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HPC centers face increasing demand for software flexibility, and there is growing consensus that Linux containers are a promising solution. However, existing container build solutions require root privileges and cannot be used directly on HPC resources. This limitation is compounded as supercomputer diversity expands and HPC architectures become more dissimilar from commodity computing resources. Our analysis suggests this problem can best be solved with low-privilege containers. We detail relevant Linux kernel features, propose a new taxonomy of container privilege, and compare two open-source implementations: mostly-unprivileged rootless Podman and fully-unprivileged Charliecloud. We demonstrate that low-privilege container build on HPC resources works now and will continue to improve, giving normal users a better workflow to securely and correctly build containers. Minimizing privilege in this way can improve HPC user and developer productivity as well as reduce support workload for exascale applications., Comment: 12 pages, 11 figures. Revision 2: clarifications, corrections of some minor errors; revision 3: further clarifications and corrections

Scientific workflows have been used almost universally across scientific domains, and have underpinned some of the most significant discoveries of the past several decades. Many of these workflows have high computational, storage, and/or communication demands, and thus must execute on a wide range of large-scale platforms, from large clouds to upcoming exascale high-performance computing (HPC) platforms. These executions must be managed using some software infrastructure. Due to the popularity of workflows, workflow management systems (WMSs) have been developed to provide abstractions for creating and executing workflows conveniently, efficiently, and portably. While these efforts are all worthwhile, there are now hundreds of independent WMSs, many of which are moribund. As a result, the WMS landscape is segmented and presents significant barriers to entry due to the hundreds of seemingly comparable, yet incompatible, systems that exist. As a result, many teams, small and large, still elect to build their own custom workflow solution rather than adopt, or build upon, existing WMSs. This current state of the WMS landscape negatively impacts workflow users, developers, and researchers. The "Workflows Community Summit" was held online on January 13, 2021. The overarching goal of the summit was to develop a view of the state of the art and identify crucial research challenges in the workflow community. Prior to the summit, a survey sent to stakeholders in the workflow community (including both developers of WMSs and users of workflows) helped to identify key challenges in this community that were translated into 6 broad themes for the summit, each of them being the object of a focused discussion led by a volunteer member of the community. This report documents and organizes the wealth of information provided by the participants before, during, and after the summit.

In this article, we consider a class of functions on $\mathbb{R}^d$, called positive homogeneous functions, which interact well with certain continuous one-parameter groups of (generally anisotropic) dilations. Generalizing the Euclidean norm, positive homogeneous functions appear naturally in the study of convolution powers of complex-valued functions on $\mathbb{Z}^d$. As the spherical measure is a Radon measure on the unit sphere which is invariant under the symmetry group of the Euclidean norm, to each positive homogeneous function $P$, we construct a Radon measure $\sigma_P$ on $S=\{\eta \in \mathbb{R}^d:P(\eta)=1\}$ which is invariant under the symmetry group of $P$. With this measure, we prove a generalization of the classical polar-coordinate integration formula and deduce a number of corollaries in this setting. We then turn to the study of convolution powers of complex functions on $\mathbb{Z}^d$ and certain oscillatory integrals which arise naturally in that context. Armed with our integration formula and the Van der Corput lemma, we establish sup norm-type estimates for convolution powers; this result is new and partially extends results of [20] and [21].

Testing is one of the most important steps in software development. It ensures the quality of software. Continuous Integration (CI) is a widely used testing system that can report software quality to the developer in a timely manner during the development progress. Performance, especially scalability, is another key factor for High Performance Computing (HPC) applications. Though there are many applications and tools to profile the performance of HPC applications, none of them are integrated into the continuous integration. On the other hand, no current continuous integration tools provide easy-to-use scalability test capabilities. In this work, we propose BeeSwarm, a scalability test system that can be easily applied to the current CI test environment enabling scalability test capability for HPC developers. As a showcase, BeeSwarm is integrated into Travis CI and GitLab CI to execute the scalability test workflow on Chameleon cloud.

We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in different directions. The heat kernels associated to these so-called positive-homogeneous operators are seen to arise naturally as the limits of convolution powers of complex-valued measures, just as the classical heat kernel appears in the central limit theorem. Building on the functional-analytic approach developed by E. B. Davies for higher-order uniformly elliptic operators with measurable coefficients, we formulate a general theory for (anisotropic) self-adjoint variable-coefficient operators, each comparable to a positive-homogeneous operator, and study their associated heat kernels. Specifically, under three abstract hypotheses, we show that the heat kernels satisfy off-diagonal (Gaussian type) estimates involving the Legendre-Fenchel transform of the operator's principle symbol. Our results extend those of E. B. Davies and G. Barbatis and partially extend results of A. F. M. ter Elst and D. Robinson., Comment: 47 pages

We show how to visualize the process of diagonalizing the Hamiltonian matrix to find the energy eigenvalues and eigenvectors of a generic one-dimensional quantum system. Starting in the familiar sine-wave basis of an embedding infinite square well, we display the Hamiltonian matrix graphically with the basis functions alongside. Each step in the diagonalization process consists of selecting a nonzero off-diagonal matrix element, then rotating the two corresponding basis vectors in their own subspace until this element is zero. We provide Mathematica code to display the effects of these rotations on both the matrix and the basis functions. As an electronic supplement we also provide a JavaScript web app to interactively carry out this process., Comment: 6 pages, 2 figures. Submitted to the American Journal of Physics