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Abstract: We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-t observations; (ii) Student-t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

Combinatorial fusion analysis (CFA) is an approach for combining multiple scoring systems using the rank-score characteristic function and cognitive diversity measure. One example is to combine diverse machine learning models to achieve better prediction quality. In this work, we apply CFA to the synthesis of metal halide perovskites containing organic ammonium cations via inverse temperature crystallization. Using a data set generated by high-throughput experimentation, four individual models (support vector machines, random forests, weighted logistic classifier, and gradient boosted trees) were developed. We characterize each of these scoring systems and explore 66 possible combinations of the models. When measured by the precision on predicting crystal formation, the majority of the combination models improves the individual model results. The best combination models outperform the best individual models by 3.9 percentage points in precision. In addition to improving prediction quality, we demonstrate how the fusion models can be used to identify mislabeled input data and address issues of data quality. In particular, we identify example cases where all single models and all fusion models do not give the correct prediction. Experimental replication of these syntheses reveals that these compositions are sensitive to modest temperature variations across the different locations of the heating element that can hinder or enhance the crystallization process. In summary, we demonstrate that model fusion using CFA can not only identify a previously unconsidered influence on reaction outcome but also be used as a form of quality control for high-throughput experimentation.

Tverberg’s theorem says that a set with sufficiently many points in Rd can always be partitioned into m parts so that the (m- 1) -simplex is the (nerve) intersection pattern of the convex hulls of the parts. The main results of our paper demonstrate that Tverberg’s theorem is just a special case of a more general situation, where other simplicial complexes must always arise as nerve complexes, as soon as the number of points is large enough. We prove that, given a set with sufficiently many points, all trees and all cycles can also be induced by at least one partition of the point set. We also discuss how some simplicial complexes can never be achieved this way, even for arbitrarily large sets of points.

The majority of crystal structures are determined by the method of molecular replacement (MR). The range of application of MR is limited mainly by the need for an accurate search model. In most cases, pre-existing experimentally determined structures are used as search models. In favorable cases, ab initio predicted structures have yielded search models adequate for MR. The ORF8 protein of SARS-CoV-2 represents a challenging case for MR using an ab initio prediction because ORF8 has an all β-sheet fold and few orthologs. We previously determined experimentally the structure of ORF8 using the single anomalous dispersion (SAD) phasing method, having been unable to find an MR solution to the crystallographic phase problem. Following a report of an accurate prediction of the ORF8 structure, we assessed whether the predicted model would have succeeded as an MR search model. A phase problem solution was found, and the resulting structure was refined, yielding structural parameters equivalent to the original experimental solution.

As data sets grow to exascale, automated data analysis and visualization are increasingly important, to intermediate human understanding and to reduce demands on disk storage via in situ analysis. Trends in architecture of high performance computing systems necessitate analysis algorithms to make effective use of combinations of massively multicore and distributed systems. One of the principal analytic tools is the contour tree, which analyses relationships between contours to identify features of more than local importance. Unfortunately, the predominant algorithms for computing the contour tree are explicitly serial, and founded on serial metaphors, which has limited the scalability of this form of analysis. While there is some work on distributed contour tree computation, and separately on hybrid GPU-CPU computation, there is no efficient algorithm with strong formal guarantees on performance allied with fast practical performance. We report the first shared SMP algorithm for fully parallel contour tree computation, with formal guarantees of O(lg V lg t) parallel steps and O(V lg V) work for data with V samples and t contour tree supernodes, and implementations with more than 30× parallel speed up on both CPU using TBB and GPU using Thrust and up 70× speed up compared to the serial sweep and merge algorithm.

Relative free energy calculations are fast becoming a critical part of early stage pharmaceutical design, making it important to know how to obtain the best performance with these calculations in applications that could span hundreds of calculations and molecules. In this work, we compared two different treatments of long-range electrostatics, Particle Mesh Ewald (PME) and Reaction Field (RF), in relative binding free energy calculations using a nonequilibrium switching protocol. We found simulations using RF achieve comparable results to those using PME but gain more efficiency when using CPU and similar performance using GPU. The results from this work encourage more use of RF in molecular simulations.

