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The Roles of Verification, Validation and Uncertainty Quantification in the NASA Standard for Models and Simulations

The National Aeronautics and Space Administration (NASA) recently issued an interim version of the Standard for Models and Simulations (M&S Standard) [1]. The action to develop the M&S Standard was identified in an internal assessment [2] of agency-wide changes needed in the wake of the Columbia Accident [3]. The primary goal of this standard is to ensure that the credibility of M&S results is properly conveyed to those making decisions affecting human safety or mission success criteria. The secondary goal is to assure that the credibility of the results from models and simulations meets the project requirements (for credibility). This presentation explains the motivation and key aspects of the M&S Standard, with a special focus on the requirements for verification, validation and uncertainty quantification. Some pilot applications of this standard to computational fluid dynamics applications will be provided as illustrations. The authors of this paper are the members of the team that developed the initial three drafts of the standard, the last of which benefited from extensive comments from most of the NASA Centers. The current version (number 4) incorporates modifications made by a team representing 9 of the 10 NASA Centers. A permanent version of the M&S Standard is expected by December 2007. The scope of the M&S Standard is confined to those uses of M&S that support program and project decisions that may affect human safety or mission success criteria. Such decisions occur, in decreasing order of importance, in the operations, the test & evaluation, and the design & analysis phases. Requirements are placed on (1) program and project management, (2) models, (3) simulations and analyses, (4) verification, validation and uncertainty quantification (VV&UQ), (5) recommended practices, (6) training, (7) credibility assessment, and (8) reporting results to decision makers. A key component of (7) and (8) is the use of a Credibility Assessment Scale, some of the details of which were developed in consultation with William Oberkampf, David Peercy and Timothy Trocano of Sandia National Laboratories. The focus of most of the requirements, including those for VV&UQ, is on the documentation of what was done and the reporting, using the Credibility Assessment Scale, of the level of rigor that was followed. The aspects of one option for the Credibilty Assessment Scale are (1) code verification, (2) solution verification, (3) validation, (4) predictive capability, (5) technical review, (6) process control, and (7) operator and analyst qualification.

Zang, Thomas A.↗

Common modeling system for digital simulation

The Joint Modeling and Simulation System is a tri-service investigation into a common modeling framework for the development digital models. The basis for the success of this framework is an X-window-based, open systems architecture, object-based/oriented methodology, standard interface approach to digital model construction, configuration, execution, and post processing. For years Department of Defense (DOD) agencies have produced various weapon systems/technologies and typically digital representations of the systems/technologies. These digital representations (models) have also been developed for other reasons such as studies and analysis, Cost Effectiveness Analysis (COEA) tradeoffs, etc. Unfortunately, there have been no Modeling and Simulation (M&S) standards, guidelines, or efforts towards commonality in DOD M&S. The typical scenario is an organization hires a contractor to build hardware and in doing so an digital model may be constructed. Until recently, this model was not even obtained by the organization. Even if it was procured, it was on a unique platform, in a unique language, with unique interfaces, and, with the result being UNIQUE maintenance required. Additionally, the constructors of the model expended more effort in writing the 'infrastructure' of the model/simulation (e.g. user interface, database/database management system, data journalizing/archiving, graphical presentations, environment characteristics, other components in the simulation, etc.) than in producing the model of the desired system. Other side effects include: duplication of efforts; varying assumptions; lack of credibility/validation; and decentralization in policy and execution. J-MASS provides the infrastructure, standards, toolset, and architecture to permit M&S developers and analysts to concentrate on the their area of interest.

Painter, Rick↗

Modeling and Simulation Credibility Assessment of Finite Element Models for Fall From Heights Injury Scenarios

