Ensemble Average Research Articles

Energy landscape of conformational changes for a single unmodified protein

Resolving the free energy landscapes that govern protein biophysics has been obscured by ensemble averaging. While the folding dynamics of single proteins have been observed using fluorescent labels and/or tethers, a simpler and more direct measurement of the conformational changes would not require modifications to the protein. We use nanoaperture optical tweezers to resolve the energy landscape of a single unmodified protein, Bovine Serum Albumin (BSA), and quantify changes in the three-state conformation dynamics with temperature. A Markov model with Kramers’ theory transition rates is used to model the dynamics, showing good agreement with the observed state transitions. This first look at the intrinsic energy landscape of proteins provides a transformative tool for protein biophysics and may be applied broadly, including mapping out the energy landscape of particularly challenging intrinsically disordered proteins.

Expanded Functionality and Portability for the Colvars Library.

Colvars is an open-source C++ library that provides a modular toolkit for collective-variable-based molecular simulations. It allows practitioners to easily create and implement descriptors that best fit a process of interest and to apply a wide range of biasing algorithms in collective variable space. This paper reviews several features and improvements to Colvars that were added since its original introduction. Special attention is given to contributions that significantly expanded the capabilities of this software or its distribution with major MD simulation packages. Collective variables can now be optimized either manually or by machine-learning methods, and the space of descriptors can be explored interactively using the graphical interface included in VMD. Beyond the spatial coordinates of individual molecules, Colvars can now apply biasing forces to mesoscale structures and alchemical degrees of freedom and perform simulations guided by experimental data within ensemble averages or probability distributions. It also features advanced computational schemes to boost the accuracy, robustness, and general applicability of simulation methods, including extended-system and multiple-walker adaptive biasing force, boundary conditions for metadynamics, replica exchange with biasing potentials, and adiabatic bias molecular dynamics. The library is made available directly within the main distributions of the academic software GROMACS, LAMMPS, NAMD, Tinker-HP, and VMD. The robustness of the software and the reliability of the results are ensured through the use of continuous integration with a test suite within the source repository.

Forecasts and Statistical Insights for Line Intensity Mapping Cross-correlations: A Case Study with 21 cm × [C ii]

Intensity mapping—the large-scale mapping of selected spectral lines without resolving individual sources—is quickly emerging as an efficient way to conduct large cosmological surveys. Multiple surveys covering a variety of lines (such as the hydrogen 21 cm hyperfine line, carbon-monoxide rotational lines, and [C ii] fine-structure lines, among others) are either observing or will soon be online, promising a panchromatic view of our Universe over a broad redshift range. With multiple lines potentially covering the same volume, cross-correlations have become an attractive prospect, both for probing the underlying astrophysics and for mitigating observational systematics. For example, cross-correlating 21 cm and [C ii] intensity maps during reionization could reveal the characteristic scale of ionized bubbles around the first galaxies, while simultaneously providing a convenient way to reduce independent foreground contaminants between the two surveys. However, many of the desirable properties of cross-correlations in principle emerge only under ideal conditions, such as infinite ensemble averages. In this paper, we construct an end-to-end pipeline for analyzing intensity mapping cross-correlations, enabling instrumental effects, foreground residuals, and analysis choices to be propagated through Monte Carlo simulations to a set of rigorous error properties, including error covariances, window functions, and full probability distributions for power-spectrum estimates. We use this framework to critically examine the applicability of simplifying assumptions such as the independence and Gaussianity of power-spectrum errors. As worked examples, we forecast the sensitivity of near-term and futuristic 21 cm × [C ii] cross-correlation measurements, providing recommendations for survey design.

