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DOE OSTI2017

Machine learning $\mathbb{Z}_2$ quantum spin liquids with quasiparticle statistics

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. In this report we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a $\mathbb{Z}_2$ quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Statistical uncertainties of the v n { 2 k } harmonics from Q cumulants

Analytic formulas to calculate statistical uncertainties of v n { 2 k } harmonics extracted from the Q cumulants are presented. The Q cumulants are multivariate polynomial functions of the weighted means of 2m-particle azimuthal correlations, $\langle\langle 2 m \rangle\rangle$. Variances and covariances of the $\langle\langle 2 m \rangle\rangle$ are included in the analytic formulas of the uncertainties that can be calculated simultaneously with the calculations of the v n { 2 k } harmonics. The calculations are performed using a simple toy model, which roughly simulates elliptic flow azimuthal anisotropy with magnitudes around 0.05. The results are compared with the results obtained by the many data subsets, and by the bootstrapping method. The first one is a common way of estimation of the statistical uncertainties of the v n { 2 k } harmonics in a real experiment. In order to increase precision in the measurement of the v n { 2 k } harmonics, a large number of 15 000 subsets and the same number of the resampling in the bootstrap method is used. Unlike the other ways of the analytic calculation of the v n { 2 k } statistical uncertainties, our proposal that includes the use of squared weights in the calculation of both the variances and covariances, gives the best agreement with the results obtained from the subsets and bootstrap method. Additionally, a recurrence equation between Q cumulants of any order is also presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Cross sections of α -induced reactions slightly below doubly magic Ca 40 from the statistical model

New experimental data for the 38 Ar (α , n) 41 Ca and 38 Ar (α, p) 41 K reactions were used to find a best-fit set of parameters for statistical model calculations. The very good agreement between the experimental data and the best-fit calculation confirms the applicability of the statistical model for nuclei in the vicinity of the doubly magic 40 Ca despite their relatively low level densities. The present study investigates the sensitivities and finds that the α -nucleus and the nucleon-nucleus potentials are the most important ingredients for the calculation of (α, n) and (α, p) reactions in the statistical model. Furthermore, the width fluctuation correction plays an essential role in the peculiar case of 38 Ar. The best-fit parameters from 38 Ar are applied to the mirror nucleus 38 Ca and the neighboring 36 Ar and 40 Ar nuclei. For 38 Ca this results in an astrophysical reaction rate of the 38 Ca (α , p) 41 Sc reaction, which has a flatter temperature dependence compared to all previous calculations. For 40 Ar a better reproduction of 40 Ar (α , p) 43 K data from literature is obtained. The disagreement between calculation and an early experimental data point for the 36 Ar (α, p) 39 K reaction persists.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy p p and p p ¯ collisions

Transverse spectra of both jets and hadrons obtained in high-energy $pp$ and $p\bar p $ collisions at central rapidity exhibit power-law behavior of $1/p_T^n$ at high $p_T$. The power index $n$ is 4-5 for jet production and is slightly greater for hadron production. Furthermore, the hadron spectra spanning over 14 orders of magnitude down to the lowest $p_T$ region in $pp$ collisions at LHC can be adequately described by a single nonextensive statistical mechanical distribution that is widely used in other branches of science. This suggests indirectly the dominance of the hard-scattering process over essentially the whole $p_T$ region at central rapidity in $pp$ collisions at LHC. We show here direct evidences of such a dominance of the hard-scattering process by investigating the power index of UA1 jet spectra over an extended $p_T$ region and the two-particle correlation data of the STAR and PHENIX Collaborations in high-energy $pp$ and $p \bar p$ collisions at central rapidity. We then study how the showering of the hard-scattering product partons alters the power index of the hadron spectra and leads to a hadron distribution that can be cast into a single-particle non-extensive statistical mechanical distribution. Lastly, because of such a connection, the non-extensive statistical mechanical distribution can be considered as a lowest-order approximation of the hard-scattering of partons followed by the subsequent process of parton showering that turns the jets into hadrons, in high energy $pp$ and $p\bar p$ collisions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Density split statistics: Joint model of counts and lensing in cells

