Search NASA⌕ Search

SEARCH · Search NASA

Results for “group representations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 487 records · Page 27

Predictive Modeling for Differential Diagnosis and Mortality Risk Assessment

The prevalence of electronic health record (EHR) systems has brought prodigious biomedical informatics opportunity. Automated machine learning methods can effectively utilize such data and have become common tools for healthcare predictive modeling. Researches in medical informatics have explored the potential of deep learning and classical models in emergent care scenarios. In particular, predicting differential diagnoses for admissions have proven useful in decreasing unnecessary lab tests and improving inpatient triage decision-making. Moreover, identification of high-risk patients for in-hospital mortality is vitally important to maximize allocation of medical resources.The Medical Information Mart for Intensive Care (MIMIC-III) database, containing de-identified critical care inpatient was used in our study. This data set captures hospital patient laboratory measurements, pharmacologic prescriptions, diagnostic data and procedure event recordings. When considering adult patients and discounting admissions with ICU length of stay less than 24 hours, there were 37,787 unique admissions and 30,414 total patients. We examined the top 25 most prevalent ICD-9 group-level disease specificities in MIMIC-III using a multi-label classification model. In-hospital mortality was modeled as binary classification with 4,155 (13%) adult patients that expired, of which 3,138 (75.5%) were in the ICU setting. The metrics AUC, F1 score, sensitivity and specificity values calculated for each disease label measured prediction performance.The usage of ICD-9 group codes reduced feature dimension from 14,567 to 942 and greatly improved distribution of patient diagnostic categories. Disease temporal patterns were captured by considering the most frequently sampled 6 vital signs and 13 laboratory values. Missing data were imputed at each time-stamp. Time-series raw hourly average values were converted into 5 summary features (mean, standard deviation, number of observations, min & max values). Patient demographic variables such as age, gender, marital status and ethnicity were also factored into the modeling. Choi et al showed that contextual embedding of medical data, diagnostic and procedural codes alone can predict future diagnoses with sensitivity as high as 0.79. We utilized an embedding technique called word2vec which allowed sparse representations of medical history to be transformed into dense word vectors. The mappings captured contextual information by treating each admission as a sentence and learning the most likely neighboring words in a sliding window fashion. Binary and multi-label classification was achieved via collapse models, which do not consider temporal information, as well as recurrent neural networks with regularization, Softmax output layer activation together with categorical cross-entropy as the loss function.

US Army collaboration↗

Data-Driven Smoothers for Extreme-Scale Computing

Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational domain. The two most common families of patch-based methods are block-Jacobi and Schwarz methods, where the former typically corresponds to non-overlapping domains and the later implies some overlap. We focus on cases where each patch consists of the degrees of freedom on a finite element method mesh cell. Patch methods often capture complex local physics much more effectively than simpler point-smoothers such as Jacobi; however, forming, inverting, and applying each patch can be prohibitively expensive in terms of both storage and computation time. To this end, we propose several approaches for performing analysis on these patches and constructing a reduced representation. The compression techniques rely on either matrix norm comparisons or unsupervised learning via a clustering approach. We illustrate how it is frequently possible to retain/factor less than 5% of all patches and still develop a method that converges only a little slower than when all patches are stored/factored.

97 MATHEMATICS AND COMPUTING↗

Algebraic Theory of Patterns as Generalized Symmetries

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.

97 MATHEMATICS AND COMPUTING↗

Toward domain-specific design environments: Some representation ideas from the telecommunications domain

ACME is an experimental environment for investigating new approaches to modeling and analysis of system requirements and designs. ACME is built on and extends object-oriented conceptual modeling techniques and knowledge representation and reasoning (KRR) tools. The most immediate intended use for ACME is to help represent, understand, and communicate system designs during the early stages of system planning and requirements engineering. While our research is ostensibly aimed at software systems in general, we are particularly motivated to make an impact in the telecommunications domain, especially in the area referred to as Intelligent Networks (IN's). IN systems contain the software to provide services to users of a telecommunications network (e.g., call processing services, information services, etc.) as well as the software that provides the internal infrastructure for providing the services (e.g., resource management, billing, etc.). The software includes not only systems developed by the network proprietors but also by a growing group of independent service software providers.

