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NASA NTRS2010

Fast and Flexible Multivariate Time Series Subsequence Search

Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical monitoring, and financial systems. Domain experts are often interested in searching for interesting multivariate patterns from these MTS databases which often contain several gigabytes of data. Surprisingly, research on MTS search is very limited. Most of the existing work only supports queries with the same length of data, or queries on a fixed set of variables. In this paper, we propose an efficient and flexible subsequence search framework for massive MTS databases, that, for the first time, enables querying on any subset of variables with arbitrary time delays between them. We propose two algorithms to solve this problem (1) a List Based Search (LBS) algorithm which uses sorted lists for indexing, and (2) a R*-tree Based Search (RBS) which uses Minimum Bounding Rectangles (MBR) to organize the subsequences. Both algorithms guarantee that all matching patterns within the specified thresholds will be returned (no false dismissals). The very few false alarms can be removed by a post-processing step. Since our framework is also capable of Univariate Time-Series (UTS) subsequence search, we first demonstrate the efficiency of our algorithms on several UTS datasets previously used in the literature. We follow this up with experiments using two large MTS databases from the aviation domain, each containing several millions of observations. Both these tests show that our algorithms have very high prune rates (>99%) thus needing actual disk access for only less than 1% of the observations. To the best of our knowledge, MTS subsequence search has never been attempted on datasets of the size we have used in this paper.

Bhaduri, Kanishka↗

NASA NTRS2010

Fast Multivariate Search on Large Aviation Datasets

Bhaduri, Kanishka↗

NASA NTRS2017

An Innovative Infrastructure with a Universal Geo-Spatiotemporal Data Representation Supporting Cost-Effective Integration of Diverse Earth Science Data

The SpatioTemporal Adaptive Resolution Encoding (STARE) is a unifying scheme encoding geospatial and temporal information for organizing data on scalable computing/storage resources, minimizing expensive data transfers. STARE provides a compact representation that turns set-logic functions into integer operations, e.g. conditional sub-setting, taking into account representative spatiotemporal resolutions of the data in the datasets. STARE geo-spatiotemporally aligns data placements of diverse data on massive parallel resources to maximize performance. Automating important scientific functions (e.g. regridding) and computational functions (e.g. data placement) allows scientists to focus on domain-specific questions instead of expending their efforts and expertise on data processing. With STARE-enabled automation, SciDB (Scientific Database) plus STARE provides a database interface, reducing costly data preparation, increasing the volume and variety of interoperable data, and easing result sharing. Using SciDB plus STARE as part of an integrated analysis infrastructure dramatically eases combining diametrically different datasets.

Rilee, Michael Lee↗

NASA NTRS1995

Managing Complexity in Multidisciplinary Visualization

As high performance computing technology progresses, computational simulations are becoming more advanced in their capabilities. In the computational aerosciences domain, single discipline steady-state simulations computed on a single grid are far from the state-of-the-art. In their place are complex, time-dependent multidisciplinary simulations that attempt to model a given geometry more realistically. The product of these multidisciplinary simulations is a massive amount of data stored in different formats, grid topologies, units of measure, etc., as a result of the differences in the simulated physical domains. In addition to the challenges posed by setting up and performing the simulation, additional challenges exist in analyzing computational results. Visualization plays an important role in the advancement of multidisciplinary simulations. To date, visualization has been used to aid in the interpretation of large amounts of simulation data. Because the human visual system is effective in digesting a large amount of information presented graphically, visualization has helped simulation scientists to understand complex simulation results. As these simulations become even more complex, integrating several different physical domains, visualization will be critical to digest the massive amount of information. Another important role for visualization is to provide a common communication medium from which the domain scientists can use to develop, debug, and analyze their work. Multidisciplinary analyses are the next step in simulation technology, not only in computational aerosciences, but in many other areas such as global climate modeling. Visualization researchers must understand and work towards the challenges posed by multidisciplinary simulation scenarios. This paper addresses some of these challenges, describing technologies that must be investigated to create a useful visualization analysis tool for domain scientists.

