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Long term sustainability of the high energy physics (HEP) research software ecosystem is essential for the field. With upgrades and new facilities coming online throughout the 2020s this will only become increasingly relevant throughout this decade. Meeting this sustainability challenge requires a workforce with a combination of HEP domain knowledge and advanced software skills. The required software skills fall into three broad groups. The first is fundamental and generic software engineering (e.g. Unix, version control,C++, continuous integration). The second is knowledge of domain specific HEP packages and practices (e.g., the ROOT data format and analysis framework). The third is more advanced knowledge involving more specialized techniques. These include parallel programming, machine learning and data science tools, and techniques to preserve software projects at all scales. This paper dis-cusses the collective software training program in HEP and its activities led by the HEP Software Foundation (HSF) and the Institute for Research and Innovation in Software in HEP (IRIS-HEP). The program equips participants with an array of software skills that serve as ingredients from which solutions to the computing challenges of HEP can be formed. Beyond serving the community by ensuring that members are able to pursue research goals, this program serves individuals by providing intellectual capital and transferable skills that are becoming increasingly important to careers in the realm of software and computing, whether inside or outside HEP, Comment: For CHEP 2021 conference,sent for publication to CSBS Springer

How do complex social systems evolve in the modern world? This question lies at the heart of social physics, and network analysis has proven critical in providing answers to it. In recent years, network analysis has also been used to gain a quantitative understanding of law as a complex adaptive system, but most research has focused on legal documents of a single type, and there exists no unified framework for quantitative legal document analysis using network analytical tools. Against this background, we present a comprehensive framework for analyzing legal documents as multi-dimensional, dynamic document networks. We demonstrate the utility of this framework by applying it to an original dataset of statutes and regulations from two different countries, the United States and Germany, spanning more than twenty years (1998-2019). Our framework provides tools for assessing the size and connectivity of the legal system as viewed through the lens of specific document collections as well as for tracking the evolution of individual legal documents over time. Implementing the framework for our dataset, we find that at the federal level, the United States legal system is increasingly dominated by regulations, whereas the German legal system remains governed by statutes. This holds regardless of whether we measure the systems at the macro, the meso, or the micro level., Comment: 32 pages, 13 figures (main paper); 32 pages, 14 figures (supplementary information)

This document captures the discussion and deliberation of the FAIR for Research Software (FAIR4RS) subgroup that took a fresh look at the applicability of the FAIR Guiding Principles for scientific data management and stewardship for research software. We discuss the vision of research software as ideally reproducible, open, usable, recognized, sustained and robust, and then review both the characteristic and practiced differences of research software and data. This vision and understanding of initial conditions serves as a backdrop for an attempt at translating and interpreting the guiding principles to more fully align with research software. We have found that many of the principles remained relatively intact as written, as long as considerable interpretation was provided. This was particularly the case for the "Findable" and "Accessible" foundational principles. We found that "Interoperability" and "Reusability" are particularly prone to a broad and sometimes opposing set of interpretations as written. We propose two new principles modeled on existing ones, and provide modified guiding text for these principles to help clarify our final interpretation. A series of gaps in translation were captured during this process, and these remain to be addressed. We finish with a consideration of where these translated principles fall short of the vision laid out in the opening.

Scientific software registries and repositories serve various roles in their respective disciplines. These resources improve software discoverability and research transparency, provide information for software citations, and foster preservation of computational methods that might otherwise be lost over time, thereby supporting research reproducibility and replicability. However, developing these resources takes effort, and few guidelines are available to help prospective creators of registries and repositories. To address this need, we present a set of nine best practices that can help managers define the scope, practices, and rules that govern individual registries and repositories. These best practices were distilled from the experiences of the creators of existing resources, convened by a Task Force of the FORCE11 Software Citation Implementation Working Group during the years 2019-2020. We believe that putting in place specific policies such as those presented here will help scientific software registries and repositories better serve their users and their disciplines., Comment: 18 pages