We present density split statistics, a framework that studies lensing and counts-in-cells as a function of foreground galaxy density, thereby providing a large-scale measurement of both 2-point and 3-point statistics. Our method extends our earlier work on trough lensing and is summarized as follows: given a foreground (low redshift) population of galaxies, we divide the sky into subareas of equal size but distinct galaxy density. We then measure lensing around uniformly spaced points separately in each of these subareas, as well as counts-in-cells statistics (CiC). The lensing signals trace the matter density contrast around regions of fixed galaxy density. Through the CiC measurements this can be related to the density profile around regions of fixed matter density. Together, these measurements constitute a powerful probe of cosmology, the skewness of the density field and the connection of galaxies and matter. In this paper we show how to model both the density split lensing signal and CiC from basic ingredients: a non-linear power spectrum, clustering hierarchy coefficients from perturbation theory and a parametric model for galaxy bias and shot-noise. Furthermore, using N-body simulations, we demonstrate that this model is sufficiently accurate for a cosmological analysis on year 1 data from the Dark Energy Survey.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Using kernel-based statistical distance to study the dynamics of charged particle beams in particle-based simulation codes

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as numerical diagnostics for simulations involving charged-particle beams. Related measures of statistical dependence are also described. The resulting diagnostics provide sensitive measures of dynamical processes important for beams in nonlinear or high-intensity systems, which are otherwise difficult to characterize. Here, the focus is on kernel-based methods such as maximum mean discrepancy, which have a well-developed mathematical foundation and reasonable computational complexity. Several benchmark problems and examples involving intense beams are discussed. While the focus is on charged-particle beams, these methods may also be applied to other many-body systems such as plasmas or gravitational systems.

47 OTHER INSTRUMENTATION↗

DOE OSTI2019

Parallel Hybrid Metaheuristics with Distributed Intensification and Diversification for Large-scale Optimization in Big Data Statistical Analysis

Important insights into many problems that are traditionally analyzed via statistical models can be obtained by re-formulating and evaluating within a large-scale optimization framework. The theoretical underpinnings of the statistical model often shift the goal of the solution space traversal from a traditional search for a single optimal solution to a traversal with the purpose of yielding a set of high quality, independent solutions. We examine statistical frameworks with astronomical solution spaces where the independence requirement constitutes a significant additional challenge for standard optimization methodologies. We design a hybrid metaheuristic with specialized intensification and diversification protocols in the base search algorithm. We extend our algorithm to the high-performance-computing realm using the Stampede2 supercomputer. We experimentally demonstrate the effectiveness of our algorithm to utilize multiple processors to collaboratively hill climb, broadcast messages to one another regarding landscape characteristics, diversify across the solution landscape, and request aid in climbing particularly difficult peaks.

Cho, Wendy K. Tam↗

DOE OSTI2021

Statistical upscaling of ecosystem CO 2 fluxes across the terrestrial tundra and boreal domain: Regional patterns and uncertainties