Miceli, Kristina D.↗

NASA NTRS1990

Programmable remapper with single flow architecture

The invention relates to image processing systems and methods and in particular to a machine which accepts a real time video image in the form of a matrix of picture elements (pixels) and remaps such image according to a selectable one of a plurality of mapping functions to create an output matrix of pixels. Such mapping functions, or transformations, may be any one of a number of different transformations depending on the objective of the user of the system. The system remaps input images from one coordinate system to another using a set of look-up tables for the data necessary for the transform. The transforms, which are operator selectable, are precomputed and loaded into massive look-up tables. Input pixels, via the look-up tables of any particular transform selected, are mapped into output pixels with the radiance information of the input pixels being appropriately weighted. An earlier embodiment of the system included two parallel processors: a collective processor which mapped multiple input pixels into a single output pixel and an interpolative processor. The interpolative processor performed an interpolation among pixels in the input image where a given input pixel may affect the value of many output pixels. Several advantages are provided over previous embodiments in that the two distinct processors are replaced by a single processor capable of performing both types of operations (collective and interpolative) with no more complexity. Previously, there has existed no image processor or 'remapper' that can operate with sufficient speed and flexibility to permit investigating different transformation patterns in real time.

Fisher, Timothy E.↗

NASA NTRS2006

Implementing Access to Data Distributed on Many Processors

A reference architecture is defined for an object-oriented implementation of domains, arrays, and distributions written in the programming language Chapel. This technology primarily addresses domains that contain arrays that have regular index sets with the low-level implementation details being beyond the scope of this discussion. What is defined is a complete set of object-oriented operators that allows one to perform data distributions for domain arrays involving regular arithmetic index sets. What is unique is that these operators allow for the arbitrary regions of the arrays to be fragmented and distributed across multiple processors with a single point of access giving the programmer the illusion that all the elements are collocated on a single processor. Today's massively parallel High Productivity Computing Systems (HPCS) are characterized by a modular structure, with a large number of processing and memory units connected by a high-speed network. Locality of access as well as load balancing are primary concerns in these systems that are typically used for high-performance scientific computation. Data distributions address these issues by providing a range of methods for spreading large data sets across the components of a system. Over the past two decades, many languages, systems, tools, and libraries have been developed for the support of distributions. Since the performance of data parallel applications is directly influenced by the distribution strategy, users often resort to low-level programming models that allow fine-tuning of the distribution aspects affecting performance, but, at the same time, are tedious and error-prone. This technology presents a reusable design of a data-distribution framework for data parallel high-performance applications. Distributions are a means to express locality in systems composed of large numbers of processor and memory components connected by a network. Since distributions have a great effect on the performance of applications, it is important that the distribution strategy is flexible, so its behavior can change depending on the needs of the application. At the same time, high productivity concerns require that the user be shielded from error-prone, tedious details such as communication and synchronization.

James, Mark↗

NASA NTRS2011

Hyperresolution Global Land Surface Modeling: Meeting a Grand Challenge for Monitoring Earth's Terrestrial Water

Monitoring Earth's terrestrial water conditions is critically important to many hydrological applications such as global food production; assessing water resources sustainability; and flood, drought, and climate change prediction. These needs have motivated the development of pilot monitoring and prediction systems for terrestrial hydrologic and vegetative states, but to date only at the rather coarse spatial resolutions (approx.10-100 km) over continental to global domains. Adequately addressing critical water cycle science questions and applications requires systems that are implemented globally at much higher resolutions, on the order of 1 km, resolutions referred to as hyperresolution in the context of global land surface models. This opinion paper sets forth the needs and benefits for a system that would monitor and predict the Earth's terrestrial water, energy, and biogeochemical cycles. We discuss six major challenges in developing a system: improved representation of surface-subsurface interactions due to fine-scale topography and vegetation; improved representation of land-atmospheric interactions and resulting spatial information on soil moisture and evapotranspiration; inclusion of water quality as part of the biogeochemical cycle; representation of human impacts from water management; utilizing massively parallel computer systems and recent computational advances in solving hyperresolution models that will have up to 10(exp 9) unknowns; and developing the required in situ and remote sensing global data sets. We deem the development of a global hyperresolution model for monitoring the terrestrial water, energy, and biogeochemical cycles a grand challenge to the community, and we call upon the international hydrologic community and the hydrological science support infrastructure to endorse the effort.