The development of reusable artificial intelligence (AI) models for wider use and rigorous validation by the community promises to unlock new opportunities in multi-messenger astrophysics. Here we develop a workflow that connects the Data and Learning Hub for Science, a repository for publishing AI models, with the Hardware Accelerated Learning (HAL) cluster, using funcX as a universal distributed computing service. Using this workflow, an ensemble of four openly available AI models can be run on HAL to process an entire month's worth (August 2017) of advanced Laser Interferometer Gravitational-Wave Observatory data in just seven minutes, identifying all four all four binary black hole mergers previously identified in this dataset and reporting no misclassifications. This approach combines advances in AI, distributed computing, and scientific data infrastructure to open new pathways to conduct reproducible, accelerated, data-driven discovery., Comment: 17 pages, 5 figures; v2: 12 pages, 6 figures. Accepted to Nature Astronomy. See also the Behind the Paper blog in Nature Astronomy "https://astronomycommunity.nature.com/posts/from-disruption-to-sustained-innovation-artificial-intelligence-for-gravitational-wave-astrophysics"

Software now lies at the heart of scholarly research. Here we argue that as well as being important from a methodological perspective, software should, in many instances, be recognised as an output of research, equivalent to an academic paper. The article discusses the different roles that software may play in research and highlights the relationship between software and research sustainability and reproducibility. It describes the challenges associated with the processes of citing and reviewing software, which differ from those used for papers. We conclude that whilst software outputs do not necessarily fit comfortably within the current publication model, there is a great deal of positive work underway that is likely to make an impact in addressing this., Comment: 6 pages. Submitted to IJDC

New facilities of the 2020s, such as the High Luminosity Large Hadron Collider (HL-LHC), will be relevant through at least the 2030s. This means that their software efforts and those that are used to analyze their data need to consider sustainability to enable their adaptability to new challenges, longevity, and efficiency, over at least this period. This will help ensure that this software will be easier to develop and maintain, that it remains available in the future on new platforms, that it meets new needs, and that it is as reusable as possible. This report discusses a virtual half-day workshop on "Software Sustainability and High Energy Physics" that aimed 1) to bring together experts from HEP as well as those from outside to share their experiences and practices, and 2) to articulate a vision that helps the Institute for Research and Innovation in Software for High Energy Physics (IRIS-HEP) to create a work plan to implement elements of software sustainability. Software sustainability practices could lead to new collaborations, including elements of HEP software being directly used outside the field, and, as has happened more frequently in recent years, to HEP developers contributing to software developed outside the field rather than reinventing it. A focus on and skills related to sustainable software will give HEP software developers an important skill that is essential to careers in the realm of software, inside or outside HEP. The report closes with recommendations to improve software sustainability in HEP, aimed at the HEP community via IRIS-HEP and the HEP Software Foundation (HSF)., Comment: A report from the "Sustainable Software in HEP" IRIS-HEP blueprint workshop: https://indico.cern.ch/event/930127/

A new method is used to resolve a long-standing conjecture of Niho concerning the crosscorrelation spectrum of a pair of maximum length linear recursive sequences of length $2^{2 m}-1$ with relative decimation $d=2^{m+2}-3$, where $m$ is even. The result indicates that there are at most five distinct crosscorrelation values. Equivalently, the result indicates that there are at most five distinct values in the Walsh spectrum of the power permutation $f(x)=x^d$ over a finite field of order $2^{2 m}$ and at most five distinct nonzero weights in the cyclic code of length $2^{2 m}-1$ with two primitive nonzeros $\alpha$ and $\alpha^d$. The method used to obtain this result proves constraints on the number of roots that certain seventh degree polynomials can have on the unit circle of a finite field. The method also works when $m$ is odd, in which case the associated crosscorrelation and Walsh spectra have at most six distinct values., Comment: 27 pages; Sage code with verification of decomposition in Lemma 5.2 included as an ancillary file

While a large number of informal factors influence how people interact, modern societies rely upon law as a primary mechanism to formally control human behaviour. How legal rules impact societal development depends on the interplay between two types of actors: the people who create the rules and the people to which the rules potentially apply. We hypothesise that an increasingly diverse and interconnected society might create increasingly diverse and interconnected rules, and assert that legal networks provide a useful lens through which to observe the interaction between law and society. To evaluate these propositions, we present a novel and generalizable model of statutory materials as multidimensional, time-evolving document networks. Applying this model to the federal legislation of the United States and Germany, we find impressive expansion in the size and complexity of laws over the past two and a half decades. We investigate the sources of this development using methods from network science and natural language processing. To allow for cross-country comparisons over time, we algorithmically reorganise the legislative materials of the United States and Germany into cluster families that reflect legal topics. This reorganisation reveals that the main driver behind the growth of the law in both jurisdictions is the expansion of the welfare state, backed by an expansion of the tax state., Comment: 22 pages, 6 figures (main paper); 28 pages, 11 figures (supplementary information)