Intrinsically disordered proteins (IDPs) are widely distributed across eukaryotic cells, playing important roles in molecular recognition, molecular assembly, post-translational modification, and other biological processes. IDPs are also associated with many diseases such as cancers, cardiovascular diseases, and neurodegenerative diseases. Due to their structural flexibility, conventional experimental methods cannot reliably capture their heterogeneous structures. Molecular dynamics simulation becomes an important complementary tool to quantify IDP structures. This review covers recent force field strategies proposed for more accurate molecular dynamics simulations of IDPs. The strategies include adjusting dihedral parameters, adding grid-based energy correction map (CMAP) parameters, refining protein-water interactions, and others. Different force fields were found to perform well on specific observables of specific IDPs but also are limited in reproducing all available experimental observables consistently for all tested IDPs. We conclude the review with perspective areas for improvements for future force fields for IDPs.

Decoding behavior, perception or cognitive state directly from neural signals is critical for brain-computer interface research and an important tool for systems neuroscience. In the last decade, deep learning has become the state-of-the-art method in many machine learning tasks ranging from speech recognition to image segmentation. The success of deep networks in other domains has led to a new wave of applications in neuroscience. In this article, we review deep learning approaches to neural decoding. We describe the architectures used for extracting useful features from neural recording modalities ranging from spikes to functional magnetic resonance imaging. Furthermore, we explore how deep learning has been leveraged to predict common outputs including movement, speech and vision, with a focus on how pretrained deep networks can be incorporated as priors for complex decoding targets like acoustic speech or images. Deep learning has been shown to be a useful tool for improving the accuracy and flexibility of neural decoding across a wide range of tasks, and we point out areas for future scientific development.

Contour trees are used for topological data analysis in scientific visualization. While originally computed with serial algorithms, recent work has introduced a vector-parallel algorithm. However, this algorithm is relatively slow for fully augmented contour trees which are needed for many practical data analysis tasks. We therefore introduce a representation called the hyperstructure that enables efficient searches through the contour tree and use it to construct a fully augmented contour tree in data parallel, with performance on average 6 times faster than the state-of-the-art parallel algorithm in the TTK topological toolkit.

Rich user interfaces like Jupyter have the potential to make interacting with a supercomputer easier and more productive, consequently attracting new kinds of users and helping to expand the application of supercomputing to new science domains. For the scientist user, the ideal rich user interface delivers a familiar, responsive, introspective, modular, and customizable platform upon which to build, run, capture, document, re-run, and share analysis workflows. From the provider or system administrator perspective, such a platform would also be easy to configure, deploy securely, update, customize, and support. Jupyter checks most if not all of these boxes. But from the perspective of leadership computing organizations that provide supercomputing power to users, such a platform should also make the unique features of a supercomputer center more accessible to users and more composable with high-performance computing (HPC) workflows. Project Jupyter's (https://jupyter.org/about) core design philosophy of extensibility, abstraction, and agnostic deployment has allowed HPC centers like National Energy Research Scientific Computing Center to bring in advanced supercomputing capabilities that can extend the interactive notebook environment. This has enabled a rich scientific discovery platform, particularly for experimental facility data analysis and machine learning problems.

The density-equalizing map, a technique developed for cartogram creation, has been widely applied to data visualization but only for 2D applications. In this work, we propose a novel method called the volumetric density-equalizing reference map for computing density-equalizing map for volumetric domains. Given a prescribed density distribution in a volumetric domain in R3, the proposed method continuously deforms the domain, with different volume elements enlarged or shrunk according to the density distribution. With the aid of the proposed method, medical and sociological data can be visualized via deformations of 3D objects. The method can also be applied to adaptive remeshing and shape modeling. Furthermore, by exploiting the time-dependent nature of the proposed method, applications to shape morphing can be easily achieved. Experimental results are presented to demonstrate the effectiveness of the proposed method.

The advent of increasingly large and complex datasets has fundamentally altered the way that scientists conduct astronomy research. The need to work closely to the data has motivated the creation of online science platforms, which include a suite of software tools and services, therefore going beyond data storage and data access. We present two example applications of Jupyter as a part of astrophysical science platforms for professional researchers and students. First, the Astro Data Lab is developed and operated by NOIRLab with a mission to serve the astronomy community with now over 1500 registered users. Second, the Dark Energy Spectroscopic Instrument science platform serves its geographically distributed team comprising about 900 collaborators from over 90 institutions. We describe the main uses of Jupyter and the interfaces that needed to be created to embed it within science platform ecosystems. We use these examples to illustrate the broader concept of empowering researchers and providing them with access to not only large datasets but also cutting-edge software, tools, and data services without requiring any local installation, which can be relevant for a wide range of disciplines. Future advances may involve science platform networks, and tools for simultaneously developing Jupyter notebooks to facilitate collaborations.