First Principles Numerical Demonstration of Emergent Decoherent Histories

Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schrödinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite-size scaling law by varying the Hilbert space dimension over 4 orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many-worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations, low-entropy initial states, or ensemble averages. Published by the American Physical Society 2024

Automated Recognition of Submerged Body-like Objects in Sonar Images Using Convolutional Neural Networks

The Police Robot for Inspection and Mapping of Underwater Evidence (PRIME) is an uncrewed surface vehicle (USV) currently being developed for underwater search and recovery teams to assist in crime scene investigation. The USV maps underwater scenes using sidescan sonar (SSS). Test exercises use a clothed mannequin lying on the seafloor as a target object to evaluate system performance. A robust, automated method for detecting human body-shaped objects is required to maximise operational functionality. The use of a convolutional neural network (CNN) for automatic target recognition (ATR) is proposed. SSS image data acquired from four different locations during previous missions were used to build a dataset consisting of two classes, i.e., a binary classification problem. The target object class consisted of 166 196 × 196 pixel image snippets of the underwater mannequin, whereas the non-target class consisted of 13,054 examples. Due to the large class imbalance in the dataset, CNN models were trained with six different imbalance ratios. Two different pre-trained models (ResNet-50 and Xception) were compared, and trained via transfer learning. This paper presents results from the CNNs and details the training methods used. Larger datasets are shown to improve CNN performance despite class imbalance, achieving average F1 scores of 97% in image classification. Average F1 scores for target vs background classification with unseen data are only 47% but the end result is enhanced by combining multiple weak classification results in an ensemble average. The combined output, represented as a georeferenced heatmap, accurately indicates the target object location with a high detection confidence and one false positive of low confidence. The CNN approach shows improved object detection performance when compared to the currently used ATR method.

Gas Transfer Across Air‐Water Interfaces in Inland Waters: From Micro‐Eddies to Super‐Statistics

AbstractIn inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air‐water interface is routinely described using a water‐side mean gas transfer velocity , where overline indicates time or ensemble averaging. The micro‐eddy surface renewal model predicts , where is the molecular Schmidt number, is the water kinematic viscosity, and is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous around , a mechanism that was not previously considered. As the coefficient of variation in increases, must be adjusted by a multiplier that was derived from a log‐normal model for the probability density function of . Reported variations in with a macro‐scale Reynolds number can also be partly attributed to intermittency effects in . Such intermittency is characterized by the long‐range (i.e., power‐law decay) spatial auto‐correlation function of . That varies with a macro‐scale Reynolds number does not necessarily violate the micro‐eddy model. Instead, it points to a coordination between the macro‐ and micro‐scales arising from the transfer of energy across scales in the energy cascade.

Projections of temperature and precipitation changes in Xinjiang from 2021 to 2050 based on the CMIP6 model.

Xinjiang is one of the most sensitive regions in China in terms of its response to climate change. Against the background of global warming, analyses and predictions using different scenarios for Xinjiang should be conducted. The spatial and temporal distribution characteristics and trends of future temperature and precipitation trends should be considered to provide a scientific basis for the government to respond to future climate change. In this paper, using the CN05.1 dataset and seven models from the sixth phase of the Coupled Model Intercomparison Project, the delta downscaling method is used to predict the temperature and precipitation changes in Xinjiang Province from 2021 to 2050 under the SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios. The results show that (1) most models of CMIP6 have a good effect on temperature simulation in Xinjiang, and the mean values as well as the trends of the temperatures expressed by the multi-model ensemble averaging are in good agreement with the observed data and have a high degree of confidence. The observed precipitation increase rate is significantly higher than that predicted by the model, and the simulation results of each model overestimate the precipitation. (2) The mean annual temperatures in the Xinjiang region increase at rates of 0.32°C/10 a, 0.46°C/10 a, 0.47°C/10 a and 0.67°C/10 a, respectively, under the four scenarios. The rates of temperature increase in the four seasons exhibit the following pattern: autumn > summer > spring > winter. (3) From 2021 to 2050, the average annual precipitation in Xinjiang will change at rates of 3.95 mm/10 a, 1.90 mm/10 a, 2.50 mm/10 a, and 8.67 mm/10 a, respectively, under the four scenarios. The precipitation amounts predicted under the different scenarios increase at the slowest rates in winter and at faster rates in spring. Spatially, the precipitation in the whole Xinjiang region under the four scenarios shows an increasing trend. Overall, except for the SSP1-2.6 scenario, the rates of increase in precipitation increase gradually in all seasons during the future period as the emission scenarios increase. Overall, the climate of the Xinjiang region will be characterized by warming and humidification from 2021 to 2050.