Abstract The regional variability in tundra and boreal carbon dioxide (CO 2 ) fluxes can be high, complicating efforts to quantify sink‐source patterns across the entire region. Statistical models are increasingly used to predict (i.e., upscale) CO 2 fluxes across large spatial domains, but the reliability of different modeling techniques, each with different specifications and assumptions, has not been assessed in detail. Here, we compile eddy covariance and chamber measurements of annual and growing season CO 2 fluxes of gross primary productivity (GPP), ecosystem respiration (ER), and net ecosystem exchange (NEE) during 1990–2015 from 148 terrestrial high‐latitude (i.e., tundra and boreal) sites to analyze the spatial patterns and drivers of CO 2 fluxes and test the accuracy and uncertainty of different statistical models. CO 2 fluxes were upscaled at relatively high spatial resolution (1 km 2 ) across the high‐latitude region using five commonly used statistical models and their ensemble, that is, the median of all five models, using climatic, vegetation, and soil predictors. We found the performance of machine learning and ensemble predictions to outperform traditional regression methods. We also found the predictive performance of NEE‐focused models to be low, relative to models predicting GPP and ER. Our data compilation and ensemble predictions showed that CO 2 sink strength was larger in the boreal biome (observed and predicted average annual NEE −46 and −29 g C m −2 yr −1 , respectively) compared to tundra (average annual NEE +10 and −2 g C m −2 yr −1 ). This pattern was associated with large spatial variability, reflecting local heterogeneity in soil organic carbon stocks, climate, and vegetation productivity. The terrestrial ecosystem CO 2 budget, estimated using the annual NEE ensemble prediction, suggests the high‐latitude region was on average an annual CO 2 sink during 1990–2015, although uncertainty remains high.

Virkkala, Anna‐Maria↗

DOE OSTI2024

Divide and conquer: using RhizoVision Explorer to aggregate data from multiple root scans using image concatenation and statistical methods

Roots are important in agricultural and natural systems for determining plant productivity and soil carbon inputs. Sometimes, the amount of roots in a sample is too much to fit into a single scanned image, so the sample is divided among several scans, and there is no standard method to aggregate the data. Here, we describe and validate two methods for standardizing measurements across multiple scans: image concatenation and statistical aggregation. We developed a Python script that identifies which images belong to the same sample and returns a single, larger concatenated image. These concatenated images and the original images were processed with RhizoVision Explorer, a free and open-source software. An R script was developed, which identifies rows of data belonging to the same sample and applies correct statistical methods to return a single data row for each sample. These two methods were compared using example images from switchgrass, poplar, and various tree and ericaceous shrub species from a northern peatland and the Arctic. Most root measurements were nearly identical between the two methods except median diameter, which cannot be accurately computed by statistical aggregation. We believe the availability of these methods will be useful to the root biology community.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

A Statistical Evaluation of Combining Human Productivity Metrics in the Indoor Environment

The potential of improving human productivity by providing healthy indoor environments has been a consistent interest in the building field for decades. This research field's long-standing challenge is to measure human productivity given the complex nature of office work. Previous studies have diversified productivity metrics, allowing greater flexibility in collecting human data; however, this diversity complicates the ability to combine productivity metrics from disparate studies within a meta-analysis. This study aims to categorize existing productivity metrics and statistically assess which categories show similar behavior when used to measure the impacts of indoor environmental quality. The 106 productivity metrics compiled were grouped into six productivity metric categories: neurobehavioral speed, accuracy, neurobehavioral response time, call handling time, self-reported productivity, and performance score. Then, this study set neurobehavioral speed as the baseline category given its fitness to the efficiency-based definition of productivity (i.e., output versus input) and conducted three statistical analyses with the other categories to evaluate their similarity. As results, the categories of neurobehavioral response time, self-reported productivity, and call handling time were found to have statistical similarity with neurobehavioral speed. This study contributes to creating a constructive research environment for future meta-analyses to understand which human productivity metrics can be combined with each other.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2014

Automatic segmentation of head and neck CT images for radiotherapy treatment planning using multiple atlases, statistical appearance models, and geodesic active contours