Wood, Eric F.↗

NASA NTRS2015

A Coordinated X-Ray and Optical Campaign of the Nearest Massive Eclipsing Binary, Delta Orionis Aa. II. X-Ray Variability

We present time-resolved and phase-resolved variability studies of an extensive X-ray high-resolution spectral data set of the delta Ori Aa binary system. The four observations, obtained with Chandra ACIS (Advanced CCD Imaging Spectrometer) HETGS (High Energy Transmission Grating), have a total exposure time approximately equal to 479 kiloseconds and provide nearly complete binary phase coverage. Variability of the total X-ray flux in the range of 5-25 angstroms is confirmed, with a maximum amplitude of about plus or minus15 percent within a single approximately equal to125 kiloseconds observation. Periods of 4.76 and 2.04 days are found in the total X-ray flux, as well as an apparent overall increase in the flux level throughout the nine-day observational campaign. Using 40 kiloseconds contiguous spectra derived from the original observations, we investigate the variability of emission line parameters and ratios. Several emission lines are shown to be variable, including S (sub XV), Si (sub XIII), and Ne (sub IX). For the first time, variations of the X-ray emission line widths as a function of the binary phase are found in a binary system, with the smallest widths at phi = 0.0 when the secondary delta Ori Aa2 is at the inferior conjunction. Using 3D hydrodynamic modeling of the interacting winds, we relate the emission line width variability to the presence of a wind cavity created by a wind-wind collision, which is effectively void of embedded wind shocks and is carved out of the X-ray-producing primary wind, thus producing phase-locked X-ray variability.

X-ray flux↗

NASA NTRS2012

Monitoring of International Space Station Telemetry Using Shewhart Control Charts

Shewhart control charts have been established as an expedient method for analyzing dynamic, trending data in order to identify anomalous subsystem performance as soon as such performance would exceed a statistically established baseline. Additionally, this leading indicator tool integrates a selection methodology that reduces false positive indications, optimizes true leading indicator events, minimizes computer processor unit duty cycles, and addresses human factor concerns (i.e., the potential for flight-controller data overload). This innovation leverages statistical process control, and provides a relatively simple way to allow flight controllers to focus their attention on subtle system changes that could lead to dramatic off-nominal system performance. Finally, this capability improves response time to potential hardware damage and/or crew injury, thereby improving space flight safety. Shewhart control charts require normalized data. However, the telemetry from the ISS Early External Thermal Control System (EETCS) was not normally distributed. A method for normalizing the data was implemented, as was a means of selecting data windows, the number of standard deviations (Sigma Level), the number of consecutive points out of limits (Sequence), and direction (increasing or decreasing trend data). By varying these options, and treating them like dial settings, the number of nuisance alerts and leading indicators were optimized. The goal was to capture all leading indicators while minimizing the number of nuisances. Lean Six Sigma (L6S) design of experiment methodologies were employed. To optimize the results, Perl programming language was used to automate the massive amounts of telemetry data, control chart plots, and the data analysis.

Fitch, Jeffery T.↗

NASA NTRS2012

An Automated Algorithm to Screen Massive Training Samples for a Global Impervious Surface Classification

