Snapshot Data Research Articles

Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

A Novel Two-Level Nested STAP Strategy for Clutter Suppression in Airborne Radar

Nested arrays have been studied recently in array signal processing field because of their closed-form expressions for the sensor locations and achievable degrees of freedom (DOFs). In this paper, the concept of nesting is further extended to space-time adaptive processing (STAP). Different from the traditional uniform-STAP method that calculates the clutter plus noise covariance matrix (CNCM) and performs the STAP filter direct using the data snapshots collected from the uniform linear array (ULA) and the transmitting pulses with uniform pulse repetition interval (PRI), we present a new optimum two-level nested STAP (O2LN-STAP) strategy which employs an optimum two-level nested array (O2LNA) and an optimum two-level nested PRI (O2LN-PRI) to exploit the enhanced DOFs embedded in the space-time O2LN structure. Similar to the difference coarray perspective, we first construct a virtual space-time snapshot from the direct covariance matrix of the received signals. Then, a new CNCM estimation corresponding to the virtual space-time snapshot can be computed by the spatial-temporal smoothing technique for STAP filter. Furthermore, the comparative simulations and analyses with the traditional uniform-STAP and the recently reported coprime-STAP are carried out to verify the effectiveness of the O2LN-STAP approach.

Signal Self-nulling Based DOA Estimation Method Using Acoustic Vector Sensor Array

The acoustic vector sensor (AVS) array is a powerful tool for direction of arrival (DOA) estimation of underwater targets. However, traditional DOA estimation algorithms generally suffer from low signal-to-noise ratio (SNR) as well as snapshot deficiency. A novel signal self-nulling based DOA estimation method is proposed. Firstly, achieve the crude estimation of the desired DOA using the traditional algorithms. Secondly, set the observation angular interval around the crudely estimated DOA. Thirdly, make the observation direction vary in the observation angular interval, and for each imaginary DOA, calculate the amplitude response of the minimum variance distortionless response (MVDR) beamformer. Finally, the pseudo spatial spectrum is achieved. Computer simulations verify that the proposed method is efficient in DOA estimation, especially in low SNR and insufficient snapshot data scenarios.

DOA and Phase Error Estimation for a Partly Calibrated Array With Arbitrary Geometry

This paper presents a novel strategy to simultaneously estimate the direction of arrival (DOA) of a source signal and the phase error of a partly calibrated array with arbitrary geometry. We add up the snapshot data of two different sensors, and then extract a knowledge associated with the DOA and phase errors of these two elements by using singular value decomposition. In such a manner, we can establish a series of linear equations with respect to the unknown DOA and phase error, by simply conducting the procedure on any two sensor elements. On this basis, it can be shown that the problem of jointly estimating DOA and phase error is equivalent to a least square (LS) problem with a quadratic equality constraint. To solve this LS problem (so that the DOA and phase error can be obtained), an effective convex-concave procedure is employed. Different from the conventional algorithms that are limited to specific array geometries, the proposed one is suitable for arrays with arbitrary geometries. More importantly, the devised method only requires one extra calibrated sensor, which is not necessarily adjacently located with the reference one. Several simulations are carried out in this paper and the effectiveness of the devised method can be clearly observed.

Super-resolution reconstruction of turbulent flows with machine learning

We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machine learning models are developed, namely, the convolutional neural network (CNN) and the hybrid downsampled skip-connection/multi-scale (DSC/MS) models. These machine learning models are applied to a two-dimensional cylinder wake as a preliminary test and show remarkable ability to reconstruct laminar flow from low-resolution flow field data. We further assess the performance of these models for two-dimensional homogeneous turbulence. The CNN and DSC/MS models are found to reconstruct turbulent flows from extremely coarse flow field images with remarkable accuracy. For the turbulent flow problem, the machine-leaning-based super-resolution analysis can greatly enhance the spatial resolution with as little as 50 training snapshot data, holding great potential to reveal subgrid-scale physics of complex turbulent flows. With the growing availability of flow field data from high-fidelity simulations and experiments, the present approach motivates the development of effective super-resolution models for a variety of fluid flows.

Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data.

Bayesian and non-Bayesian moment-based inference methods are commonly used to estimate the parameters defining stochastic models of gene regulatory networks from noisy single cell or population snapshot data. However, a systematic investigation of the accuracy of the predictions of these methods remains missing. Here, we present the results of such a study using synthetic noisy data of a negative auto-regulatory transcriptional feedback loop, one of the most common building blocks of complex gene regulatory networks. We study the error in parameter estimation as a function of (i) number of cells in each sample; (ii) the number of time points; (iii) the highest-order moment of protein fluctuations used for inference; (iv) the moment-closure method used for likelihood approximation. We find that for sample sizes typical of flow cytometry experiments, parameter estimation by maximizing the likelihood is as accurate as using Bayesian methods but with a much reduced computational time. We also show that the choice of moment-closure method is the crucial factor determining the maximum achievable accuracy of moment-based inference methods. Common likelihood approximation methods based on the linear noise approximation or the zero cumulants closure perform poorly for feedback loops with large protein–DNA binding rates or large protein bursts; this is exacerbated for highly heterogeneous cell populations. By contrast, approximating the likelihood using the linear-mapping approximation or conditional derivative matching leads to highly accurate parameter estimates for a wide range of conditions.

Decomposition of wake dynamics in fluid–structure interaction via low-dimensional models

We present a dynamic decomposition analysis of the wake flow in fluid–structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational FSI solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Reynolds number ($Re$). The snapshot data from high-dimensional FSI simulations are projected to a low-dimensional subspace using the proper orthogonal decomposition (POD). We utilize each corresponding POD mode to detect features of the organized motions, namely, the vortex street, the shear layer and the near-wake bubble. We find that the vortex shedding modes contribute solely to the lift force, while the near-wake and shear layer modes play a dominant role in the drag force. We further examine the fundamental mechanism of this dynamical behaviour and propose a force decomposition technique via low-dimensional approximation. To elucidate the frequency lock-in, we systematically analyse the decomposed modes and their dynamical contributions to the force fluctuations for a range of reduced velocity at low Reynolds number laminar flow. These quantitative mode energy contributions demonstrate that the shear layer feeds the vorticity flux to the wake vortices and the near-wake bubble during the wake–body synchronization. Based on the decomposition of wake dynamics, we suggest an interaction cycle for the frequency lock-in during the wake–body interaction, which provides the interrelationship between the high-amplitude motion and the dominating wake features. Through our investigation of wake–body synchronization below critical $Re$ range, we discover that the bluff body can undergo a synchronized high-amplitude vibration due to flexibility-induced unsteadiness. Owing to the wake turbulence at a moderate Reynolds number of $Re=22\,000$, a distorted set of POD modes and the broadband energy distribution are observed, while the interaction cycle for the wake synchronization is found to be valid for the turbulent wake flow.

Ultimate: Unearthing Latent Time Profiled Temporal Associations

Discovery of temporal association patterns, temporal association rules from temporal databases is extensively studied by academic research community and applied in various industrial applications. Temporal association pattern discovery is extended to similarity based temporal association pattern discovery from time-stamped transaction datasets by researchers Yoo and Sashi Sekhar. They introduced methods for pruning through distance bounds, and have also introduced SEQUENTIAL and SPAMINE algorithms for pattern mining that are based on snapshot data scan and lattice data scan strategies respectively. Our previous research introduced algorithms G-SPAMINE, MASTER, Z-SPAMINE for time profiled association pattern discovery. These algorithms applied distance measures SRIHASS, ASTRA, and KRISHNA SUDARSANA for similarity computations. SEQUENTIAL, SPAMINE, G-SPAMINE, MASTER, Z-SPAMINE approaches are all based on snapshot and lattice database scan strategies and prunes temporal itemsets by making use of lower bound, upper bound support time sequences and upper-lower distance bound, lower bound distance values. The major limitation of all these algorithms is their inevitability to eliminate dataset scanning process for knowing true supports of itemsets and essential need to have dataset available in memory. To eliminate the requirement of retaining dataset in main memory, algorithms VRKSHA and GANDIVA are two pioneering research contributions that introduced tree structure for time profiled temporal association mining. VRKSHA is based on snapshot tree scan technique while GANDIVA is a lattice tree scan based approach. VRKSHA and GANDIVA both apply Euclidean distance function, but they do not estimate support and distance bounds. This research introduces the pioneering work ULTIMATE that uses a novel tree structure. The tree is generated using similarity measure ASTRA. ULTIMATE uses support bound and distance bound computations for pruning temporal patterns. Experiment results showed that ULTIMATE outperforms SEQUENTIAL, SPAMINE, G-SPAMINE, MASTER, VRKSHA, GANDIVA algorithms.