Greenspan, Sol↗

Conformal field theories are magical

“Magic” is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z 3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q = 3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. Here, we explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT.

1-dimensional spin chains↗

Revisiting the Definition of Rapid Intensification of Tropical Cyclones by Clustering the Initial Intensity and Inner‐Core Size

Abstract Rapid intensification (RI) of tropical cyclones (TCs) provides a great challenge in operational forecasting and contributes significantly to the development of major TCs. RI is commonly defined as an increase in the maximum sustained surface wind speed of at least a certain threshold within 24 hr. The most widely used threshold is 30 kt (15.4 m/s), which was determined statistically. Here we propose a new definition for RI by objectively clustering TCs using the intensification rate, initial intensity, and radius of the maximum wind speed (RMW). A group of 770 samples is separated at a threshold of 45 kt (23.2 m/s). The threshold is 40 kt (20.6 m/s) for the western North Atlantic, where TC size measurements are more reliable. Monte Carlo experiments demonstrate that the proposed threshold is robust even considering the uncertainty in RMW of as high as 30 km. We show that, when a TC undergoes RI, its maximum wind speed is approximately 60 ± 15 kt (30.9 ± 7.7 m/s) and the RMW is 45 ± 20 km. The new threshold outperforms the conventional threshold of 30 kt/24 hr in describing the bimodal distribution of lifetime maximum intensity and explaining the annual count of Category 5 TCs. This new definition provides a more physically based threshold and describes a more reliable representation of extreme events. Although more comparisons are needed for operational application, it is likely to be desirable for case‐based process studies and could provide a more valuable metric for TC intensification classification and research.

Li, Yi↗

Genome-wide association study identifies four pan-ancestry loci for suicidal ideation in the Million Veteran Program

Suicidal ideation (SI) often precedes and predicts suicide attempt and death, is the most common suicidal phenotype and is over-represented in veterans. The genetic architecture of SI in the absence of suicide attempt (SA) is unknown, yet believed to have distinct and overlapping risk with other suicidal behaviors. We performed the first GWAS of SI without SA in the Million Veteran Program (MVP), identifying 99,814 SI cases from electronic health records without a history of SA or suicide death (SD) and 512,567 controls without SI, SA or SD. GWAS was performed separately in the four largest ancestry groups, controlling for sex, age and genetic substructure. Ancestry-specific results were combined via meta-analysis to identify pan-ancestry loci. Four genome-wide significant (GWS) loci were identified in the pan-ancestry meta-analysis with loci on chromosomes 6 and 9 associated with suicide attempt in an independent sample. Pan-ancestry gene-based analysis identified GWS associations with DRD2, DCC, FBXL19, BCL7C, CTF1, ANNK1, and EXD3. Gene-set analysis implicated synaptic and startle response pathways (q’s<0.05). European ancestry (EA) analysis identified GWS loci on chromosomes 6 and 9, as well as GWS gene associations in EXD3, DRD2, and DCC. No other ancestry-specific GWS results were identified, underscoring the need to increase representation of diverse individuals. The genetic correlation of SI and SA within MVP was high (r G = 0.87; p = 1.09e-50), as well as with post-traumatic stress disorder (PTSD; r G = 0.78; p = 1.98e-95) and major depressive disorder (MDD; r G = 0.78; p = 8.33e-83). Conditional analysis on PTSD and MDD attenuated most pan-ancestry and EA GWS signals for SI without SA to nominal significance, with the exception of EXD3 which remained GWS. Our novel findings support a polygenic and complex architecture for SI without SA which is largely shared with SA and overlaps with psychiatric conditions frequently comorbid with suicidal behaviors.