Efficient Estimation of Climate State and Its Uncertainty Using Kalman Filtering with Application to Policy Thresholds and Volcanism

Abstract We present the Energy Balance Model – Kalman Filter (EBM-KF), a hybrid model projecting and assimilating the global mean surface temperature (GMST) and ocean heat content anomaly (OHCA). It combines an annual energy balance model (difference equations) with 17 parameters drawn from the literature and a statistical Extended Kalman Filter assimilating GMST and OHCA, either observed timeseries or simulated by earth system models. Our motivation is to create an efficient and natural estimator of the climate state and its uncertainty, which we believe to be Gaussian at a global scale. We illustrate four applications: 1) EBM-KF generates a similar estimate to the 30-year time-averaged climate state 15 years sooner, or a model-simulated hindcasts’ annual ensemble average, depending on whether volcanic forcing is filtered or not. 2) EBM-KF conveniently assesses annually likelihoods of crossing a policy threshold. For example, based on temperature records up to the end of 2023, p=0.0017 that the climate state was 1.5°C over preindustrial, but there is a 16% likelihood that the GMST in 2023 itself could have been over that threshold. 3) A variant of the EBM-KF also approximates the spread of an entire climate model large ensemble using only one or a few ensemble members. 4) All variants of the EBM-KF are sufficiently fast to allow thorough sampling from non-Gaussian probabilistic futures, e.g., the impact of rare but significant volcanic eruptions. This sampling with the EBM-KF better determines how future volcanism may affect when policy thresholds will be crossed and what an ensemble with thousands of members exploring future intermittent volcanism reveals.

An applicability discussion of the in-situ measurement method using the ensemble averaging technique for sound absorption characteristics

In our former papers, the authors have proposed a measurement method for sound absorption characteristics, surface impedance and sound absorption coefficient, of materials using the ensemble averaging technique. We named it EA-method, for short. So far, we have shown the robustness as well as the reproducibility of the results obtained by the method at various environments. The method consists of two kinds according to sensor types employed: i.e. two-microphone and PU-sensor. In this paper, the applicability of the EA-method is discussed onto three types of absorption: porous, panel, and resonator. At first, the outline of the EA-method is summarized and measurement mechanism is explained. Then, the robustness as well as the reproducibility of the method are discussed based on accumulated results of measurements conducted in various environments including reverberation rooms and in-situ conditions.

Data-Efficient Active Learning for Thermodynamic Integration: Acidity Constants of BiVO4 in Water.

The protonation state of molecules and surfaces is pivotal in various disciplines, including (electro-)catalysis, geochemistry, biochemistry, and pharmaceutics. Accurately and efficiently determining acidity constants is critical yet challenging, particularly when explicitly considering the electronic structure, thermal fluctuations, anharmonic vibrations, and solvation effects. In this research, we employ thermodynamic integration accelerated by com- mittee Neural Network potentials, training a single machine learning model that accurately describes the relevant protonated, deprotonated, and intermediate states. We investigate two deprotonation reactions at the BiVO4 (010)-water interface, a promising candidate for efficient photocatalytic water splitting. Our results illustrate the convergence of the required ensemble averages over simulation time and of the final acidity constant as a function of the Kirkwood coupling parameter. We demonstrate that simulation times on the order of nanoseconds are required for statistical convergence. This time scale is currently unachievable with explicit ab-initio molecular dynamics simulations at the hybrid DFT level of theory. In contrast, our machine learning workflow only requires a few hundred DFT single point calculations for training and testing. Exploiting the extended time scales accessible, we furthermore asses the effect of commonly applied bias potentials. Thus, our study significantly advances calculating free energy differences with ab-initio accuracy.