GDG in UNIX? No Way!

IBM mainframes in the z/OS environment provide a generational structure often referred to as Generation Data Group (GDG) for file storage to maintain data snapshots of related data.[1] These data resulting from business operations within a servicing organization are not uncommon. This structure can hold TEXT data sets without a problem. However, in the case of a UNIX or Linux platform, a comparable structure is unavailable for use by SAS for storing data as TEXT files. This paper contains a solution to this problem and shows a comparison of what the mainframe GDG offers and the solution offered. A developer or a programmer may find that the solution, TextGDS (SAS macro) is even better than the mainframe GDG structure in certain respects. Although there are both limitations and delimitations when using TextGDS, the tool helps to fill the void with UNIX-SAS.

Dynamic mode decomposition of cavitating flow around ALE 15 hydrofoil

The Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) are employed to analyze the coherent structure of cavitating flow around ALE 15 hydrofoil. The snapshot data sequence is obtained from the numerical simulations by means of LES approach and modified Schnerr-Sauer cavitation model. Under cavitation number σ = 2.3, the cavitating flow around ALE 15 hydrofoil sheds at the short side while it almost remains stable at the long side. The eigenvalue distribution of DMD is symmetrical along the real axis of the plane, and the eigenvalues appear as conjugate pairs. The DMD method can accurately extract the frequency characteristics, and results show that the decomposed Mode at St = 2.224 is related to the shedding frequency of cloud cavitation, which agrees well with the shedding frequency of 2.208–2.805 in experimental measurement. The POD method can effectively analyze the major structure of high energy, in which the first four modes contain over 60% total energy of flow field. In comparison of POD, the DMD is more effective to decompose the complex flow field into uncoupled coherent structures with specific dynamic modes and corresponding frequencies.

In-Depth Exploration of Signal Self-Cancellation Phenomenon to Achieve DOA Estimation of Underwater Acoustic Sources

In the ocean environment, the minimum variance distortionless response beamformer usually has the problem of signal self-cancellation, that is, the acoustic signal of interest is erroneously suppressed as interference. By exploring the useful information behind the signal self-cancellation phenomenon, a high-precision direction estimation method for underwater acoustic sources is proposed. First, a pseudo spatial power spectrum is obtained by performing unit circle mapping on the beam response in the direction interval. Second, the online calculation process is given for reducing the computational complexity. The computer simulation results show that the proposed algorithm can obtain satisfactory direction estimation accuracy under the conditions of low intensity of acoustic source, strong interference and noise, and less array snapshot data.

DVID: Distributed Versioned Image-Oriented Dataservice.

Open-source software development has skyrocketed in part due to community tools like github.com, which allows publication of code as well as the ability to create branches and push accepted modifications back to the original repository. As the number and size of EM-based datasets increases, the connectomics community faces similar issues when we publish snapshot data corresponding to a publication. Ideally, there would be a mechanism where remote collaborators could modify branches of the data and then flexibly reintegrate results via moderated acceptance of changes. The DVID system provides a web-based connectomics API and the first steps toward such a distributed versioning approach to EM-based connectomics datasets. Through its use as the central data resource for Janelia's FlyEM team, we have integrated the concepts of distributed versioning into reconstruction workflows, allowing support for proofreader training and segmentation experiments through branched, versioned data. DVID also supports persistence to a variety of storage systems from high-speed local SSDs to cloud-based object stores, which allows its deployment on laptops as well as large servers. The tailoring of the backend storage to each type of connectomics data leads to efficient storage and fast queries. DVID is freely available as open-source software with an increasing number of supported storage options.