An algorithm is developed to automatically screen the outliers from massive training samples for Global Land Survey - Imperviousness Mapping Project (GLS-IMP). GLS-IMP is to produce a global 30 m spatial resolution impervious cover data set for years 2000 and 2010 based on the Landsat Global Land Survey (GLS) data set. This unprecedented high resolution impervious cover data set is not only significant to the urbanization studies but also desired by the global carbon, hydrology, and energy balance researches. A supervised classification method, regression tree, is applied in this project. A set of accurate training samples is the key to the supervised classifications. Here we developed the global scale training samples from 1 m or so resolution fine resolution satellite data (Quickbird and Worldview2), and then aggregate the fine resolution impervious cover map to 30 m resolution. In order to improve the classification accuracy, the training samples should be screened before used to train the regression tree. It is impossible to manually screen 30 m resolution training samples collected globally. For example, in Europe only, there are 174 training sites. The size of the sites ranges from 4.5 km by 4.5 km to 8.1 km by 3.6 km. The amount training samples are over six millions. Therefore, we develop this automated statistic based algorithm to screen the training samples in two levels: site and scene level. At the site level, all the training samples are divided to 10 groups according to the percentage of the impervious surface within a sample pixel. The samples following in each 10% forms one group. For each group, both univariate and multivariate outliers are detected and removed. Then the screen process escalates to the scene level. A similar screen process but with a looser threshold is applied on the scene level considering the possible variance due to the site difference. We do not perform the screen process across the scenes because the scenes might vary due to the phenology, solar-view geometry, and atmospheric condition etc. factors but not actual landcover difference. Finally, we will compare the classification results from screened and unscreened training samples to assess the improvement achieved by cleaning up the training samples. Keywords:

Tan, Bin↗

DOE OSTI2024

A Million Person Study Innovation: Evaluating Cognitive Impairment and other Morbidity Outcomes from Chronic Radiation Exposure Through Linkages with the Centers for Medicaid and Medicare Services Assessment and Claims Data

Here, the study of One Million U.S. Radiation Workers and Veterans, the Million Person Study (MPS), examines the health consequences, both cancer and non-cancer, of exposure to ionizing radiation received gradually over time. Recently the MPS has focused on mortality patterns from neurological and behavioral conditions, e.g., Parkinson's disease, Alzheimer's disease, dementia, and motor neuron disease such as amyotrophic lateral sclerosis. A fuller picture of radiation-related late effects comes from studying both mortality and the occurrence (incidence) of conditions not leading to death. Accordingly, the MPS is identifying neurocognitive diagnoses from fee-for-service insurance claims from the Centers for Medicare and Medicaid Services (CMS), among Medicare beneficiaries beginning in 1999 (the earliest date claims data are available). Linkages to date have identified ∼540,000 workers with available health information. Such linkages provide individual information on important co-factor and confounding variables such as smoking, alcohol consumption, blood pressure, obesity, diabetes and many other health and demographic characteristics. The total person-level set of time-dependent variables, outcomes, organ-specific dose measures, co-factors, and demographics will be massive and much too large to be evaluated with standard software. Thus, development of specialized open-source software designed for large datasets (Colossus) is nearly complete. The wealth of information available from CMS claims data, coupled with individual dose reconstructions, will thus greatly enhance the quality and precision of health evaluations for this new field of low-dose radiation and neurocognitive effects.

Dauer, Lawrence T.↗

NASA NTRS2013

A CANDELS-3d-HST Synergy: Resolved Star Formation Patterns at 0.7 less than z less than 1.5

We analyze the resolved stellar populations of 473 massive star-forming galaxies at 0.7 < z < 1.5, with multiwavelength broadband imaging from CANDELS andHalpha surface brightness profiles at the same kiloparsec resolution from 3D-HST. Together, this unique data set sheds light on how the assembled stellar mass is distributed within galaxies, and where new stars are being formed. We find the Halpha morphologies to resemble more closely those observed in the ACS I band than in the WFC3 H band, especially for the larger systems. We next derive a novel prescription for Halpha dust corrections, which accounts for extra extinction toward H II regions. The prescription leads to consistent star formation rate (SFR) estimates and reproduces the observed relation between the Halpha/UV luminosity ratio and visual extinction, on both a pixel-by-pixel and a galaxy-integrated level. We find the surface density of star formation to correlate with the surface density of assembled stellar mass for spatially resolved regions within galaxies, akin to the so-called "main sequence of star formation" established on a galaxy-integrated level. Deviations from this relation toward lower equivalent widths are found in the inner regions of galaxies. Clumps and spiral features, on the other hand, are associated with enhanced H alpha equivalent widths, bluer colors, and higher specific SFRs compared to the underlying disk. Their Halpha/UV luminosity ratio is lower than that of the underlying disk, suggesting that the ACS clump selection preferentially picks up those regions of elevated star formation activity that are the least obscured by dust. Our analysis emphasizes that monochromatic studies of galaxy structure can be severely limited by mass-to-light ratio variations due to dust and spatially inhomogeneous star formation histories.