Subdiffusive dynamics in photonic random walks probed with classical light.

The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the random walk of intense classical light under dephasing dynamics can disentangle quantum and ensemble averaging, making it possible to observe subdiffusive walker dynamics, i.e., a behavior very distinct from both a classical and a quantum walker. These findings are demonstrated through proposing photonic random walk in synthetic temporal lattices, based on pulse dynamics in coupled fiber loops.

Beyond Ensemble Averages: Leveraging Climate Model Ensembles for Subseasonal Forecasting

Abstract Producing high-quality forecasts of key climate variables, such as temperature and precipitation, on subseasonal time scales has long been a gap in operational forecasting. This study explores an application of machine learning (ML) models as postprocessing tools for subseasonal forecasting. Lagged numerical ensemble forecasts (i.e., an ensemble where the members have different initialization dates) and observational data, including relative humidity, pressure at sea level, and geopotential height, are incorporated into various ML methods to predict monthly average precipitation and 2-m temperature 2 weeks in advance for the continental United States. For regression, quantile regression, and tercile classification tasks, we consider using linear models, random forests, convolutional neural networks, and stacked models (a multimodel approach based on the prediction of the individual ML models). Unlike previous ML approaches that often use ensemble mean alone, we leverage information embedded in the ensemble forecasts to enhance prediction accuracy. Additionally, we investigate extreme event predictions that are crucial for planning and mitigation efforts. Considering ensemble members as a collection of spatial forecasts, we explore different approaches to using spatial information. Trade-offs between different approaches may be mitigated with model stacking. Our proposed models outperform standard baselines such as climatological forecasts and ensemble means. In addition, we investigate feature importance, trade-offs between using the full ensemble or only the ensemble mean, and different modes of accounting for spatial variability. Significance Statement Accurately forecasting temperature and precipitation on subseasonal time scales—2 weeks–2 months in advance—is extremely challenging. These forecasts would have immense value in agriculture, insurance, and economics. Our paper describes an application of machine learning techniques to improve forecasts of monthly average precipitation and 2-m temperature using lagged physics-based predictions and observational data 2 weeks in advance for the entire continental United States. For lagged ensembles, the proposed models outperform standard benchmarks such as historical averages and averages of physics-based predictions. Our findings suggest that utilizing the full set of physics-based predictions instead of the average enhances the accuracy of the final forecast.

Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of a Single Molecule.

Single-molecule fluorescence spectroscopy is a powerful method that avoids ensemble averaging, but its temporal resolution is limited by the fluorescence lifetime to nanoseconds at most. At the ensemble level, two-dimensional spectroscopy provides insight into ultrafast femtosecond processes, such as energy transfer and line broadening, even beyond the Fourier limit, by correlating pump and probe spectra. Here, we combine these two techniques and demonstrate coherent 2D spectroscopy of individual dibenzoterrylene (DBT) molecules at room temperature. We excite the molecule in a confocal microscope with a phase-modulated train of femtosecond pulses and detect the emitted fluorescence with single-photon counting detectors. Using a phase-sensitive detection scheme, we were able to measure the nonlinear 2D spectra of most of the DBT molecules that we studied. Our method is applicable to a wide range of single emitters and opens new avenues for understanding energy transfer in single quantum objects on ultrafast time scales.

Local volume concentration, packing domains, and scaling properties of chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally defined domains observed by single-cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as RAD21 degradation.