A significant cybersecurity event has recently been discovered in which malicious actors gained access to the source code for the Orion monitoring and management software made by the company SolarWinds and inserted malware into that source code. This article describes brief perspectives from a few experts regarding that incident and probable solutions. The attackers inserted malware into that source code so that, when the software was distributed to and deployed by SolarWinds customers as part of an update, the malicious software could be used to surveil customers who unknowingly installed the malware and gain potentially arbitrary control over the systems managed by Orion. One of the solutions is to improve government software procurement. Software is critical to national security. Any system of procuring that software needs to evaluate the security of the software and the security practices of the company, in detail, to ensure that they are sufficient to meet the security needs of the network they are being installed in. If these evaluations are made public, along with the list of companies that meet them, all network buyers can benefit from them.

Project Jupyter is an open-source project for interactive computing widely used in data science, machine learning, and scientific computing. We argue that even though Jupyter helps users perform complex, technical work, Jupyter itself solves problems that are fundamentally human in nature. Namely, Jupyter helps humans to think and tell stories with code and data. We illustrate this by describing three dimensions of Jupyter: 1) interactive computing; 2) computational narratives; and 3) the idea that Jupyter is more than software. We illustrate the impact of these dimensions on a community of practice in earth and climate science.

Enrichment of ligands versus property-matched decoys is widely used to test and optimize docking library screens. However, the unconstrained optimization of enrichment alone can mislead, leading to false confidence in prospective performance. This can arise by over-optimizing for enrichment against property-matched decoys, without considering the full spectrum of molecules to be found in a true large library screen. Adding decoys representing charge extrema helps mitigate over-optimizing for electrostatic interactions. Adding decoys that represent the overall characteristics of the library to be docked allows one to sample molecules not represented by ligands and property-matched decoys but that one will encounter in a prospective screen. An optimized version of the DUD-E set (DUDE-Z), as well as Extrema and sets representing broad features of the library (Goldilocks), is developed here. We also explore the variability that one can encounter in enrichment calculations and how that can temper one's confidence in small enrichment differences. The new tools and new decoy sets are freely available at http://tldr.docking.org and http://dudez.docking.org.

Pantetheine is ubiquitous in nature in various forms of pantetheine-containing ligands (PCLs), including coenzyme A and phosphopantetheine. Lack of scalable force field libraries for PCLs has hampered the computational studies of biological macromolecules containing PCLs. We describe here the development of the first generation Pantetheine Force Field (PFF) library that is compatible with Amber force fields; parameterized using Gasteiger, AM1-BCC, or RESP charging methods combined with gaff2 and ff14SB parameter sets. In addition, a "plug-and-play" strategy was employed to enable the systematic charging of computationally expensive molecules sharing common substructural motifs. The validation studies performed on the PFF library showed promising performance where molecular dynamics (MD) simulations results were compared with experimental data of three representative systems. The PFF library represents the first force field library capable of modeling systems containing PCLs in silico and will aid in various applications including protein engineering and drug discovery.

We investigate the problem of constructing spatial C2 closed loops from a single polynomial curve segment r(t), t∈[0,1] with a prescribed arc length S and continuity of the Frenet frame and curvature at the juncture point r(1)=r(0). Adopting canonical coordinates to fix the initial/final point and tangent, a closed-form solution for a two-parameter family of interpolants to the given data can be constructed in terms of degree 7 Pythagorean-hodograph (PH) space curves, and continuity of the torsion is also obtained when one of the parameters is set to zero. The geometrical properties of these closed-loop PH curves are elucidated, and certain symmetry properties and degenerate cases are identified. The two-parameter family of closed-loop​ C2 PH curves is also used to construct certain swept surfaces and tubular surfaces, and a selection of computed examples is included to illustrate the methodology.