Purpose: Accurate delineation of organs at risk (OARs) is a precondition for intensity modulated radiation therapy. However, manual delineation of OARs is time consuming and prone to high interobserver variability. Because of image artifacts and low image contrast between different structures, however, the number of available approaches for autosegmentation of structures in the head-neck area is still rather low. In this project, a new approach for automated segmentation of head-neck CT images that combine the robustness of multiatlas-based segmentation with the flexibility of geodesic active contours and the prior knowledge provided by statistical appearance models is presented. Methods: The presented approach is using an atlas-based segmentation approach in combination with label fusion in order to initialize a segmentation pipeline that is based on using statistical appearance models and geodesic active contours. An anatomically correct approximation of the segmentation result provided by atlas-based segmentation acts as a starting point for an iterative refinement of this approximation. The final segmentation result is based on using model to image registration and geodesic active contours, which are mutually influencing each other. Results: 18 CT images in combination with manually segmented labels of parotid glands and brainstem were used in a leave-one-out cross validation scheme in order to evaluate the presented approach. For this purpose, 50 different statistical appearance models have been created and used for segmentation. Dice coefficient (DC), mean absolute distance and max. Hausdorff distance between the autosegmentation results and expert segmentations were calculated. An average Dice coefficient of DC = 0.81 (right parotid gland), DC = 0.84 (left parotid gland), and DC = 0.86 (brainstem) could be achieved. Conclusions: The presented framework provides accurate segmentation results for three important structures in the head neck area. Compared to a segmentation approach based on using multiple atlases in combination with label fusion, the proposed hybrid approach provided more accurate results within a clinically acceptable amount of time.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2014

SU-F-BRD-05: Dosimetric Comparison of Protocol-Based SBRT Lung Treatment Modalities: Statistically Significant VMAT Advantages Over Fixed- Beam IMRT

Purpose: The purpose of this study is to inter-compare and find statistically significant differences between flattened field fixed-beam (FB) IMRT with flattening-filter free (FFF) volumetric modulated arc therapy (VMAT) for stereotactic body radiation therapy SBRT. Methods: SBRT plans using FB IMRT and FFF VMAT were generated for fifteen SBRT lung patients using 6 MV beams. For each patient, both IMRT and VMAT plans were created for comparison. Plans were generated utilizing RTOG 0915 (peripheral, 10 patients) and RTOG 0813 (medial, 5 patients) lung protocols. Target dose, critical structure dose, and treatment time were compared and tested for statistical significance. Parameters of interest included prescription isodose surface coverage, target dose heterogeneity, high dose spillage (location and volume), low dose spillage (location and volume), lung dose spillage, and critical structure maximum- and volumetric-dose limits. Results: For all criteria, we found equivalent or higher conformality with VMAT plans as well as reduced critical structure doses. Several differences passed a Student's t-test of significance: VMAT reduced the high dose spillage, evaluated with conformality index (CI), by an average of 9.4%±15.1% (p=0.030) compared to IMRT. VMAT plans reduced the lung volume receiving 20 Gy by 16.2%±15.0% (p=0.016) compared with IMRT. For the RTOG 0915 peripheral lesions, the volumes of lung receiving 12.4 Gy and 11.6 Gy were reduced by 27.0%±13.8% and 27.5%±12.6% (for both, p<0.001) in VMAT plans. Of the 26 protocol pass/fail criteria, VMAT plans were able to achieve an average of 0.2±0.7 (p=0.026) more constraints than the IMRT plans. Conclusions: FFF VMAT has dosimetric advantages over fixed beam IMRT for lung SBRT. Significant advantages included increased dose conformity, and reduced organs-at-risk doses. The overall improvements in terms of protocol pass/fail criteria were more modest and will require more patient data to establish difference trends of more statistical significance.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

SU-C-BRD-01: A Statistical Modeling Method for Quality Control of Intensity- Modulated Radiation Therapy Planning