Acceleration and escape processes of high-energy particles in turbulence inside hot accretion flows

Abstract We investigate acceleration and propagation processes of high-energy particles inside hot accretion flows. The magnetorotational instability (MRI) creates turbulence inside accretion flows, which triggers magnetic reconnection and may produce non-thermal particles. They can be further accelerated stochastically by the turbulence. To probe the properties of such relativistic particles, we perform magnetohydrodynamic simulations to obtain the turbulent fields generated by the MRI, and calculate orbits of the high-energy particles using snapshot data of the MRI turbulence. We find that the particle acceleration is described by a diffusion phenomenon in energy space with a diffusion coefficient of the hard-sphere type: Dε ∝ ε2, where ε is the particle energy. Eddies in the largest scale of the turbulence play a dominant role in the acceleration process. On the other hand, the stochastic behaviour in configuration space is not usual diffusion but superdiffusion: the radial displacement increases with time faster than that in the normal diffusion. Also, the magnetic field configuration in the hot accretion flow creates outward bulk motion of high-energy particles. This bulk motion is more effective than the diffusive motion for higher energy particles. Our results imply that typical active galactic nuclei that host hot accretion flows can accelerate CRs up to ε ∼ 0.1−10 PeV.

Angle-of-Arrival Estimation Using an Adaptive Machine Learning Framework

Angle-of-arrival (AoA) estimation is of great interest, particularly for using radio to localize a device; good estimates of angles result in good estimates of location. In this letter, we propose a signal processing and machine learning combined tool for the AoA estimation. In particular, we utilize regression models trained using the snapshot data collected using multiple antennas for estimating the angle of arrival. Based on a set of simulation and real measurements underthe Bluetooth 5 low-energy system in an indoor environment, the proposed method is able to provide a considerable and consistent improvement without significant additional computational effort. We show that the proposed approach for AoA estimation provides an improvement of at least 20% compared with the baseline approach of traditional Multiple Signal Classification algorithm. We evaluate the performance of the proposed methods and show a consistent improvement using a range of channel parameters, including elevation angles, SNRs, and channel configurations.

A Map of Human Type 1 Diabetes Progression by Imaging Mass Cytometry

Type 1 diabetes (T1D) results from the autoimmune destruction of insulin-producing β cells. A comprehensive picture of the changes during T1D development is lacking due to limited sample availability, inability to sample longitudinally, and the paucity oftechnologies enabling comprehensive tissue profiling. Here, we analyzed 1,581 islets from 12 human donors, including eight with T1D, using imaging mass cytometry (IMC). IMC enabled simultaneous measurement of 35 biomarkers with single-cell and spatial resolution. We performed pseudotime analysis of islets through T1D progression from snapshot data to reconstruct the evolution of β cell loss and insulitis. Our analyses revealed that β cell destruction is preceded by a β cell marker loss and by recruitment of cytotoxic and helper Tcells. The approaches described herein demonstrate the value of IMC for improving our understanding of T1D pathogenesis, and our data lay the foundation for hypothesis generation and follow-on experiments.

Explicit Characterization of Spatial Heterogeneity Based on Water Quality, Sediment Contamination, and Ichthyofauna in a Riverine-to-Coastal Zone.