Finite element (FE) computational models of the whole human body are being used to investigate the injury modalities and mechanisms arising from suited astronauts’ ExtraVehicular Activities (EVAs). These FE whole body models – simplified Elemance and THUMS pedestrian versions – have undergone a series of verification and validation (V&V) assessments for applications in automotive, domestic, and contact sports arenas. However, the FE models’ Modeling and Simulation (M&S) credibility assessments for simulating suited astronaut injuries due to fall from heights in altered gravity environments are limited. The current study evaluates the M&S credibility of simplified Elemance and THUMS pedestrian FE models based on eight credibility factors – data pedigree, input pedigree, code verification, solution verification, conceptual validation, referent validation, results uncertainty, and results robustness – as per NASA-STD-7009A [1]. These credibility factors were assigned ordinal scores ranging between 0 to 4, with a score of 0 in the case of insufficient evidence and 4 when all data for the model is known, used appropriately, and traceable to the Real-World System (RWS) with acceptable accuracy, precision, and uncertainty. The credibility factor sufficiency thresholds were assigned upon guidance from NASA EVA subject matter experts. The factor scores were ascertained through the evaluation of M&S credibility assessment procedures described in the published literature and FE model reports. The M&S credibility scores for the Elemance and THUMS FE models vary between 1 and 3 for data pedigree, input pedigree, and referent validation credibility factors, and between 0 and 1 for code verification, solution verification, conceptual validation, results uncertainty and results robustness. The results show that these FE models are credible for simulating fall from heights injury scenarios in specific kinematic and kinetic ranges that correlate with highway and contact sports-related external conditions. Multiple credibility elevation strategies are prescribed to improve the Elemance and THUMS models’ credibility for use in the EVA fall from height injury scenarios.

R A Perkins↗

Digital Lunar Exploration Sites (DLES)

After an almost 50-year absence, NASA along with a group of international and commercial partners will return humans to the surface of the Moon as part of the Artemis program. As with the preceding Apollo program, modeling and simulation (M&S) will be an enabling technology for achieving the Artemis mission objectives. Fortunately, M&S has advanced considerably in the past half century, permitting much more detailed and encompassing integrated representations of the Artemis systems. One modeling area of critical importance to simulating the Artemis elements and mission activities is the accurate and efficient modeling of the operational lunar environment. This is particularly challenging since the Artemis program is considering exploration sites in the area of the Lunar South Pole (LSP), far away from any previous surface exploration sites. Fortunately, we now have considerably more and better data from recent lunar sensing missions. A planetary science team and a human exploration simulation team at NASA’s Johnson Space Center are developing a suite of products called the Digital Lunar Exploration Sites (DLES). DLES is intended to provide some of the necessary lunar environmental data products. This paper describes the fundamental need for DLES, the science data sets that are going into DLES, some of the processes used to integrate this data into DLES products, the basic products that constitute DLES, and some examples of DLES in use.

DLES↗

Digital Lunar Exploration Sites (DLES)

After an almost 50-year absence, NASA along with a group of international and commercial partners will return humans to the surface of the Moon as part of the Artemis program. As with the preceding Apollo program, modeling and simulation (M&S) will be an enabling technology for achieving the Artemis mission objectives. Fortunately, M&S has advanced considerably in the past half century, permitting much more detailed and encompassing integrated representations of the Artemis systems. One modeling area of critical importance to simulating the Artemis elements and mission activities is the accurate and efficient modeling of the operational lunar environment. This is particularly challenging since the Artemis program is considering exploration sites in the area of the Lunar South Pole (LSP), far away from any previous surface exploration sites. Fortunately, we now have considerably more and better data from recent lunar sensing missions. A planetary science team and a human exploration simulation team at NASA’s Johnson Space Center are developing a suite of products called the Digital Lunar Exploration Sites (DLES). DLES is intended to provide some of the necessary lunar environmental data products. This paper describes the fundamental need for DLES, the science data sets that are going into DLES, some of the processes used to integrate this data into DLES products, the basic products that constitute DLES, and some examples of DLES in use.

DLES↗

Towards a Credibility Assessment of Models and Simulations

A scale is presented to evaluate the rigor of modeling and simulation (M&S) practices for the purpose of supporting a credibility assessment of the M&S results. The scale distinguishes required and achieved levels of rigor for a set of M&S elements that contribute to credibility including both technical and process measures. The work has its origins in an interest within NASA to include a Credibility Assessment Scale in development of a NASA standard for models and simulations.