Purpose: To apply a statistical modeling approach, threshold modeling (TM), for quality control of intensity-modulated radiation therapy (IMRT) treatment plans. Methods: A quantitative measure, which was the weighted sum of violations of dose/dose-volume constraints, was first developed to represent the quality of each IMRT plan. Threshold modeling approach, which is is an extension of extreme value theory in statistics and is an effect way to model extreme values, was then applied to analyze the quality of the plans summarized by our quantitative measures. Our approach modeled the plans generated by planners as a series of independent and identically distributed random variables and described the behaviors of them if the plan quality was controlled below certain threshold. We tested our approach with five locally advanced head and neck cancer patients retrospectively. Two statistics were incorporated for numerical analysis: probability of quality improvement (PQI) of the plans and expected amount of improvement on the quantitative measure (EQI). Results: After clinical planners generated 15 plans for each patient, we applied our approach to obtain the PQI and EQI as if planners would generate additional 15 plans. For two of the patients, the PQI was significantly higher than the other three (0.17 and 0.18 comparing to 0.08, 0.01 and 0.01). The actual percentage of the additional 15 plans that outperformed the best of initial 15 plans was 20% and 27% comparing to 11%, 0% and 0%. EQI for the two potential patients were 34.5 and 32.9 and the rest of three patients were 9.9, 1.4 and 6.6. The actual improvements obtained were 28.3 and 20.5 comparing to 6.2, 0 and 0. Conclusion: TM is capable of reliably identifying the potential quality improvement of IMRT plans. It provides clinicians an effective tool to assess the trade-off between extra planning effort and achievable plan quality. This work was supported in part by NIH/NCI grant CA130814.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

WE-E-201-01: Use and Abuse of Common Statistics in Radiological Physics

Physicists are often expected to have a solid grounding in experimental design and statistical analysis, sometimes filling in when biostatisticians or other experts are not available for consultation. Unfortunately, graduate education on these topics is seldom emphasized and few opportunities for continuing education exist. Clinical physicists incorporate new technology and methods into their practice based on published literature. A poor understanding of experimental design and analysis could Result in inappropriate use of new techniques. Clinical physicists also improve current practice through quality initiatives that require sound experimental design and analysis. Academic physicists with a poor understanding of design and analysis may produce ambiguous (or misleading) results. This can Result in unnecessary rewrites, publication rejection, and experimental redesign (wasting time, money, and effort). This symposium will provide a practical review of error and uncertainty, common study designs, and statistical tests. Instruction will primarily focus on practical implementation through examples and answer questions such as: where would you typically apply the test/design and where is the test/design typically misapplied (i.e., common pitfalls)? An analysis of error and uncertainty will also be explored using biological studies and associated modeling as a specific use case. Learning Objectives: Understand common experimental testing and clinical trial designs, what questions they can answer, and how to interpret the results Determine where specific statistical tests are appropriate and identify common pitfalls Understand the how uncertainty and error are addressed in biological testing and associated biological modeling.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Statistical iterative reconstruction to improve image quality for digital breast tomosynthesis

Purpose: Digital breast tomosynthesis (DBT) is a novel modality with the potential to improve early detection of breast cancer by providing three-dimensional (3D) imaging with a low radiation dose. 3D image reconstruction presents some challenges: cone-beam and flat-panel geometry, and highly incomplete sampling. A promising means to overcome these challenges is statistical iterative reconstruction (IR), since it provides the flexibility of accurate physics modeling and a general description of system geometry. The authors’ goal was to develop techniques for applying statistical IR to tomosynthesis imaging data. Methods: These techniques include the following: a physics model with a local voxel-pair based prior with flexible parameters to fine-tune image quality; a precomputed parameter λ in the prior, to remove data dependence and to achieve a uniform resolution property; an effective ray-driven technique to compute the forward and backprojection; and an oversampled, ray-driven method to perform high resolution reconstruction with a practical region-of-interest technique. To assess the performance of these techniques, the authors acquired phantom data on the stationary DBT prototype system. To solve the estimation problem, the authors proposed an optimization-transfer based algorithm framework that potentially allows fewer iterations to achieve an acceptably converged reconstruction. Results: IR improved the detectability of low-contrast and small microcalcifications, reduced cross-plane artifacts, improved spatial resolution, and lowered noise in reconstructed images. Conclusions: Although the computational load remains a significant challenge for practical development, the superior image quality provided by statistical IR, combined with advancing computational techniques, may bring benefits to screening, diagnostics, and intraoperative imaging in clinical applications.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Statistical-learning strategies generate only modestly performing predictive models for urinary symptoms following external beam radiotherapy of the prostate: A comparison of conventional and machine-learning methods