SYNERGY↗

NASA NTRS1983

Massively parallel processor computer

An apparatus for processing multidimensional data with strong spatial characteristics, such as raw image data, characterized by a large number of parallel data streams in an ordered array is described. It comprises a large number (e.g., 16,384 in a 128 x 128 array) of parallel processing elements operating simultaneously and independently on single bit slices of a corresponding array of incoming data streams under control of a single set of instructions. Each of the processing elements comprises a bidirectional data bus in communication with a register for storing single bit slices together with a random access memory unit and associated circuitry, including a binary counter/shift register device, for performing logical and arithmetical computations on the bit slices, and an I/O unit for interfacing the bidirectional data bus with the data stream source. The massively parallel processor architecture enables very high speed processing of large amounts of ordered parallel data, including spatial translation by shifting or sliding of bits vertically or horizontally to neighboring processing elements.

Fung, L. W.↗

DOE OSTI2025

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗

NASA NTRS1997

High redshift quasars and high metallicities

A large-scale code called Cloudy was designed to simulate non-equilibrium plasmas and predict their spectra. The goal was to apply it to studies of galactic and extragalactic emission line objects in order to reliably deduce abundances and luminosities. Quasars are of particular interest because they are the most luminous objects in the universe and the highest redshift objects that can be observed spectroscopically, and their emission lines can reveal the composition of the interstellar medium (ISM) of the universe when it was well under a billion years old. The lines are produced by warm (approximately 10(sup 4)K) gas with moderate to low density (n less than or equal to 10(sup 12) cm(sup -3)). Cloudy has been extended to include approximately 10(sup 4) resonance lines from the 495 possible stages of ionization of the lightest 30 elements, an extension that required several steps. The charge transfer database was expanded to complete the needed reactions between hydrogen and the first four ions and fit all reactions with a common approximation. Radiative recombination rate coefficients were derived for recombination from all closed shells, where this process should dominate. Analytical fits to Opacity Project (OP) and other recent photoionization cross sections were produced. Finally, rescaled OP oscillator strengths were used to compile a complete set of data for 5971 resonance lines. The major discovery has been that high redshift quasars have very high metallicities and there is strong evidence that the quasar phenomenon is associated with the birth of massive elliptical galaxies.

Ferland, Gary J.↗

NASA NTRS1998

The Soft X-Ray Emission Component of Spiral Galaxies

Work included the analysis of the HRJ observations of the Sombrero galaxy (Fabbiano and Juda) published in Ap.J. This paper discussed the discovery of a point-like x-ray source at the nucleus of the galaxy, which is suspected to host a massive black hole. More work was done on the analysis of the Observation of M94 in support of an AXAF proposal. We have also analyzed the M81 data by adding to our observation the entire set of the archival ROSAT data. We plan to write up the results for publication. Both galaxies have nuclei optically similar to that of the Sombrero galaxy. The nucleus of M81 is a known x-ray source. The M94 data has revealed a point-like nuclear source superposed on more diffuse emission.

Fabbiano, Giuseppina↗

NASA NTRSDate not supplied

Informing Wildfire Needs: The Expanded User Interface of NASA's Fire Information for Resource Management System (Firms)