Motivated by the problem of bounding the number of iterations of the simplex algorithm, we investigate the possible lengths of monotone paths followed inside the oriented graphs of polyhedra (oriented by the objective function). We consider both the shortest and the longest monotone paths and estimate the monotone diameter and height of polyhedra. Our analysis applies to transportation polytopes, matroid polytopes, matching polytopes, shortest-path polytopes, and the traveling salesman polytope, among others. We begin by showing that combinatorial cubes have monotone diameter and Bland simplex height upper bounded by their dimension and that in fact all monotone paths of zonotopes are no larger than the number of edge directions of the zonotope. We later use this to show that several polytopes have polynomial-size monotone diameter. In contrast, we show that for many well-known combinatorial polytopes, the height is at least exponential. Surprisingly, for some famous pivot rules, e.g., greatest improvement and steepest edge, these same polytopes have polynomial-size simplex paths.

The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these stochastic process models within a host of economic sectors and scientific disciplines is undercut by the processes' computational burden: complexity of likelihood evaluations grows quadratically in the number of observations for both the temporal and spatiotemporal Hawkes processes. We show that, with care, one may parallelize these calculations using both central and graphics processing unit implementations to achieve over 100-fold speedups over single-core processing. Using a simple adaptive Metropolis-Hastings scheme, we apply our high-performance computing framework to a Bayesian analysis of big gunshot data generated in Washington D.C. between the years of 2006 and 2019, thereby extending a past analysis of the same data from under 10,000 to over 85,000 observations. To encourage widespread use, we provide hpHawkes, an open-source R package, and discuss high-level implementation and program design for leveraging aspects of computational hardware that become necessary in a big data setting.

New X-ray crystallography and cryo-electron microscopy (cryo-EM) approaches yield vast amounts of structural data from dynamic proteins and their complexes. Modeling the full conformational ensemble can provide important biological insights, but identifying and modeling an internally consistent set of alternate conformations remains a formidable challenge. qFit efficiently automates this process by generating a parsimonious multiconformer model. We refactored qFit from a distributed application into software that runs efficiently on a small server, desktop, or laptop. We describe the new qFit 3 software and provide some examples. qFit 3 is open-source under the MIT license, and is available at https://github.com/ExcitedStates/qfit-3.0.

Bio3D is a family of R packages for the analysis of biomolecular sequence, structure, and dynamics. Major functionality includes biomolecular database searching and retrieval, sequence and structure conservation analysis, ensemble normal mode analysis, protein structure and correlation network analysis, principal component, and related multivariate analysis methods. Here, we review recent package developments, including a new underlying segregation into separate packages for distinct analysis, and introduce a new method for structure analysis named ensemble difference distance matrix analysis (eDDM). The eDDM approach calculates and compares atomic distance matrices across large sets of homologous atomic structures to help identify the residue wise determinants underlying specific functional processes. An eDDM workflow is detailed along with an example application to a large protein family. As a new member of the Bio3D family, the Bio3D-eddm package supports both experimental and theoretical simulation-generated structures, is integrated with other methods for dissecting sequence-structure-function relationships, and can be used in a highly automated and reproducible manner. Bio3D is distributed as an integrated set of platform independent open source R packages available from: http://thegrantlab.org/bio3d/.

This paper presents an adaptive randomized algorithm for computing the butterfly factorization of an m × n matrix with m ≈ n provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of O(log n) sparse factors, each containing O(n) nonzero entries. The factorization can be attained using O(n3/2 log n) computation and O(n log n) memory resources. The proposed algorithm can be implemented in parallel and can apply to matrices with strong or weak admissibility conditions arising from surface integral equation solvers as well as multi-frontal-based finite-difference, finite-element, or finite-volume solvers. A distributed-memory parallel implementation of the algorithm demonstrates excellent scaling behavior.