Blattnig, Steve R.↗

Dimensions of Credibility in Models and Simulations

Based on the National Aeronautics and Space Administration's (NASA's) work in developing a standard for models and simulations (M&S), the subject of credibility in M&S became a distinct focus. This is an indirect result from the Space Shuttle Columbia Accident Investigation Board (CAIB), which eventually resulted in an action, among others, to improve the rigor in NASA's M&S practices. The focus of this action came to mean a standardized method for assessing and reporting results from any type of M&S. As is typical in the standards development process, this necessarily developed into defming a common terminology base, common documentation requirements (especially for M&S used in critical decision making), and a method for assessing the credibility of M&S results. What surfaced in the development of the NASA Standard was the various dimensions credibility to consider when accepting the results from any model or simulation analysis. The eight generally relevant factors of credibility chosen in the NASA Standard proved only one aspect in the dimensionality of M&S credibility. At the next level of detail, the full comprehension of some of the factors requires an understanding along a couple of dimensions as well. Included in this discussion are the prerequisites for the appropriate use of a given M&S, the choice of factors in credibility assessment with their inherent dimensionality, and minimum requirements for fully reporting M&S results.

Steele, Martin J.↗

Modeling and Simulation Verification, Validation and Accreditation (VV&A): A New Undertaking for the Exploration Systems Mission Directorate

and Accreditation (VV&A) session audience, a snapshot review of the Exploration Space Mission Directorate s (ESMD) investigation into implementation of a modeling and simulation (M&S) VV&A program. The presentation provides some legacy ESMD reference material, including information on the then-current organizational structure, and M&S (Simulation Based Acquisition (SBA)) focus contained therein, to provide a context for the proposed M&S VV&A approach. This reference material briefly highlights the SBA goals and objectives, and outlines FY05 M&S development and implementation consistent with the Subjective Assessment, Constructive Assessment, Operator-in-the-Loop Assessment, Hardware-in-the-Loop Assessment, and In Service Operations Assessment M&S construct, the NASA Exploration Information Ontology Model (NExIOM) data model, and integration with the Windchill-based Integrated Collaborative Environment (ICE). The presentation then addresses the ESMD team s initial conclusions regarding an M&S VV&A program, summarizes the general VV&A implementation approach anticipated, and outlines some of the recognized VV&A program challenges, all within a broader context of the overarching Integrated Modeling and Simulation (IM&S) environment at both the ESMD and Agency (NASA) levels. The presentation concludes with a status on the current M&S organization s progress to date relative to the recommended IM&S implementation activity. The overall presentation was focused to provide, for the Verification, Validation,

Prill, Mark E.↗

Verification Testing: Meet User Needs Figure of Merit

Verification is the process through which Modeling and Simulation(M&S) software goes to ensure that it has been rigorously tested and debugged for its intended use. Validation confirms that said software accurately models and represents the real world system. Credibility gives an assessment of the development and testing effort that the software has gone through as well as how accurate and reliable test results are. Together, these three components form Verification, Validation, and Credibility(VV&C), the process by which all NASA modeling software is to be tested to ensure that it is ready for implementation. NASA created this process following the CAIB (Columbia Accident Investigation Board) report seeking to understand the reasons the Columbia space shuttle failed during reentry. The reports conclusion was that the accident was fully avoidable, however, among other issues, the necessary data to make an informed decision was not there and the result was complete loss of the shuttle and crew. In an effort to mitigate this problem, NASA put out their Standard for Models and Simulations, currently in version NASA-STD-7009A, in which they detailed their recommendations, requirements and rationale for the different components of VV&C. They did this with the intention that it would allow for people receiving MS software to clearly understand and have data from the past development effort. This in turn would allow the people who had not worked with the MS software before to move forward with greater confidence and efficiency in their work. This particular project looks to perform Verification on several MATLAB (Registered Trademark)(The MathWorks, Inc.) scripts that will be later implemented in a website interface. It seeks to take note and define the limits of operation, the units and significance, and the expected datatype and format of the inputs and outputs of each of the scripts. This is intended to prevent the code from attempting to make incorrect or impossible calculations. Additionally, this project will look at the coding generally and note inconsistencies, redundancies, and other aspects that may become problematic or slow down the codes run time. Certain scripts lacking in documentation also will be commented and cataloged.

validation↗

Understanding Group/Party Affiliation Using Social Networks and Agent-Based Modeling

The dynamics of group affiliation and group dispersion is a concept that is most often studied in order for political candidates to better understand the most efficient way to conduct their campaigns. While political campaigning in the United States is a very hot topic that most politicians analyze and study, the concept of group/party affiliation presents its own area of study that producers very interesting results. One tool for examining party affiliation on a large scale is agent-based modeling (ABM), a paradigm in the modeling and simulation (M&S) field perfectly suited for aggregating individual behaviors to observe large swaths of a population. For this study agent based modeling was used in order to look at a community of agents and determine what factors can affect the group/party affiliation patterns that are present. In the agent-based model that was used for this experiment many factors were present but two main factors were used to determine the results. The results of this study show that it is possible to use agent-based modeling to explore group/party affiliation and construct a model that can mimic real world events. More importantly, the model in the study allows for the results found in a smaller community to be translated into larger experiments to determine if the results will remain present on a much larger scale.