Purpose: Given the paucity of available data concerning radiotherapy-induced urinary toxicity, it is important to ensure derivation of the most robust models with superior predictive performance. This work explores multiple statistical-learning strategies for prediction of urinary symptoms following external beam radiotherapy of the prostate. Methods: The performance of logistic regression, elastic-net, support-vector machine, random forest, neural network, and multivariate adaptive regression splines (MARS) to predict urinary symptoms was analyzed using data from 754 participants accrued by TROG03.04-RADAR. Predictive features included dose-surface data, comorbidities, and medication-intake. Four symptoms were analyzed: dysuria, haematuria, incontinence, and frequency, each with three definitions (grade ≥ 1, grade ≥ 2 and longitudinal) with event rate between 2.3% and 76.1%. Repeated cross-validations producing matched models were implemented. A synthetic minority oversampling technique was utilized in endpoints with rare events. Parameter optimization was performed on the training data. Area under the receiver operating characteristic curve (AUROC) was used to compare performance using sample size to detect differences of ≥0.05 at the 95% confidence level. Results: Logistic regression, elastic-net, random forest, MARS, and support-vector machine were the highest-performing statistical-learning strategies in 3, 3, 3, 2, and 1 endpoints, respectively. Logistic regression, MARS, elastic-net, random forest, neural network, and support-vector machine were the best, or were not significantly worse than the best, in 7, 7, 5, 5, 3, and 1 endpoints. The best-performing statistical model was for dysuria grade ≥ 1 with AUROC ± standard deviation of 0.649 ± 0.074 using MARS. For longitudinal frequency and dysuria grade ≥ 1, all strategies produced AUROC>0.6 while all haematuria endpoints and longitudinal incontinence models produced AUROC<0.6. Conclusions: Logistic regression and MARS were most likely to be the best-performing strategy for the prediction of urinary symptoms with elastic-net and random forest producing competitive results. The predictive power of the models was modest and endpoint-dependent. New features, including spatial dose maps, may be necessary to achieve better models.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Perspective on Tsallis statistics for nuclear and particle physics

This is a concise introduction to the topic of nonextensive Tsallis statistics meant especially for those interested in its relation to high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions. The three types of Tsallis statistics are reviewed. Only one of them is consistent with the fundamental hypothesis of equilibrium statistical mechanics. The single-particle distributions associated with it, namely Boltzmann, Fermi–Dirac and Bose–Einstein, are derived. These are not equilibrium solutions to the conventional Boltzmann transport equation which must be modified in a rather nonintuitive manner for them to be so. Nevertheless, the Boltzmann limit of the Tsallis distribution is extremely efficient in representing a wide variety of single-particle distributions in high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions with only three parameters, one of them being the so-called nonextensitivity parameter [Formula: see text]. This distribution interpolates between an exponential at low transverse energy, reflecting thermal equilibrium, to a power law at high transverse energy, reflecting the asymptotic freedom of Quantum Chromodynamics (QCD). It should not be viewed as a fundamental new parameter representing nonextensive behavior in these collisions.

Physics↗

DOE OSTI2018

Designing Size Consistent Statistics for Accurate Anomaly Detection in Dynamic Networks

An important task in network analysis is the detection of anomalous events in a network time series. These events could merely be times of interest in the network timeline or they could be examples of malicious activity or network malfunction. Hypothesis testing using network statistics to summarize the behavior of the network provides a robust framework for the anomaly detection decision process. Unfortunately, choosing network statistics that are dependent on confounding factors like the total number of nodes or edges can lead to incorrect conclusions (e.g., false positives and false negatives). In this article, we describe the challenges that face anomaly detection in dynamic network streams regarding confounding factors. We also provide two solutions to avoiding error due to confounding factors: the first is a randomization testing method that controls for confounding factors, and the second is a set of size-consistent network statistics that avoid confounding due to the most common factors, edge count and node count.

97 MATHEMATICS AND COMPUTING↗