Significant investments to upgrade and construct large-scale scientific facilities demand commensurate investments in R&D to design algorithms and computing approaches to enable scientific and engineering breakthroughs in the big data era. Innovative Artificial Intelligence (AI) applications have powered transformational solutions for big data challenges in industry and technology that now drive a multi-billion dollar industry, and which play an ever increasing role shaping human social patterns. As AI continues to evolve into a computing paradigm endowed with statistical and mathematical rigor, it has become apparent that single-GPU solutions for training, validation, and testing are no longer sufficient for computational grand challenges brought about by scientific facilities that produce data at a rate and volume that outstrip the computing capabilities of available cyberinfrastructure platforms. This realization has been driving the confluence of AI and high performance computing (HPC) to reduce time-to-insight, and to enable a systematic study of domain-inspired AI architectures and optimization schemes to enable data-driven discovery. In this article we present a summary of recent developments in this field, and describe specific advances that authors in this article are spearheading to accelerate and streamline the use of HPC platforms to design and apply accelerated AI algorithms in academia and industry., Comment: White paper accepted to the NSF Workshop on Smart Cyberinfrastructure, February 25-27, 2020 http://smartci.sci.utah.edu/. v2: Survey paper accepted to Journal of Big Data

Multi-messenger astrophysics is a fast-growing, interdisciplinary field that combines data, which vary in volume and speed of data processing, from many different instruments that probe the Universe using different cosmic messengers: electromagnetic waves, cosmic rays, gravitational waves and neutrinos. In this Expert Recommendation, we review the key challenges of real-time observations of gravitational wave sources and their electromagnetic and astroparticle counterparts, and make a number of recommendations to maximize their potential for scientific discovery. These recommendations refer to the design of scalable and computationally efficient machine learning algorithms; the cyber-infrastructure to numerically simulate astrophysical sources, and to process and interpret multi-messenger astrophysics data; the management of gravitational wave detections to trigger real-time alerts for electromagnetic and astroparticle follow-ups; a vision to harness future developments of machine learning and cyber-infrastructure resources to cope with the big-data requirements; and the need to build a community of experts to realize the goals of multi-messenger astrophysics., Comment: Invited Expert Recommendation for Nature Reviews Physics. The art work produced by E. A. Huerta and Shawn Rosofsky for this article was used by Carl Conway to design the cover of the October 2019 issue of Nature Reviews Physics

The Theory-Software Translation Workshop, held in New Orleans in February 2019, explored in depth the process of both instantiating theory in software - for example, implementing a mathematical model in code as part of a simulation - and using the outputs of software - such as the behavior of a simulation - to advance knowledge. As computation within research is now ubiquitous, the workshop provided a timely opportunity to reflect on the particular challenges of research software engineering - the process of developing and maintaining software for scientific discovery. In addition to the general challenges common to all software development projects, research software additionally must represent, manipulate, and provide data for complex theoretical constructs. Ensuring this process is robust is essential to maintaining the integrity of the science resulting from it, and the workshop highlighted a number of areas where the current approach to research software engineering would benefit from an evidence base that could be used to inform best practice. The workshop brought together expert research software engineers and academics to discuss the challenges of Theory-Software Translation over a two-day period. This report provides an overview of the workshop activities, and a synthesises of the discussion that was recorded. The body of the report presents a thematic analysis of the challenges of Theory-Software Translation as identified by workshop participants, summarises these into a set of research areas, and provides recommendations for the future direction of this work.

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify pivotal components to which coarse-grained, or aggregate, properties are sensitive. As an example, we introduce our approach on a reduced toy model with a median voter who always votes in the majority. The sensitivity of majority-minority divisions to changing voter behaviour pinpoints the unique role of the median. More generally, the sensitivity identifies pivotal components that precisely determine collective outcomes generated by a complex network of interactions. Using perturbations to target pivotal components in the models, we analyse datasets from political voting, finance and Twitter. Across these systems, we find remarkable variety, from systems dominated by a median-like component to those whose components behave more equally. In the context of political institutions such as courts or legislatures, our methodology can help describe how changes in voters map to new collective voting outcomes. For economic indices, differing system response reflects varying fiscal conditions across time. Thus, our information-geometric approach provides a principled, quantitative framework that may help assess the robustness of collective outcomes to targeted perturbation and compare social institutions, or even biological networks, with one another and across time.