Campbell, Kenyth↗

Digital Lunar Exploration Sites (DLES)

It has been almost 50 years since humans last set foot on the Moon. With NASA’s Artemis program, the United States and its international and commercial partners are embarking on a new endeavor to explore the lunar surface. Before we return, we will have simulated every aspect of these future missions. Many of these models and simulations (M&S) will rely on well-known and commonly-used technologies, some of which trace their origins back to the Apollo program. However, M&S has advanced significantly, as have the underlying computational capabilities. As a result, we are able to model many more aspects of the Artemis vehicles and support systems with significantly improved detail and confidence. Accurately and efficiently modeling the lunar environment will be critical to simulating the Artemis elements and mission activities. This includes characterizing and modeling lunar topography, smaller craters, exposed surface rocks, lunar regolith, surface lighting, and ambient thermal environment. These are all necessary for understanding fundamental behaviors and performance of vehicles and support systems in the lunar environment and are often determining factors in the selection of exploration sites and defining mission profiles. The Astromaterials Research and Exploration Sciences (ARES) team in the Exploration Integration and Science Directorate at NASA’s Johnson Space Center (JSC) and the NASA Exploration Systems Simulations (NExSyS) team in the Simulation and Graphics Branch at JSC are developing and maintaining the Digital Lunar Exploration Sites (DLES) data, documentation, and software packages. This data is being fed directly into a diverse collection of graphics and simulation environments, where it is used to construct the closest known truth for numerous potential Lunar South Pole landing sites. DLES is available to projects across NASA and particularly the Artemis program to support coordinated digital representations of the lunar environment. This paper describes the fundamental need for DLES, the science data sets that are going into DLES, some of the processes used to integrate this data into DLES products, the basic products that constitute DLES, and some examples of DLES in use.

Lunar↗

Can We Trust Computational Modeling for Medical Applications?

Operations in extreme environments such as spaceflight pose human health risks that are currently not well understood and potentially unanticipated. In addition, there are limited clinical and research data to inform development and implementation of therapeutics for these unique health risks. In this light, NASA's Human Research Program (HRP) is leveraging biomedical computational models and simulations (M&S) to help inform, predict, assess and mitigate spaceflight health and performance risks, and enhance countermeasure development. To ensure that these M&S can be applied with confidence to the space environment, it is imperative to incorporate a rigorous verification, validation and credibility assessment (VV&C) processes to ensure that the computational tools are sufficiently reliable to answer questions within their intended use domain. In this presentation, we will discuss how NASA's Integrated Medical Model (IMM) and Digital Astronaut Project (DAP) have successfully adapted NASA's Standard for Models and Simulations, NASA-STD-7009 (7009) to achieve this goal. These VV&C methods are also being leveraged by organization such as the Food and Drug Administration (FDA), National Institute of Health (NIH) and the American Society of Mechanical Engineers (ASME) to establish new M&S VV&C standards and guidelines for healthcare applications. Similarly, we hope to provide some insight to the greater aerospace medicine community on how to develop and implement M&S with sufficient confidence to augment medical research and operations.