59 BASIC BIOLOGICAL SCIENCES↗

Method for Tracking and Communicating Aggregate Risk Through the Use of Model-Based Systems Engineering (MBSE) Tools

Large, complex projects can identify a significant number and variety of risks, throughout the project life cycle. These risks are analyzed, mitigated, closed or accepted as independent uncertainties. Once closed or accepted, it is easy for projects to lose awareness of their impact. In reality, each of these risks contributes some amount to the overall risk posture of the project. The ability to track and effectively communicate this aggregate risk has represented a challenge to project management. There have been previous attempts to create a schema to communicate the aggregate effect of risks, without notable success. Most of these attempts have centered on some additive metric derived from the scoring of likelihood and consequence values. This, in and of itself, is a logical approach, but all too often the scores were then aggregated to a level where all context was lost. One weakness has been a lack of attempt to create linkages or logical groups of the risks upon which useful aggregation could then occur. The overall move to model-based (systems) engineering (MBSE) has opened up a vast frontier of opportunities to better integrate all project data. MBSE provides an underlying layer that links data items to each other. Objectives link to requirements, which then link to functions, functions to physical architecture items, and so on, as far down as projects want to model. While it started with a focus on modeling requirements based on things like use cases, efforts are now underway to integrate safety and mission assurance (S&MA) information and analyses, such as risks. This effort, called Model Based Mission Assurance (MBMA), is yielding models that are more useful and are a more accurate representations of the systems. MBSE models, with this ability to link related items, provide a new means of tracking and communicating aggregate risks. In the proposed method, risks are added into the models as distinct items, having attributes that communicate a scoring derived from the likelihood and consequence values as charted on the standard NASA 5x5 risk matrix. Like earlier efforts, each box in the 5x5 has an associated scoring, which may include both a current score and potential post-mitigation/control score. The risk items are then linked to elements of the model, such as system objectives/goals, requirements, functions, or physical architecture items, with "Risk to" relationships. These risks will then be communicated by use of reports generated from the model, detailing all risks and/or hazards linked to model elements. These reports can include aggregate impacts, including a current scoring and potential future state scoring based on the planned mitigations and/or controls. These reports will show all risks, open, accepted, and closed, linked to project objectives or requirements. When run as part of an upcoming risk acceptance discussion, these reports will serve to remind the team of all previous risks that relate to the effected portion of the system. When included as part of periodic program or project reviews, risk reviews, and safety reviews, this method can improve the overall understanding of the system's true risk posture. This proposed method takes full advantage of the advances that modern modeling techniques provide, with a minimal investment of additional time. Utilizing the model environment also enables a near constant access to current state of aggregate risks.

model based mission assurance↗

Integrating Arctic Plant Functional Types in a Land Surface Model Using Above‐ and Belowground Field Observations

Abstract Accurate simulations of high‐latitude ecosystems are critical for confident Earth system model (ESM) projections of carbon cycle feedbacks to global climate change. Land surface model components of ESMs, including the E3SM Land Model (ELM), simulate vegetation growth and ecosystem responses to changing climate and atmospheric CO 2 concentrations by grouping heterogeneous vegetation into like sets of plant functional types (PFTs). Many such models represent high‐latitude vegetation using only two PFTs (shrub and grass), thereby missing the diversity of vegetation growth forms and functional traits in the Arctic. Here, we use field observations of biomass and leaf traits across a gradient of plant communities on the Seward Peninsula in northwest Alaska to replace the original ELM configuration for the first time with nine Arctic‐specific PFTs. The newly developed PFTs include: (1) nonvascular mosses and lichens, (2) deciduous and evergreen shrubs of various height classes, including an alder PFT, (3) graminoids, and (4) forbs. Improvements relative to the original model configuration included greater belowground biomass allocation, persistent fine roots and rhizomes of nonwoody plants, and better representation of variability in total plant biomass across sites with varying plant communities and depth to bedrock. Simulations through 2100 using the RCP8.5 climate scenario and constant PFT fractional areas showed alder‐dominated plant communities gaining more biomass and lichen‐dominated communities gaining less biomass compared to default PFTs. Our results highlight how representing the diversity of arctic vegetation and confronting models with measurements from varied plant communities improves the representation of arctic vegetation in terrestrial ecosystem models.