As the global community continues to experience, and respond to, living in a changing environment, access to tools, technologies, and timely data utilized by an increasingly diverse set of stakeholders is increasing. This year, 2023, has thus far seen an unprecedented number of extreme events, increasingly driven by changes in the climate and a strong 2023 ENSO pattern. In Canada, a record number of wildfires, and associated weather events, evacuations, and infrastructure and habitat destruction has taken place, and is ongoing. Large swaths of Greece have experienced similar wildfire destruction. Most recently, Maui has experienced destructive wildfires, and early 2023 saw massive wildfires in Chile. NASA's Fire Information for Resource Management System, or FIRMS, has a fifteen-year history of providing timely and comprehensive data and information on wildfires to stakeholders. FIRMS was initially developed in 2007 by the University of Maryland, with funds from NASA's Applied Sciences Program and the United Nations Food and Agriculture Organization (UN FAO), to provide near real-time active fire Locations to natural resource managers that faced challenges obtaining timely satellite-derived fire information. FIRMS has consistently evolved to address the needs of stakeholders Living in a changing environment; in 2012 it transitioned to NASA LANCE and in 2021 through a partnership between NASA and the US Forest Service, an updated version of FIRMS was released for the US and Canada. As NASA and other federal agencies continue to accelerate Open Science through integrated efforts such as the Year of Open Science, the provision of readily discoverable, findable, accessible, interoperable, reusable data represents a major focus to facilitate equitable outcomes. FIRMS supports this acceleration in Open Science by continuing to provision data and information for its traditional user base, while addressing the novel user needs of an increasingly diverse set of stakeholders seeking robust, reliable, transparently generated data and information. Increasingly, FIRMS is utilized by citizen scientists and individuals directly affected by wildfires - through evacuations, risks to structures/homes, poor air quality. etc. FIRMS has also been Leveraged to detect and assess the impacts resulting from ongoing conflicts. This further highlights the multi-faceted impacts of wildfires and other events. In the Fall of 2023, FIRMS will release an expanded User Interface (UI). This interface captures and reflects the needs of, and input from, a multitude of users. These users range from federal agency representatives to non-government organizations to the private sector to citizen science entities. To respond to this expansive and diverse user need base, the updated FIRMS UI will capture a range of features to support those beginning to explore the range of data and tools available to inform wildfire awareness and knowledge. These users are supported through a Basic Mode interface, furnishing access to a light set of functionalities that provision straight-forward, readily usable information and data, and ingestible knowledge. The Advanced Mode interface supports those stakeholder groups already proficient in navigating FIRMS. These stakeholders, representing fire managers and others, perform active fire management and tactical wildfire response activities. For these stakeholders, additional datasets have been included which require in-depth knowledge of both the utility as well as the caveats of such datasets. Additional functionalities have also been embedded to aid specific user queries. The expanded UI will introduce a new Experimental Mode. The focus of this UI will be to support the provision of emerging and innovative datasets that are in development for review and comment by the user community Examples include post-fire products generated by NASA's Earth Information System (EIS) Fire. This presentation will provide an overview of the expanded FIRMS UI. We will discuss how this UI is designed to be scalable and support the unique needs of an expanding and diverse user base. We will highlight key features, elements, and datasets, and describe how user needs have informed and guided the design of the UI. We will also share recent use cases to convey, and increase awareness, among conference participants. As the global community faces more extreme wildfires, due to climate variability and change, there is an increased need for reliable data to inform, manage, and mitigate the impacts of these events. Through this work, NASA FIRMS is striving to level the playing field, by making information accessible to all; from policy makers to the private sector to historically marginalized communities. In doing so, NASA is promoting the all-hands-on-deck response needed to minimize the impacts of wildfires and harness the strengths of open science to address the greatest environmental challenge faced.

Jenny Hewson↗

NASA NTRS1988

The topology of large-scale structure. II - Nonlinear evolution of Gaussian models

The evolution of non-Gaussian behavior in the large-scale universe from Gaussian initial conditions is studied. Topology measures developed in previous papers are applied to the smoothed initial, final, and biased matter distributions of cold dark matter, white noise, and massive neutrino simulations. When the smoothing length is approximately twice the mass correlation length or larger, the evolved models look like the initial conditions, suggesting that random phase hypotheses in cosmology can be tested with adequate data sets. When a smaller smoothing length is used, nonlinear effects are recovered, so nonlinear effects on topology can be detected in redshift surveys after smoothing at the mean intergalaxy separation. Hot dark matter models develop manifestly non-Gaussian behavior attributable to phase correlations, with a topology reminiscent of bubble or sheet distributions. Cold dark matter models remain Gaussian, and biasing does not disguise this.

Melott, Adrian L.↗