Mulugeta, Lealem↗

Intelligent Entity Behavior Within Synthetic Environments

This paper describes some elements in the development of realistic performance and behavior in the synthetic entities (players) which support Modeling and Simulation (M&S) applications, particularly military training. Modern human-in-the-loop (virtual) training systems incorporate sophisticated synthetic environments, which provide: 1. The operational environment, including, for example, terrain databases; 2. Physical entity parameters which define performance in engineered systems, such as aircraft aerodynamics; 3. Platform/system characteristics such as acoustic, IR and radar signatures; 4. Behavioral entity parameters which define interactive performance, including knowledge/reasoning about terrain, tactics; and, 5. Doctrine, which combines knowledge and tactics into behavior rule sets. The resolution and fidelity of these model/database elements can vary substantially, but as synthetic environments are designed to be compose able, attributes may easily be added (e.g., adding a new radar to an aircraft) or enhanced (e.g. Amending or replacing missile seeker head/ Electronic Counter Measures (ECM) models to improve the realism of their interaction). To a human in the loop with synthetic entities, their observed veridicality is assessed via engagement responses (e.g. effect of countermeasures upon a closing missile), as seen on systems displays, and visual (image) behavior. The realism of visual models in a simulation (level of detail as well as motion fidelity) remains a challenge in realistic articulation of elements such as vehicle antennae and turrets, or, with human figures; posture, joint articulation, response to uneven ground. Currently the adequacy of visual representation is more dependant upon the quality and resolution of the physical models driving those entities than graphics processing power per Se. Synthetic entities in M&S applications traditionally have represented engineered systems (e.g. aircraft) with human-in-the-loop performance characteristics (e.g. visual acuity) included in the system behavioral specification. As well, performance affecting human parameters such as experience level, fatigue and stress are coming into wider use (via AI approaches) to incorporate more uncertainty as to response type as well as performance (e.g. Where an opposing entity might go and what it might do, as well as how well it might perform).

Kruk, R. V.↗

NASA Standard for Models and Simulations: Credibility Assessment Scale

As one of its many responses to the 2003 Space Shuttle Columbia accident, NASA decided to develop a formal standard for models and simulations (M and S)ii. Work commenced in May 2005. An interim version was issued in late 2006. This interim version underwent considerable revision following an extensive Agency-wide review in 2007 along with some additional revisions as a result of the review by the NASA Engineering Management Board (EMB) in the first half of 2008. Issuance of the revised, permanent version,hereafter referred to as the M and S Standard or just the Standard, occurred in July 2008.

verification↗

Strategy for Developing Technologies for Megawatt-class Nuclear Electric Propulsion Systems

In late fiscal year 2020, the Space Nuclear Propulsion (SNP) project began the process of formulating an investment strategy to support development of the technologies required for a high-power (megawatt-class) nuclear electric propulsion (NEP) system capable of performing human-scale missions. This activity was initiated concurrent with several high-level studies and assessments were either under way or had just concluded. Studies of human-scale Mars missions have been performed several times over the past two decades. One of the most recent studies examined opposition-class human Mars missions to occur in the late 2030s timeframe [1,2]. The mission architecture assumed a hybrid NEP/chem-propelled vehicle that used a high specific impulse (Isp) NEP-system and a liquid oxygen (LOx)-liquid methane high thrust chemical stage (two 110 kN (25 klbf) thrust, 365 s Isp engines) for maneuvers performed to enter and exit gravity wells. Trajectory analyses performed in this study showed that such a mission could be performed with 2-4 MWe directed into the electric propulsion system (operating for 20,000+ hours), with the large range representing different opposition-class Mars mission opportunities and permutations on the trajectory design, concept of operations, and technology choices. In 2020, the NASA Engineering and Safety Center (NESC) performed a study to evaluate the maturity of the different technologies required for nuclear propulsion systems [3]. The executive summary of this report provided the following top-level conclusions: • “The majority of critical technologies for… NEP/Chem… systems are relatively immature” • “TRLs [technology readiness levels] in the literature are often overestimated” • “The majority of critical technologies… for NEP/Chem… systems are at a relatively high level of advancement degree of difficulty (AD2 > 4) for maturation, requiring a dual development approach” • “The proper assessment of baseline TRL and AD2 values and the estimation of requirements and resources required for advancement have been consistent issues for NEP,” • “Non-advocate reviews should occur at the start of a technology program and at all key milestones.” In 2021, the National Academies of Science, Engineering, and Medicine (NASEM) issued a separate report [4] identifying the “primary technical and programmatic challenges, merits, and risks for maturing space nuclear propulsion technologies of interest to a future human Mars exploration mission.” That work contained several important findings, including: • “Developing a MWe-class NEP system for the baseline mission would require increasing power by orders of magnitude relative to NEP system flight- or ground-based technology demonstrations completed to date.” • “Subscale in-space flight testing of NEP systems cannot address many of the risks and potential failure modes associated with the baseline mission NEP system. With sufficient M&S [modeling & simulation] and ground testing, including modular subsystem tests at full scale and power, flight qualification requirements can be met by the cargo missions that will precede the first crewed mission to Mars. Fully integrated ground testing may not be required.” • “As a result of low and intermittent investment over the past several decades, it is unclear if even an aggressive program would be able to develop an NEP system capable of executing the baseline mission in 2039.” These efforts motivated the SNP project to investigate the technologies available for a megawatt-class high power nuclear electric propulsion system. That system is illustrated schematically in Figure 1 and is comprised of five separate top-level critical technology elements (CTEs). 1. Nuclear Reactor – Thermal power source for the system, utilizing high-assay low enriched uranium (HALEU) as the nuclear fuel. Reactor radiation shielding is also included in this CTE. 2. Power Conversion – Operates as a thermodynamic cycle, accepting nuclear reactor thermal power as an input and converting it to mechanical power. 3. Power Management and Distribution (PMAD) – Accepts as an input mechanical power from the power conversion system, which is used to generate electrical power. The PMAD system also distributes the generated electrical power to all other parts of the spacecraft, including the high-power EP system. The PMAD system may also perform duties such as isolation, fault detection, and power transformation/rectification for different spacecraft systems, including the thrusters. 4. Electric Propulsion (EP) – Accepts as an input electrical power, which is used to accelerate a propellant to high speeds to produce thrust. This system includes the power processing unit (PPU), which converts the power it receives to the correct current and voltage required by the thrusters, and the propellant storage and feed systems, which contain and meter the flow of propellant to the thrusters. 5. Thermal Management (Radiators/Heat Rejection) – The cold side of the thermodynamic power conversion cycle, accepts thermal power from the power conversion system and radiatively rejects that heat to space. In this paper, we describe the SNP project formulation and investment strategy that aims to accomplish the research and development required to advance the technology readiness for each CTE. The strategy relies heavily upon experimental testing supported by modeling and simulation to yield realistic assessments of the technologies, which in turn will be used to inform future NEP system-level design decisions and any potential technology downselects.