54 ENVIRONMENTAL SCIENCES↗

Digital Earth Initiative: A Joint Interagency Program

The Digital Earth is a virtual representation of our planet that enables a person to explore and interact with the vast amounts of natural and cultural information gathered about the Earth. The Digital Earth comprises data interfaces and standards enabling access to geo-referenced data from remote sensing, cartographic, demographic, medical, and other sources to respond to questions posed by the user. In a recent address at the California Science Center in Los Angeles, Vice President Al Gore articulated a Digital Earth Vision. That vision spoke to developing a multi-resolution, three-dimensional representation of the planet, into which we can roam and zoom into vast quantities of embedded geo-referenced data. The vision was not limited to moving through space but also allowing travel over a time-line, which can be set for days, years, centuries, or even geological epochs. As prototypes become available, it would also be possible to interact with the Digital Earth in multiple places around the country with access to high-speed networks and at a more limited level of access over the Internet. NASA was asked by the Vice President to lead an interagency initiative that would take steps to bring this vision to the public. This talk describes the start-up and plans of the Digital Earth Interagency Working Group in the formulation of its charter, an architecture reference model for Digital Earth, public/private partnerships, cooperative agreement notices, Digital Earth prototypes, and testbeds. Animations employing technologies for virtual roaming and zooming through multi-resolution satellite data set as prototype systems will be presented along with examples of potential user scenarios. Plans for engaging academia and industry in implementing the Digital Earth initiative will be discussed.

Halem, Milton↗

Exploiting the Convergence of Evidence in Satellite Data for Advanced Weather Index Insurance Design

The goal of drought-related weather index insurance (WII) is to protect smallholder farmers against the risk of weather shocks and to increase their agricultural productivity. Estimates of precipitation and vegetation greenness are the two dominant satellite datasets. However, ignoring additional moisture- and energy-related processes that influence the response of vegetation to rainfall leads to an incomplete representation of the hydrologic cycle. This study evaluates the added value of considering multiple independent satellite-based variables to design, calibrate, and validate weather insurance indices on the African continent. The satellite data include two rainfall datasets, soil moisture, the evaporative stress index (ESI), and vegetation greenness. We limit artificial advantages by resampling all datasets to the same spatial (0.25°) and temporal (monthly) resolution, although datasets with a higher spatial resolution might have an added value, if considered as the single source of information for localized applications. A higher correlation coefficient between the moisture-focused variables and the normalized difference vegetation index (NDVI), an indicator for vegetation vigor, provides evidence for the datasets’ capability to capture agricultural drought conditions on the ground. The Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) rainfall dataset, soil moisture, and ESI show higher correlations with the (lagged) NDVI in large parts of Africa, for different land covers and various climate zones, than the African Rainfall Climatology, version 2 (ARC2), rainfall dataset, which is often used in WII. A comparison to drought years as reported by farmers in Ethiopia, Senegal, and Zambia indicates a high “hit rate” of all satellite-derived anomalies regarding the detection of severe droughts but limitations regarding moderate drought events.

drought↗

BGen: A UML Behavior Network Generator Tool

BGen software was designed for autogeneration of code based on a graphical representation of a behavior network used for controlling automatic vehicles. A common format used for describing a behavior network, such as that used in the JPL-developed behavior-based control system, CARACaS ["Control Architecture for Robotic Agent Command and Sensing" (NPO-43635), NASA Tech Briefs, Vol. 32, No. 10 (October 2008), page 40] includes a graph with sensory inputs flowing through the behaviors in order to generate the signals for the actuators that drive and steer the vehicle. A computer program to translate Unified Modeling Language (UML) Freeform Implementation Diagrams into a legacy C implementation of Behavior Network has been developed in order to simplify the development of C-code for behavior-based control systems. UML is a popular standard developed by the Object Management Group (OMG) to model software architectures graphically. The C implementation of a Behavior Network is functioning as a decision tree.