The oralome is the summary of the dynamic interactions orchestrated between the ecological community of oral microorganisms (comprised of up to approximately 1000 species of bacteria, fungi, viruses, archaea and protozoa - the oral microbiome) that live in the oral cavity and the host. These microorganisms form a complex ecosystem that thrive in the dynamic oral environment in a symbiotic relationship with the human host. However, the microbial composition is significantly affected by interspecies and host-microbial interactions, which in turn, can impact the health and disease status of the host. In this review, we discuss the composition of the oralome and inter-species and host-microbial interactions that take place in the oral cavity and examine how these interactions change from healthy (eubiotic) to disease (dysbiotic) states. We further discuss the dysbiotic signatures associated with periodontitis and caries and their sequalae, (e.g., tooth/bone loss and pulpitis), and the systemic diseases associated with these oral diseases, such as infective endocarditis, atherosclerosis, diabetes, Alzheimer's disease and head and neck/oral cancer. We then discuss current computational techniques to assess dysbiotic oral microbiome changes. Lastly, we discuss current and novel techniques for modulation of the dysbiotic oral microbiome that may help in disease prevention and treatment, including standard hygiene methods, prebiotics, probiotics, use of nano-sized drug delivery systems (nano-DDS), extracellular polymeric matrix (EPM) disruption, and host response modulators.

BackgroundCOVID-19 has infected over 35 million people worldwide and led to over 1 million deaths. Several risk factors that increase COVID-19 severity have emerged, including age and a history of cardiovascular disease, hypertension, or kidney disease. However, a number of outstanding questions persist, including whether the above comorbidities correlate with increased mortality from COVID-19 or whether age is a significant confounding variable that accounts for the observed relationship between COVID-19 severity and other comorbidities.Methods and findingsWe conducted a systematic review and meta-analysis of studies documenting COVID-19 patients with hypertension, cardiovascular disease, cerebrovascular disease, or chronic kidney disease. We classified COVID-19 cases into severe/non-severe or deceased/surviving and calculated the odds ratio (OR) for each of the four comorbidities in these cohorts. 36 studies, comprising 22,573 patients, are included in our meta-analysis. We found that hypertension is the most prevalent comorbidity in deceased COVID-19 patients (55.4%; CI: 49.4-61.3%), followed by cardiovascular disease (30.7%; CI: 22.6-38.8%), cerebrovascular disease (13.4%; CI: 9.12-19.2%), then chronic kidney disease (9.05%; CI: 5.57-15.0%). The risk of death is also significantly higher for patients with these comorbidities, with the greatest risk factor being chronic kidney disease (OR: 8.86; CI: 5.27-14.89), followed by cardiovascular disease (OR: 6.87; CI: 5.56-8.50), hypertension (OR: 4.87; CI: 4.19-5.66), and cerebrovascular disease (OR: 4.28; CI: 2.86-6.41). These risks are significantly higher than previously reported, while correlations between comorbidities and COVID-19 severity are similar to previously reported figures. Using meta-regression analysis with age as a moderating variable, we observed that age contributes to the observed risks but does not explain them fully.ConclusionsIn this meta-analysis, we observed that cardiovascular, cerebrovascular, and kidney-related comorbidities in COVID-19 significantly contributes to greater risk of mortality and increased disease severity. We also demonstrated that age may not be a confounder to these associations.

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional problems often rely on speciffic, restrictive problem structures or are valid only locally around some nominal trajectory. In this paper, we propose a data- driven method to approximate semiglobal solutions to HJB equations for general high-dimensional nonlinear systems and compute candidate optimal feedback controls in real-time. To accomplish this, we model solutions to HJB equations with neural networks (NNs) trained on data generated without discretizing the state space. Training is made more effective and data-efficient by leveraging the known physics of the problem and using the partially trained NN to aid in adaptive data generation. We demonstrate the effectiveness of our method by learning solutions to HJB equations corresponding to the attitude control of a six-dimensional nonlinear rigid body and nonlinear systems of dimension up to 30 arising from the stabilization of a Burgers'-type partial differential equation. The trained NNs are then used for real-time feedback control of these systems.