Kurt A Polzin↗

Promoting A-Priori Interoperability of HLA-Based Simulations in the Space Domain: The SISO Space Reference FOM Initiative

Distributed and Real-Time Simulation plays a key-role in the Space domain being exploited for missions and systems analysis and engineering as well as for crew training and operational support. One of the most popular standards is the 1516-2010 IEEE Standard for Modeling and Simulation (M&S) High Level Architecture (HLA). HLA supports the implementation of distributed simulations (called Federations) in which a set of simulation entities (called Federates) can interact using a Run-Time Infrastructure (RTI). In a given Federation, a Federate can publish and/or subscribes objects and interactions on the RTI only in accordance with their structures as defined in a FOM (Federation Object Model). Currently, the Space domain is characterized by a set of incompatible FOMs that, although meet the specific needs of different organizations and projects, increases the long-term cost for interoperability. In this context, the availability of a reference FOM for the Space domain will enable the development of interoperable HLA-based simulators for related joint projects and collaborations among worldwide organizations involved in the Space domain (e.g. NASA, ESA, Roscosmos, and JAXA). The paper presents a first set of results achieved by a SISO standardization effort that aims at providing a Space Reference FOM for international collaboration on Space systems simulations.

Moller, Bjorn↗

A Model of Rapid Radicalization Behavior Using Agent-Based Modeling and Quorum Sensing

Understanding the dynamics of radicalization, especially rapid radicalization, has become increasingly important to US policy in the past several years. Traditionally, radicalization is considered a slow process, but recent social and political events demonstrate that the process can occur quickly. Examining this rapid process, in real time, is impossible. However, recreating an event using modeling and simulation (M&S) allows researchers to study some of the complex dynamics associated with rapid radicalization. We propose to adapt the biological mechanism of quorum sensing as a tool to explore, or possibly explain, rapid radicalization. Due to the complex nature of quorum sensing, M&S allows us to examine events that we could not otherwise examine in real time. For this study, we employ Agent Based Modeling (ABM), an M&S paradigm suited to modeling group behavior. The result of this study was the successful creation of rapid radicalization using quorum sensing. The Battle of Mogadishu was the inspiration for this model and provided the testing conditions used to explore quorum sensing and the ideas behind rapid radicalization. The final product has wider applicability however, using quorum sensing as a possible tool for examining other catalytic rapid radicalization events.

Schwartz, Noah↗