The main output of the FORCE11 Software Citation working group (https://www.force11.org/group/software-citation-working-group) was a paper on software citation principles (https://doi.org/10.7717/peerj-cs.86) published in September 2016. This paper laid out a set of six high-level principles for software citation (importance, credit and attribution, unique identification, persistence, accessibility, and specificity) and discussed how they could be used to implement software citation in the scholarly community. In a series of talks and other activities, we have promoted software citation using these increasingly accepted principles. At the time the initial paper was published, we also provided guidance and examples on how to make software citable, though we now realize there are unresolved problems with that guidance. The purpose of this document is to provide an explanation of current issues impacting scholarly attribution of research software, organize updated implementation guidance, and identify where best practices and solutions are still needed.

High-level programming languages such as Python are increasingly used to provide intuitive interfaces to libraries written in lower-level languages and for assembling applications from various components. This migration towards orchestration rather than implementation, coupled with the growing need for parallel computing (e.g., due to big data and the end of Moore's law), necessitates rethinking how parallelism is expressed in programs. Here, we present Parsl, a parallel scripting library that augments Python with simple, scalable, and flexible constructs for encoding parallelism. These constructs allow Parsl to construct a dynamic dependency graph of components that it can then execute efficiently on one or many processors. Parsl is designed for scalability, with an extensible set of executors tailored to different use cases, such as low-latency, high-throughput, or extreme-scale execution. We show, via experiments on the Blue Waters supercomputer, that Parsl executors can allow Python scripts to execute components with as little as 5 ms of overhead, scale to more than 250 000 workers across more than 8000 nodes, and process upward of 1200 tasks per second. Other Parsl features simplify the construction and execution of composite programs by supporting elastic provisioning and scaling of infrastructure, fault-tolerant execution, and integrated wide-area data management. We show that these capabilities satisfy the needs of many-task, interactive, online, and machine learning applications in fields such as biology, cosmology, and materials science.

The identification of the electromagnetic counterpart of the gravitational wave event, GW170817, and discovery of neutrinos and gamma-rays from TXS 0506+056 heralded the new era of multi-messenger astrophysics. As the number of multi-messenger events rapidly grow over the next decade, the cyberinfrastructure requirements to handle the increase in data rates, data volume, need for event follow up, and analysis across the different messengers will also explosively grow. The cyberinfrastructure requirements to enhance multi-messenger astrophysics will both be a major challenge and opportunity for astronomers, physicists, computer scientists and cyberinfrastructure specialists. Here we outline some of these requirements and argue for a distributed cyberinfrastructure institute for multi-messenger astrophysics to meet these challenges., Comment: 7 pages, astro2020 white paper

Modern research in the sciences, engineering, humanities, and other fields depends on software, and specifically, research software. Much of this research software is developed in universities, by faculty, postdocs, students, and staff. In this paper, we focus on the role of university staff. We examine three different, independently-developed models under which these staff are organized and perform their work, and comparatively analyze these models and their consequences on the staff and on the software, considering how the different models support software engineering practices and processes. This information can be used by software engineering researchers to understand the practices of such organizations and by universities who want to set up similar organizations and to better produce and maintain research software., Comment: 2019 Intl. Work. on Soft. Eng. for Science (SE4Science), May 28, 2019, with ICSE'19

Many science advances have been possible thanks to the use of research software, which has become essential to advancing virtually every Science, Technology, Engineering and Mathematics (STEM) discipline and many non-STEM disciplines including social sciences and humanities. And while much of it is made available under open source licenses, work is needed to develop, support, and sustain it, as underlying systems and software as well as user needs evolve. In addition, the changing landscape of high-performance computing (HPC) platforms, where performance and scaling advances are ever more reliant on software and algorithm improvements as we hit hardware scaling barriers, is causing renewed tension between sustainability of software and its performance. We must do more to highlight the trade-off between performance and sustainability, and to emphasize the need for sustainability given the fact that complex software stacks don't survive without frequent maintenance; made more difficult as a generation of developers of established and heavily-used research software retire. Several HPC forums are doing this, and it has become an active area of funding as well. In response, the authors organized and ran a panel at the SC18 conference. The objectives of the panel were to highlight the importance of sustainability, to illuminate the tension between pure performance and sustainability, and to steer SC community discussion toward understanding and addressing this issue and this tension. The outcome of the discussions, as presented in this paper, can inform choices of advance compute and data infrastructures to positively impact future research software and future research., Comment: The 2018 International Conference for High Performance Computing, Networking, Storage, and Analysis (SC18), Dallas, Texas, USA, November 2018