Designing antiviral therapeutics is of great concern per current pandemics caused by novel coronavirus or SARS-CoV-2. The core polymerase enzyme in the viral replication/transcription machinery is generally conserved and serves well for drug target. In this work we briefly review structural biology and computational clues on representative single-subunit viral polymerases that are more or less connected with SARS-CoV-2 RNA dependent RNA polymerase (RdRp), in particular, to elucidate how nucleotide substrates and potential drug analogs are selected in the viral genome synthesis. To do that, we first survey two well studied RdRps from Polio virus and hepatitis C virus in regard to structural motifs and key residues that have been identified for the nucleotide selectivity. Then we focus on related structural and biochemical characteristics discovered for the SARS-CoV-2 RdRp. To further compare, we summarize what we have learned computationally from phage T7 RNA polymerase (RNAP) on its stepwise nucleotide selectivity, and extend discussion to a structurally similar human mitochondria RNAP, which deserves special attention as it cannot be adversely affected by antiviral treatments. We also include viral phi29 DNA polymerase for comparison, which has both helicase and proofreading activities on top of nucleotide selectivity for replication fidelity control. The helicase and proofreading functions are achieved by protein components in addition to RdRp in the coronavirus replication-transcription machine, with the proofreading strategy important for the fidelity control in synthesizing a comparatively large viral genome.

We examine a new variant of the classic prisoners and light switches puzzle: A warden leads his $n$ prisoners in and out of $r$ rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The rooms are indistinguishable, except that each one has $s$ light switches; the prisoners win their freedom if at some point a prisoner can correctly declare that each prisoner has been in every room at least once. What is the minimum number of switches per room, $s$, such that the prisoners can manage this? We show that if the prisoners do not know the switches' starting configuration, then they have no chance of escape—but if the prisoners do know the starting configuration, then the minimum sufficient $s$ is surprisingly small. The analysis gives rise to a number of puzzling open questions, as well.

Biology is advanced by producing structural models of biological systems, such as protein complexes. Some systems are recalcitrant to traditional structure determination methods. In such cases, it may still be possible to produce useful models by integrative structure determination that depends on simultaneous use of multiple types of data. An ensemble of models that are sufficiently consistent with the data is produced by a structural sampling method guided by a data-dependent scoring function. The variation in the ensemble of models quantified the uncertainty of the structure, generally resulting from the uncertainty in the input information and actual structural heterogeneity in the samples used to produce the data. Here, we describe how to generate, assess, and interpret ensembles of integrative structural models using our open source Integrative Modeling Platform program (https://integrativemodeling.org).

As we enter the exascale computing regime, powerful supercomputers continue to produce much higher amounts of data than what can be stored for offline data processing. To utilize such high compute capabilities on these machines, much of the data processing needs to happen in situ, when the full high-resolution data is available at the supercomputer memory. In this article, we discuss our MFiX-Exa simulation, which models multiphase flow by tracking a very large number of particles through the simulation domain. In one of the use cases, the carbon particles interact with air to produce carbon dioxide bubbles from the reactor. These bubbles are of primary interest to the domain experts for these simulations. For this particle-based simulation, we propose a streaming technique that can be deployed in situ to efficiently identify the bubbles, track them over time, and use them to down-sample the data with minimal loss in these features.

We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume, or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate O(N log2 N) computation and O(N) memory complexity when applied to an N × N sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

The US Department of Energy Computational Graduate Fellowship Program, celebrating 30 years of existence in 2021, is one of the most successful graduate fellowships in the world as well as one of the longest running programs in the US Department of Energy. This article discusses the conception, early years and evolution of the fellowship over the past thirty years.

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε ≪ 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε− 1). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε ≪ 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε3/2) and mesh size h = O(ε1/2). A large number of numerical results are reported to verify the error estimates.

UCSF ChimeraX is the next-generation interactive visualization program from the Resource for Biocomputing, Visualization, and Informatics (RBVI), following UCSF Chimera. ChimeraX brings (a) significant performance and graphics enhancements; (b) new implementations of Chimera's most highly used tools, many with further improvements; (c) several entirely new analysis features; (d) support for new areas such as virtual reality, light-sheet microscopy, and medical imaging data; (e) major ease-of-use advances, including toolbars with icons to perform actions with a single click, basic "undo" capabilities, and more logical and consistent commands; and (f) an app store for researchers to contribute new tools. ChimeraX includes full user documentation and is free for noncommercial use, with downloads available for Windows, Linux, and macOS from https://www.rbvi.ucsf.edu/chimerax.

The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.