Huntsberger, Terry↗

Molecular NMR shieldings, J -couplings, and magnetizabilities from numeric atom-centered orbital based density-functional calculations

This paper reports and benchmarks a new implementation of nuclear magnetic resonance shieldings, magnetizabilities, and J-couplings for molecules within semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. NAO basis sets are attractive for the calculation of these nuclear magnetic resonance (NMR) parameters because NAOs provide accurate atomic orbital representations especially near the nucleus, enabling high-quality results at modest computational cost. Moreover, NAOs are readily adaptable for linear scaling methods, enabling efficient calculations of large systems. Here, the paper has five main parts: (1) It reviews the formalism of density functional calculations of NMR parameters in one comprehensive text to make the mathematical background available in a self-contained way. (2) The paper quantifies the attainable precision of NAO basis sets for shieldings in comparison to specialized Gaussian basis sets, showing similar performance for similar basis set size. (3) The paper quantifies the precision of calculated magnetizabilities, where the NAO basis sets appear to outperform several established Gaussian basis sets of similar size. (4) The paper quantifies the precision of computed J-couplings, for which a group of customized NAO basis sets achieves precision of ~Hz for smaller basis set sizes than some established Gaussian basis sets. (5) The paper demonstrates that the implementation is applicable to systems beyond 1000 atoms in size.

74 ATOMIC AND MOLECULAR PHYSICS↗

Noble dark matter: Surprising elusiveness of dark baryons

Dark matter could be a baryonic composite of stronglyc upled constituents transforming under SU⁡(2) 𝐿 . We classify the SU⁡(2) 𝐿 representations of baryons in a class of simple confining dark sectors and find that the lightest state can be a pure singlet or a singlet that mixes with other neutral components of SU⁡(2) 𝐿 representations, which strongly suppresses the dark matter candidate’s interactions with the Standard Model. We focus on models with a confining SU⁡(𝑁 𝑐 ) and heavy dark quarks constituting vectorlike 𝑁 𝑓 -plet of SU⁢(2) 𝐿 . For benchmark 𝑁 𝑐 and 𝑁 𝑓 , we calculate baryon mass spectra, incorporating electroweak gauge boson exchange in the nonrelativistic quark model, and demonstrate that above TeV mass scales, dark matter is dominantly a singlet state. The combination of this singlet nature with the recently discovered ℋ-parity results in an inert state analogous to noble gases, hence we coin the term noble dark matter. Our results can be understood in the nonrelativistic effective theory that treats the dark baryons as elementary states, where we find singlets accompanying triplets, 5-plets, or more exotic representations. This generalization of WIMP-like theories is more difficult to find or rule out than dark matter models that include only a single SU⁡(2) 𝐿 multiplet (such as a wino), motivating new searches in colliders and a reanalysis of direct and indirect detection prospects in astrophysical observations.

dark matter direct detection↗

The first ensemble of kilometer-scale simulations of a hydrological year over the third pole

An accurate understanding of the current and future water cycle over the Third Pole is of great societal importance, given the role this region plays as a water tower for densely populated areas downstream. An emerging and promising approach for skillful climate assessments over regions of complex terrain is kilometer-scale climate modeling. As a foundational step towards such simulations over the Third Pole, we present a multi-model and multi-physics ensemble of kilometer-scale regional simulations for the hydrological year of October 2019 to September 2020. The ensemble consists of 13 simulations performed by an international consortium of 10 research groups, configured with a horizontal grid spacing ranging from 2.2 to 4 km covering all of the Third Pole region. These simulations are driven by ERA5 and are part of a Coordinated Regional Climate Downscaling EXperiment Flagship Pilot Study on Convection-Permitting Third Pole. The simulations are compared against available gridded and in-situ observations and remote-sensing data, to assess the performance and spread of the model ensemble compared to the driving reanalysis during the cold and warm seasons. Although ensemble evaluation is hindered by large differences between the gridded precipitation datasets used as a reference over this region, we show that the ensemble improves on many warm-season precipitation metrics compared with ERA5, including most wet-day and hour statistics, and also adds value in the representation of wet spells in both seasons. As such, the ensemble will provide an invaluable resource for future improvements in the process understanding of the hydroclimate of this remote but important region.

