for given data stack, randomness in physical parameters of tested ground always occurs. An introduction of randomness to the physical parameters of tested models by creating stochastic collocation (SC) ensembles incorporating randomness to B-scan via successive A-scans, SC-SE, and SC-TE ensembles enables sensitivity analysis (SA) study of GPR raw data which gives a tool to change the physical properties of the ground in search for better ground matching. This method can be added to GPR machines or simulation software to enhance raw data analysis. A field experiment of small non-metallic objects’ allocation was carried out as a platform for assessing the realistic performance of the method.

Ensemble completeness in conformer sampling: the case of small macrocycles

In this study we compare the three algorithms for the generation of conformer ensembles Biovia BEST, Schrödinger Prime macrocycle sampling (PMM) and Conformator (CONF) form the University of Hamburg, with ensembles derived for exhaustive molecular dynamics simulations applied to a dataset of 7 small macrocycles in two charge states and three solvents. Ensemble completeness is a prerequisite to allow for the selection of relevant diverse conformers for many applications in computational chemistry. We apply conformation maps using principal component analysis based on ring torsions. Our major finding critical for all applications of conformer ensembles in any computational study is that maps derived from MD with explicit solvent are significantly distinct between macrocycles, charge states and solvents, whereas the maps for post-optimized conformers using implicit solvent models from all generator algorithms are very similar independent of the solvent. We apply three metrics for the quantification of the relative covered ensemble space, namely cluster overlap, variance statistics, and a novel metric, Mahalanobis distance, showing that post-optimized MD ensembles cover a significantly larger conformational space than the generator ensembles, with the ranking PMM > BEST >> CONF. Furthermore, we find that the distributions of 3D polar surface areas are very similar for all macrocycles independent of charge state and solvent, except for the smaller and more strained compound 7, and that there is also no obvious correlation between 3D PSA and intramolecular hydrogen bond count distributions.

Conformational Landscape, Chirality Recognition and Chiral Analyses: Rotational Spectroscopy of Tetrahydro-2-Furoic Acid⋅⋅⋅Propylene Oxide Conformers.

A chiral adduct formed between a chiral carboxylic acid, tetrahydro-2-furoic acid (THFA), and a chiral ester, propylene oxide (PO), was investigated using rotational spectroscopy and DFT calculations. Isolated THFA exists dominantly as three different conformers: I, II, and III in a jet, with I and II taking on the trans-COOH configuration and III having the cis-COOH configuration. We utilized CREST, a conformational ensemble space exploration tool, to identify the possible conformations of the binary adduct, THFA⋅⋅⋅PO. Subsequent DFT geometry optimizations predicted about two hundred homochiral and heterochiral binary structures with 28 low energy structures within an energy window of 15 kJ mol-1 . A rich broadband rotational spectrum was obtained with a mixture of trace amounts of THFA+PO in neon in a supersonic jet expansion. Six THFA⋅⋅⋅PO conformers were identified experimentally. Kinetically favored binary products which contain trans-COOH I dominate among the observed conformers, while thermodynamically more stable adducts were also detected. Detailed analyses of the structures of the observed conformers show interesting chirality-controlled structural preferences. Such non-covalently bound chiral contact pairs are the foundation of chiral-tag rotational spectroscopy, an exciting new analytical application of rotational spectroscopy for determination of enantiomeric excess. Enantiomeric excess analyses were performed and the results are discussed.

Tightness of Bernoulli Gibbsian line ensembles

A Bernoulli Gibbsian line ensemble $\mathfrak{L} = (L_1, \dots, L_N)$ is the law of the trajectories of $N-1$ independent Bernoulli random walkers $L_1, \dots, L_{N-1}$ with possibly random initial and terminal locations that are conditioned to never cross each other or a given random up-right path $L_N$ (i.e. $L_1 \geq \cdots \geq L_N$). In this paper we investigate the asymptotic behavior of sequences of Bernoulli Gibbsian line ensembles $\mathfrak{L}^N = (L^N_1, \dots, L^N_N)$ when the number of walkers $N$ tends to infinity. We prove that if one has mild but uniform control of the one-point marginals of the lowest-indexed (or top) curves $L_1^N$ then the sequence $\mathfrak{L}^N$ is tight in the space of line ensembles. Furthermore, we show that if the top curves $L_1^N$ converge in the finite dimensional sense to the parabolic Airy$_2$ process then $\mathfrak{L}^N$ converge to the parabolically shifted Airy line ensemble.

Adaptive steered molecular dynamics of biomolecules

ABSTRACT Adaptive steered molecular dynamics (ASMD) is a variant of steered molecular dynamics (SMD) in which the driving of the auxiliary – viz steered – particle is performed in stages. In SMD, many nonequilibrium trajectories are generated allowing for fast sampling of the ensemble space and access to rare events. Equilibrium observables, such as the potential of mean force along the pathway, result from averaging over these trajectories using Jarzynski's Equality (JE). Unfortunately, in SMD, a large number of trajectories are needed to cover all possible configurations in order to obtain converged quantities in the exponential average of the JE, and this is computationally expensive. ASMD reduces the number of trajectories that must be sampled by discarding those trajectories that have deviated far from the equilibrium path in stages. At the end of a stage, one chooses – or contracts – one (in naïve ASMD) or some (in multi-branched ASMD or MB-ASMD) of the configurations produced from the previous stage to initiate the trajectories in the next stage. Alternatively, in full-relaxation ASMD (FR-ASMD), all generated structures are relaxed under the constraint of a fixed auxiliary particle exerting no net work on the system. We provide a direct comparison of the energetics and other observables obtained from these approaches. We find that FR-ASMD is preferred when the unfolding pathways follow up along a single funnel and the system is sufficiently small that computational resources are not a limiting concern. It gives the highest accuracy in such cases while avoiding the inefficiencies of SMD. However, for complex energy landscapes typical of most multi-domain proteins, MB-ASMD is preferred because it provides a mechanism to sample alternative pathways while suffering only a modest loss in accuracy compared to FR-ASMD.

GrpClassifierEC: a novel classification approach based on the ensemble clustering space

BackgroundAdvances in molecular biology have resulted in big and complicated data sets, therefore a clustering approach that able to capture the actual structure and the hidden patterns of the data is required. Moreover, the geometric space may not reflects the actual similarity between the different objects. As a result, in this research we use clustering-based space that convert the geometric space of the molecular to a categorical space based on clustering results. Then we use this space for developing a new classification algorithm.ResultsIn this study, we propose a new classification method named GrpClassifierEC that replaces the given data space with categorical space based on ensemble clustering (EC). The EC space is defined by tracking the membership of the points over multiple runs of clustering algorithms. Different points that were included in the same clusters will be represented as a single point. Our algorithm classifies all these points as a single class. The similarity between two objects is defined as the number of times that these objects were not belong to the same cluster. In order to evaluate our suggested method, we compare its results to the k nearest neighbors, Decision tree and Random forest classification algorithms on several benchmark datasets. The results confirm that the suggested new algorithm GrpClassifierEC outperforms the other algorithms.ConclusionsOur algorithm can be integrated with many other algorithms. In this research, we use only the k-means clustering algorithm with different k values. In future research, we propose several directions: (1) checking the effect of the clustering algorithm to build an ensemble clustering space. (2) Finding poor clustering results based on the training data, (3) reducing the volume of the data by combining similar points based on the EC.Availability and implementationThe KNIME workflow, implementing GrpClassifierEC, is available at https://malikyousef.com