Multitask deep neural networks learn to predict ligand-target binding by example, yet public pharmacological data sets are sparse, imbalanced, and approximate. We constructed two hold-out benchmarks to approximate temporal and drug-screening test scenarios, whose characteristics differ from a random split of conventional training data sets. We developed a pharmacological data set augmentation procedure, Stochastic Negative Addition (SNA), which randomly assigns untested molecule-target pairs as transient negative examples during training. Under the SNA procedure, drug-screening benchmark performance increases from R2 = 0.1926 ± 0.0186 to 0.4269 ± 0.0272 (122%). This gain was accompanied by a modest decrease in the temporal benchmark (13%). SNA increases in drug-screening performance were consistent for classification and regression tasks and outperformed y-randomized controls. Our results highlight where data and feature uncertainty may be problematic and how leveraging uncertainty into training improves predictions of drug-target relationships.

CRISPR-Cas12a is a genome-editing system, recently also harnessed for nucleic acid detection, which is promising for the diagnosis of the SARS-CoV-2 coronavirus through the DETECTR technology. Here, a collective ensemble of multimicrosecond molecular dynamics characterizes the key dynamic determinants allowing nucleic acid processing in CRISPR-Cas12a. We show that DNA binding induces a switch in the conformational dynamics of Cas12a, which results in the activation of the peripheral REC2 and Nuc domains to enable cleavage of nucleic acids. The simulations reveal that large-amplitude motions of the Nuc domain could favor the conformational activation of the system toward DNA cleavages. In this process, the REC lobe plays a critical role. Accordingly, the joint dynamics of REC and Nuc shows the tendency to prime the conformational transition of the DNA target strand toward the catalytic site. Most notably, the highly coupled dynamics of the REC2 region and Nuc domain suggests that REC2 could act as a regulator of the Nuc function, similar to what was observed previously for the HNH domain in the CRISPR-associated nuclease Cas9. These mutual domain dynamics could be critical for the nonspecific binding of DNA and thereby for the underlying mechanistic functioning of the DETECTR technology. Considering that REC is a key determinant in the system's specificity, our findings provide a rational basis for future biophysical studies aimed at characterizing its function in CRISPR-Cas12a. Overall, our outcomes advance our mechanistic understanding of CRISPR-Cas12a and provide grounds for novel engineering efforts to improve genome editing and viral detection.

Identifying and purchasing new small molecules to test in biological assays are enabling for ligand discovery, but as purchasable chemical space continues to grow into the tens of billions based on inexpensive make-on-demand compounds, simply searching this space becomes a major challenge. We have therefore developed ZINC20, a new version of ZINC with two major new features: billions of new molecules and new methods to search them. As a fully enumerated database, ZINC can be searched precisely using explicit atomic-level graph-based methods, such as SmallWorld for similarity and Arthor for pattern and substructure search, as well as 3D methods such as docking. Analysis of the new make-on-demand compound sets by these and related tools reveals startling features. For instance, over 97% of the core Bemis-Murcko scaffolds in make-on-demand libraries are unavailable from "in-stock" collections. Correspondingly, the number of new Bemis-Murcko scaffolds is rising almost as a linear fraction of the elaborated molecules. Thus, an 88-fold increase in the number of molecules in the make-on-demand versus the in-stock sets is built upon a 16-fold increase in the number of Bemis-Murcko scaffolds. The make-on-demand library is also more structurally diverse than physical libraries, with a massive increase in disc- and sphere-like shaped molecules. The new system is freely available at zinc20.docking.org.

In 1932, von Neumann proposed classifying the statistical behavior of differentiable systems. Joint work of B. Weiss and the author proved that the classification problem is complete analytic. Based on techniques in that proof, one is able to show that the collection of recursive diffeomorphisms of the 2-torus that are isomorphic to their inverses is -hard via a computable 1-1 reduction. As a corollary there is a diffeomorphism that is isomorphic to its inverse if and only if the Riemann Hypothesis holds, a different one that is isomorphic to its inverse if and only if Goldbach's conjecture holds and so forth. Applying the reduction to the Π01 sentence expressing "ZFC"is consistent gives a diffeomorphism T of the 2-torus such that the question of whether T ≅ T-1 is independent of ZFC.