Multi‐Zone Visco‐Node‐Pore Sensing: A Microfluidic Platform for Multi‐Frequency Viscoelastic Phenotyping of Single Cells

AbstractThis study introduces multi‐zone visco‐Node‐Pore Sensing (mz‐visco‐NPS), an electronic‐based microfluidic platform for single‐cell viscoelastic phenotyping. mz‐visco‐NPS implements a series of sinusoidal‐shaped contraction zones that periodically deform a cell at specific strain frequencies, leading to changes in resistance across the zones that correspond to the cell's frequency‐dependent elastic G′ and viscous G″ moduli. mz‐visco‐NPS is validated by measuring the viscoelastic changes of MCF‐7 cells when their cytoskeleton is disrupted. mz‐visco‐NPS is also employed to measure the viscoelastic properties of human mammary epithelial cells across the entire continuum of epithelial transformation states, from average‐ and high‐risk primary epithelial cells, to immortal non‐malignant (MCF‐10A), malignant (MCF‐7), and metastatic (MDA‐MB‐231) cell lines. With a throughput of 600 cells per hour and demonstrated ease‐of‐use, mz‐visco‐NPS reveals a remarkable level of single‐cell heterogeneity that would otherwise be masked by ensemble averaging.

Flow Field Characteristics at the Spanwise Edge of a Vegetative Canopy Model

This study investigates the complex flow field across a spanwise vegetative model canopy edge focusing on turbulent transport processes. Utilizing stereoscopic particle image velocimetry, the three velocity components were measured in wall-parallel planes at various elevations within canopy across the spanwise canopy edge. Conventional ensemble averaged results were contrasted with those obtained by conditionally averaged flow properties across instantaneous internal interfaces in the flow to understand their contribution to the ensemble average. The conditional average captured the strong gradients in mean velocities, Reynolds stresses, vorticity, swirling strength, and turbulent kinetic energy production across the dynamically changing instantaneous interface. In contrast, the conventional ensemble average smeared out the strong gradients. Small magnitudes of advective terms in the turbulent kinetic energy transport equation suggested weak secondary transverse flows in the present model canopy. The turbulent flow structure across the spanwise canopy edge was further investigated using Quadrant-Hole analysis for both averaging approaches. Conventional ensemble averaged results indicated a shift from sweep to ejection dominance when moving from canopy into the open patch, while the conditional average showed only sweep dominated transport. In contrast to a homogeneous canopy layout, below canopy height at the canopy edge, sweeps and ejections lose their dominance in vertical turbulent transport. The present results show that the dynamics of internal interfaces govern the ensemble averaged results and a possible implementation into existing models is proposed. The present results are expected to increase understanding of spanwise turbulent transport and aid in developing strategies to mitigate desertification.

Estimating capacity limitations in ensemble averaging using set size manipulations and individual differences in search performance

Estimating capacity limitations in ensemble averaging using set size manipulations and individual differences in search performance

Investigating the Use of Traveltime and Reflection Tomography for Deep Learning-Based Sound-Speed Estimation in Ultrasound Computed Tomography.

Ultrasound computed tomography (USCT) quantifies acoustic tissue properties such as the speed-of-sound (SOS). Although full-waveform inversion (FWI) is an effective method for accurate SOS reconstruction, it can be computationally challenging for large-scale problems. Deep learning-based image-to-image learned reconstruction (IILR) methods can offer computationally efficient alternatives. This study investigates the impact of the chosen input modalities on IILR methods for high-resolution SOS reconstruction in USCT. The selected modalities are traveltime tomography (TT) and reflection tomography (RT), which produce a low-resolution SOS map and a reflectivity map, respectively. These modalities have been chosen for their lower computational cost relative to FWI and their capacity to provide complementary information: TT offers a direct SOS measure, while RT reveals tissue boundary information. Systematic analyses were facilitated by employing a virtual USCT imaging system with anatomically realistic numerical breast phantoms. Within this testbed, a supervised convolutional neural network (CNN) was trained to map dual-channel (TT and RT images) to a high-resolution SOS map. Single-input CNNs were trained separately using inputs from each modality alone (TT or RT) for comparison. The accuracy of the methods was systematically assessed using normalized root mean squared error (NRMSE), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR). For tumor detection performance, receiver operating characteristic analysis was employed. The dual-channel IILR method was also tested on clinical human breast data. Ensemble average of the NRMSE, SSIM, and PSNR evaluated on this clinical dataset were 0.2355, 0.8845, and 28.33 dB, respectively.