54 ENVIRONMENTAL SCIENCES↗

CMIP6 Models Predict Significant 21st Century Decline of the Atlantic Meridional Overturning Circulation

We explore the representation of the Atlantic Meridional Overturning Circulation (AMOC) in 27 models from the CMIP6 multi-model ensemble. Comparison with RAPID and SAMBA observations suggests that the ensemble mean represents the AMOC strength and vertical profile reasonably well. Linear trends over the entire historical period (1850-2014) are generally neutral, but many models exhibit an AMOC peak around the 1980’s. Ensemble-mean AMOC decline in future (SSP) scenarios is stronger in CMIP6 than CMIP5 models. In fact, AMOC decline in CMIP6 is surprisingly insensitive to the scenario at least up to 2060. We find an emergent relationship among a majority of models between AMOC strength and 21st century AMOC decline. Constraining this relationship with RAPID observations suggests that the AMOC might decline between 6 and 8 Sv (34-45%) by 2100. A smaller group of models projects much less AMOC weakening of only up to 30%.

58 GEOSCIENCES↗

Modeling of the TRIGA IPR-R1 research reactor with the Serpent2/RINNOVO Nodal core analysis package

The Serpent2/RINNOVO nodal core analysis code system, a dedicated tool for modeling research reactors, has the capability to accurately predict important core physics parameters involved in the safety of reactor operation, such as various reactivity coefficients, control rod and bank worths including the shutdown margin, power distributions as well as local neutron flux predictions at various core locations of high importance, e.g., at irradiation rigs. In this work, a hexagonal model of the unrodded initial core of the Brazilian IPR-R1 Mark I type TRIGA nuclear reactor has been created using the Serpent2/RINNOVO code system. The choice of employing a hexagonal core geometry representation has mainly been made to facilitate subsequent fuel shuffling operations and core follow calculations of this reactor. Numerical results in terms of the core eigenvalue and the assembly power distribution have then been compared against corresponding full core Serpent2 results to prove feasibility of using the Serpent2/RINNOVO code system for modeling small and highly heterogeneous TRIGA reactors. Overall, RINNOVO predicts the power distribution very accurately but the eigenvalue error still remains quite large. In light of being the very first evaluation of a TRIGA reactor with the RINNOVO nodal core simulator, these results are also considered to be very preliminary. Improved accuracy is expected by incorporating a proper methodology in the current code system for computing discontinuity factors for multi-assembly configurations. Furthermore, improved results are expected by increasing the number of energy groups used by RINNOVO in these core calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Dynamics and configurations of galaxy triplets

The purpose is to infer the probable dynamical states of galaxy triplets by the observed data on their configurations. Two methods are proposed for describing the distributions of the triplet configuration parameters characterizing a tendency to alignment and hierarchy: (1) obtaining a representative sample of configurations and determining its statistical parameters (moments and percentages); and (2) dividing the region of possible configurations of triple systems (Agekian and Anosova, 1967) into a set of segments and finding the probabilities for the configurations to find themselves in each of them. Both these methods allow representation of the data by numerical simulations as well as observations. The effect of projection was studied. It rather overestimates the alignment and hierarchy of the triple systems. Among the parameters of interest there are found some parameters that are least sensitive to projection effects. The samples consist of simulated galaxy triplets (with hidden mass) as well as of 46 probably physical triple galaxies (Karachentseva et al., 1979). The observed triples as well as numerical models show a tendency to alignment. The triple galaxies do not show any tendency to hierarchy (formation of the temporary binaries), but this tendency may be present for simulated triplets without significant dark matter. The significant hidden mass (of order ten times the total mass of a triplet) decreases the probability of forming a binary and so weakens the hierarchy. Small galaxy groups consisting of 3 to 7 members are probably the most prevalent types of galaxy aggregate (Gorbatsky, 1987). Galaxy triplets are the simplest groups, but dynamically nontrivial ones.

Anosova, Joanna P.↗