Our study aims to identify the spatial characteristics of water quality and sediment conditions in relation to fisheries resources, since the productivity of fisheries resources is closely related to the ambient conditions of the resource areas. We collected water quality samples and sediment contaminants from twenty-one sites at Gwangyang Bay, Korea, in the summer of 2018. Our study sites covered the area from the Seomjin River estuary to the inner and outer bays. To spatially characterize physicochemical features of Gwangyang Bay, we used Self-Organizing Map (SOM), which is known as a robust and powerful tool of unsupervised neural networks for pattern recognition. The present environmental conditions of Gwangyang Bay were spatially characterized according to four different attributes of water quality and sediment contamination. From the results, we put emphasis on several interesting points: (i) the SOM manifests the dominant physicochemical attributes of each geographical zone associated with the patterns of water quality and sediment contamination; (ii) fish populations appear to be closely associated with their food sources (e.g., shrimps and crabs) as well as the ambient physicochemical conditions; and (iii) in the context of public health and ecosystem services, the SOM result can potentially offer guidance for fish consumption associated with sediment heavy metal contamination. The present study may have limitations in representing general features of Gwangyang Bay, given the inability of snapshot data to characterize a complex ecosystem. In this regard, consistent sampling and investigation are needed to capture spatial variation and to delineate the temporal dynamics of water quality, sediment contamination, and fish populations. However, the SOM application is helpful and useful as a first approximation of an environmental assessment for the effective management of fisheries resources.

Intrinsic and extrinsic noise of gene expression in lineage trees

Cell-to-cell heterogeneity is driven by stochasticity in intracellular reactions and the population dynamics. While these sources are usually studied separately, we develop an agent-based framework that accounts for both factors while tracking every single cell of a growing population. Apart from the common intrinsic variability, the framework also predicts extrinsic noise without the need to introduce fluctuating rate constants. Instead, extrinsic fluctuations are explained by cell cycle fluctuations and differences in cell age. We provide explicit formulas to quantify mean molecule numbers, intrinsic and extrinsic noise statistics in two-colour experiments. We find that these statistics differ significantly depending on the experimental setup used to observe the cells. We illustrate this fact using (i) averages over an isolated cell lineage tracked over many generations as observed in the mother machine, (ii) population snapshots with known cell ages as recorded in time-lapse microscopy, and (iii) snapshots with unknown cell ages as measured from static images or flow cytometry. Applying the method to models of stochastic gene expression and feedback regulation elucidates that isolated lineages, as compared to snapshot data, can significantly overestimate the mean number of molecules, overestimate extrinsic noise but underestimate intrinsic noise and have qualitatively different sensitivities to cell cycle fluctuations.

Sensor array calibration with joint-block-sparsity in the presence of multiple separable observations

In sparsity-based optimization problems, one of the major issue is computational complexity, especially when the unknown signal is represented in multi-dimensions such as in the problem of 2-D (azimuth and elevation) direction-of-arrival (DOA) estimation. In this paper, a low-complexity sparsity-based method is proposed for DOA estimation in the presence of array imperfections such as mutual coupling. In order to reduce the complexity of the optimization problem, this paper introduces a new sparsity structure that can be used to model the optimization problem in case of multiple data snapshots and multiple separable observations where the dictionary can be decomposed into two parts: azimuth and elevation dictionaries. The proposed sparsity structure is called joint-block-sparsity which exploits the sparsity in both multiple dimensions, namely azimuth and elevation, and data snapshots. In order to model the joint-block-sparsity in the optimization problem, triple mixed norms are used. In the simulations, the proposed method is compared with both sparsity-based techniques and subspace-based methods as well as the Cramer–Rao lower bound. It is shown that the proposed method effectively calibrates the sensor array with significantly low complexity and sufficient accuracy.

A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics.

Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intra-cellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and population-average parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.

Reduced-Order Modeling of a Radiative Heating Process with Movable Radiators

A reduced-order model for a heating process with dominant radiation and movable radiators is derived. The process is described by a nonlinear integro-partial differential equation with full domain coupling for the thermal part and ordinary differential equations for the mechanical part, which contains a moving radiator. The model reduction is performed with a tailored Proper Orthogonal Decomposition (POD)-Galerkin approach. In contrast to the existing works in the literature, a new computationally efficient approach is proposed to account for the nonlinear full domain coupling term due to radiation. The reduced-order model shall be used in a model predictive control in the future. Therefore, special attention is paid to the choice of the actuation function used to construct the snapshot data set. Here, a stationary distributed feedforward controller is designed and approximated using a multi-scale approach by splitting the mechanical and thermal parts. Simulative results illustrate the accuracy and computational efficiency of the proposed reduced-order model.