Cardiac Time Intervals under Motion Using Bimodal Chest E-Tattoos and Multistage Processing.

We present a thin, soft, and chest conformable bimodal sensor, known as the chest e-tattoo, coupled with an advanced signal processing framework to accurately identify various cardiac events, and thereby extract cardiac time intervals even during body motion. We built a wireless electronic tattoo that features synchronous electrocardiography (ECG) and seismocardiography (SCG). The SCG measures chest vibrations due to heartbeat, providing information on cardiovascular health that is complementary to the ECG. However, the efficacy of the SCG is compromised by motion-induced artifacts. The slim and stretchy design of the e-tattoo allows it to be strategically placed near the xiphoid process, facilitating high-quality monitoring of the ECG and SCG for increased signal quality. Nine participants were measured during walking and cycling. We propose a multistage signal processing framework, integrating an adaptive Normalized Least Mean Squares (NLMS) filter, ensemble averaging, and Empirical Mode Decomposition (EMD), together named the FAD framework, to accurately extract cardiac time intervals (CTIs).

Spatiotemporal Variation in Absorption Aerosol Optical Depth over China

Absorbing aerosols can absorb solar radiation, affect the atmospheric radiation balance, and further have a profound influence on the global and regional climates. The absorption aerosol optical depth (AAOD) as well as the absorption Angstrom exponent (AAE) across China over 2005–2018 were systematically studied through the Ozone Monitoring Instrument (OMI) dataset. The monthly AAOD samples from the OMI generally showed a good correlation (~0.55) compared to the monthly data from AERONET at four typical sites (North: Xianghe, East: Taihu, South: Hongkong Polytechnic Univ; Northwest: Sacol) across China. The ensemble annual average of the OMI AAOD at 388 and 500 nm is 0.046 and 0.022, with minor changes during 2005–2015, and a relatively fast increase after that. The winter and spring seasons depict the maximum mean AAODs, followed by autumn, whereas summer shows minimum levels. On the contrary, the high AAE values appear in summer and low values in winter. The order of the annual average AAOD500 from 2005 to 2018 is the Tarim Basin (TB, 0.041) > the Yellow River Basin (YRB, 0.023) > Beijing and Tianjin (BT, 0.026) > the Sichuan Basin (SB, 0.023) > Nanjing and Shanghai (NS, 0.021) > the Pearl River Delta (PRD, 0.017), whereas the AAE388–500 exhibits the opposite trend except for the TB (3.058). From 2005 to 2018, the AAOD rises by nearly 1.5–2.0 fold in the six typical regions, implying a severe situation of dust and/or BC aerosol pollution in the last several years. The monthly mean AAOD388 over the TB, the SB, the YRB, BT, the PRD, and NS is estimated to be smallest at 0.072, 0.024, 0.026, and 0.027 in July, 0.024 in June, and 0.025 in September, respectively, whilst largest in January for NS, the YRB and BT, April for the TB, February for the SB, and March for the PRD with 0.055, 0.077 and 0.067, 0.123, and 0.073 and 0.075, respectively. The monthly averaged AAOD500 in each region is consistently about half of the AAOD388. The highest AAE appears in June while the lowest values are in December and January, and the daily AAE values in episode days slightly decrease as compared to non-episode days. Our study indicates that northwestern China plays an important role in the overall AAOD as a result of dust aerosols stemming from desert areas. Moreover, the meteorological conditions in winter and early spring are associated with more energy consumption conducive to the accumulation of high black carbon (BC) aerosol pollution, causing high alert levels of AAOD from November to the following March.