This report provides an overview of recent work that harnesses the Big Data Revolution and Large Scale Computing to address grand computational challenges in Multi-Messenger Astrophysics, with a particular emphasis on real-time discovery campaigns. Acknowledging the transdisciplinary nature of Multi-Messenger Astrophysics, this document has been prepared by members of the physics, astronomy, computer science, data science, software and cyberinfrastructure communities who attended the NSF-, DOE- and NVIDIA-funded "Deep Learning for Multi-Messenger Astrophysics: Real-time Discovery at Scale" workshop, hosted at the National Center for Supercomputing Applications, October 17-19, 2018. Highlights of this report include unanimous agreement that it is critical to accelerate the development and deployment of novel, signal-processing algorithms that use the synergy between artificial intelligence (AI) and high performance computing to maximize the potential for scientific discovery with Multi-Messenger Astrophysics. We discuss key aspects to realize this endeavor, namely (i) the design and exploitation of scalable and computationally efficient AI algorithms for Multi-Messenger Astrophysics; (ii) cyberinfrastructure requirements to numerically simulate astrophysical sources, and to process and interpret Multi-Messenger Astrophysics data; (iii) management of gravitational wave detections and triggers to enable electromagnetic and astro-particle follow-ups; (iv) a vision to harness future developments of machine and deep learning and cyberinfrastructure resources to cope with the scale of discovery in the Big Data Era; (v) and the need to build a community that brings domain experts together with data scientists on equal footing to maximize and accelerate discovery in the nascent field of Multi-Messenger Astrophysics., Comment: 15 pages, no figures. White paper based on the "Deep Learning for Multi-Messenger Astrophysics: Real-time Discovery at Scale" workshop, hosted at NCSA, October 17-19, 2018 http://www.ncsa.illinois.edu/Conferences/DeepLearningLSST/

Software is the key crosscutting technology that enables advances in mathematics, computer science, and domain-specific science and engineering to achieve robust simulations and analysis for science, engineering, and other research fields. However, software itself has not traditionally received focused attention from research communities; rather, software has evolved organically and inconsistently, with its development largely as by-products of other initiatives. Moreover, challenges in scientific software are expanding due to disruptive changes in computer hardware, increasing scale and complexity of data, and demands for more complex simulations involving multiphysics, multiscale modeling and outer-loop analysis. In recent years, community members have established a range of grass-roots organizations and projects to address these growing technical and social challenges in software productivity, quality, reproducibility, and sustainability. This article provides an overview of such groups and discusses opportunities to leverage their synergistic activities while nurturing work toward emerging software ecosystems.

To improve the quality and efficiency of research, groups within the scientific community seek to exploit the value of data sharing. Funders, institutions, and specialist organizations are developing and implementing strategies to encourage or mandate data sharing within and across disciplines, with varying degrees of success. Academic journals in ecology and evolution have adopted several types of public data archiving policies requiring authors to make data underlying scholarly manuscripts freely available. Yet anecdotes from the community and studies evaluating data availability suggest that these policies have not obtained the desired effects, both in terms of quantity and quality of available datasets. We conducted a qualitative, interview-based study with journal editorial staff and other stakeholders in the academic publishing process to examine how journals enforce data archiving policies. We specifically sought to establish who editors and other stakeholders perceive as responsible for ensuring data completeness and quality in the peer review process. Our analysis revealed little consensus with regard to how data archiving policies should be enforced and who should hold authors accountable for dataset submissions. Themes in interviewee responses included hopefulness that reviewers would take the initiative to review datasets and trust in authors to ensure the completeness and quality of their datasets. We highlight problematic aspects of these thematic responses and offer potential starting points for improvement of the public data archiving process., Comment: 35 pages, 1 figure, 1 table

The advent of experimental science facilities-instruments and observatories, such as the Large Hadron Collider, the Laser Interferometer Gravitational Wave Observatory, and the upcoming Large Synoptic Survey Telescope-has brought about challenging, large-scale computational and data processing requirements. Traditionally, the computing infrastructure to support these facility's requirements were organized into separate infrastructure that supported their high-throughput needs and those that supported their high-performance computing needs. We argue that to enable and accelerate scientific discovery at the scale and sophistication that is now needed, this separation between high-performance computing and high-throughput computing must be bridged and an integrated, unified infrastructure provided. In this paper, we discuss several case studies where such infrastructure has been implemented. These case studies span different science domains, software systems, and application requirements as well as levels of sustainability. A further aim of this paper is to provide a basis to determine the common characteristics and requirements of such infrastructure, as well as to begin a discussion of how best to support the computing requirements of existing and future experimental science facilities., Comment: 13 pages, 7 figures. Accepted to Computing and Software for Big Science

In most fields, computational models and data analysis have become a significant part of how research is performed, in addition to the more traditional theory and experiment. Mathematics is no exception to this trend. While the system of publication and credit for theory and experiment (journals and books, often monographs) has developed and has become an expected part of the culture, how research is shared and how candidates for hiring, promotion are evaluated, software (and data) do not have the same history. A group working as part of the FORCE11 community developed a set of principles for software citation that fit software into the journal citation system, allow software to be published and then cited, and there are now over 50,000 DOIs that have been issued for software. However, some challenges remain, including: promoting the idea of software citation to developers and users; collaborating with publishers to ensure that systems collect and retain required metadata; ensuring that the rest of the scholarly infrastructure, particularly indexing sites, include software; working with communities so that software efforts "count" and understanding how best to cite software that has not been published.

This article summarizes motivations, organization, and activities of the Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE5.1) held in Manchester, UK in September 2017. The WSSSPE series promotes sustainable research software by positively impacting principles and best practices, careers, learning, and credit. This article discusses the Code of Conduct, idea papers, position papers, experience papers, demos, and lightning talks presented during the workshop. The main part of the article discusses the speed-blogging groups that formed during the meeting, along with the outputs of those sessions.

Chebotar\"ev proved that every minor of a discrete Fourier matrix of prime order is nonzero. We prove a generalization of this result that includes analogues for discrete cosine and discrete sine matrices as special cases. We establish these results via a generalization of the Bir\'o-Meshulam-Tao uncertainty principle to functions with symmetries that arise from certain group actions, with some of the simplest examples being even and odd functions. We show that our result is best possible and in some cases is stronger than that of Bir\'o-Meshulam-Tao. Some of these results hold in certain circumstances for non-prime fields; Gauss sums play a central role in such investigations., Comment: 30 pages

The profile of research software engineering has been greatly enhanced by developments at institutions around the world to form groups and communities that can support effective, sustainable development of research software. We observe, however, that there is still a long way to go to build a clear understanding about what approaches provide the best support for research software developers in different contexts, and how such understanding can be used to suggest more formal structures, models or frameworks that can help to further support the growth of research software engineering. This paper sets out some preliminary thoughts and proposes an initial high-level model based on discussions between the authors around the concept of a set of pillars representing key activities and processes that form the core structure of a successful research software engineering offering., Comment: 5 pages, 1 figure, submitted to the 9th International Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE6.1)

The rapid evolution of technology and the parallel increasing complexity of algorithmic analysis in HEP requires developers to acquire a much larger portfolio of programming skills. Young researchers graduating from universities worldwide currently do not receive adequate preparation in the very diverse fields of modern computing to respond to growing needs of the most advanced experimental challenges. There is a growing consensus in the HEP community on the need for training programmes to bring researchers up to date with new software technologies, in particular in the domains of concurrent programming and artificial intelligence. We review some of the initiatives under way for introducing new training programmes and highlight some of the issues that need to be taken into account for these to be successful.

A growing number of largely uncoordinated initiatives focus on research software sustainability. A comprehensive mapping of the research software sustainability space can help identify gaps in their efforts, track results, and avoid duplication of work. To this end, this paper suggests enhancing an existing schematic of activities in research software sustainability, and formalizing it in a directed graph model. Such a model can be further used to define a classification schema which, applied to research results in the field, can drive the identification of past activities and the planning of future efforts., Comment: 5 pages, 3 figures, 1 table, accepted as a long paper for the 9th International Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE6.1), co-locating with IEEE eScience 2018