To improve lead optimization efforts in finding the right ligand, pharmaceutical industries need to know the ligand's binding kinetics, such as binding and unbinding rate constants, which often correlate with the ligand's efficacy in vivo. To predict binding kinetics efficiently, enhanced sampling methods, such as milestoning and the weighted ensemble (WE) method, have been used in molecular dynamics (MD) simulations of these systems. However, a comparison of these enhanced sampling methods in ranking ligands has not been done. Hence, a WE approach called the concurrent adaptive sampling (CAS) algorithm that uses MD simulations was used to rank seven ligands for β-cyclodextrin, a system in which a multiscale milestoning approach called simulation enabled estimation of kinetic rates (SEEKR) was also used, which uses both MD and Brownian dynamics simulations. Overall, the CAS algorithm can successfully rank ligands using the unbinding rate constant koff values and binding free energy ΔG values, as SEEKR did, with reduced computational cost that is about the same as SEEKR. We compare the CAS algorithm simulations with different parameters and discuss the impact of parameters in ranking ligands and obtaining rate constant and binding free energy estimates. We also discuss similarities and differences and advantages and disadvantages of SEEKR and the CAS algorithm for future use.

Biofilms are accumulations of microorganisms embedded in extracellular matrices that protect against external factors and stressful environments. Cyanobacterial biofilms are ubiquitous and have potential for treatment of wastewater and sustainable production of biofuels. But the underlying mechanisms regulating cyanobacterial biofilm formation are unclear. Here, we report the solution NMR structure of a protein, Se0862, conserved across diverse cyanobacterial species and involved in regulation of biofilm formation in the cyanobacterium Synechococcus elongatus PCC 7942. Se0862 is a class α+β protein with ααββββαα topology and roll architecture, consisting of a four-stranded β-sheet that is flanked by four α-helices on one side. Conserved surface residues constitute a hydrophobic pocket and charged regions that are likely also present in Se0862 orthologs.

We provide a general framework for computing upper bounds on mixing times offinite Markov chains when its minimal ideal is left zero. Our analysis is basedon combining results by Brown and Diaconis with our previous work on stationarydistributions of finite Markov chains. Stationary distributions can be computedfrom the Karnofsky--Rhodes and McCammond expansion of the right Cayley graph ofthe finite semigroup underlying the Markov chain. Using loop graphs, which areplanar graphs consisting of a straight line with attached loops, there arerational expressions for the stationary distribution in the probabilities. Fromthese we obtain bounds on the mixing time. In addition, we provide a new Markovchain on linear extension of a poset with $n$ vertices, inspired by butdifferent from the promotion Markov chain of Ayyer, Klee and the last author.The mixing time of this Markov chain is $O(n \log n)$.

Using the DUD-E+ benchmark, we explore the impact of using a single protein pocket or ligand for virtual screening compared with using ensembles of alternative pockets, ligands, and sets thereof. For both structure-based and ligand-based approaches, the precise characterization of the binding site in question had a significant impact on screening performance. Using the single original DUD-E protein, Surflex-Dock yielded mean ROC area of 0.81 ± 0.11. Using the cognate ligand instead, with the eSim method for screening, yielded 0.77 ± 0.14. Moving to ensembles of five protein pocket variants increased docking performance to 0.84 ± 0.09. Results for the analogous ligand-based approach (using the five crystallographically aligned cognate ligands) was 0.83 ± 0.11. Using the same ligands, but making use of an automatically generated mutual alignment, yielded mean AUC nearly as good as from single-structure docking: 0.80 ± 0.12. Detailed results and statistical analyses show that structure- and ligand-based methods are complementary and can be fruitfully combined to enhance screening efficiency. A hybrid approach combining ensemble docking with eSim-based screening produced the best and most consistent performance (mean ROC area of 0.89 ± 0.08 and 1% early enrichment of 46-fold). Based on results from both the docking and ligand-similarity approaches, it is clearly unwise to make use of a single arbitrarily chosen protein structure for docking or single ligand query for similarity-based screening.

The COVID-2019 pandemic is the most severe acute public health threat of the twenty-first century. To properly address this crisis with both robust testing and novel treatments, we require a deep understanding of the life cycle of the causative agent, the SARS-CoV-2 coronavirus. Here, we examine the architecture and self-assembly properties of the SARS-CoV-2 nucleocapsid protein, which packages viral RNA into new virions. We determined a 1.4 Å resolution crystal structure of this protein's N2b domain, revealing a compact, intertwined dimer similar to that of related coronaviruses including SARS-CoV. While the N2b domain forms a dimer in solution, addition of the C-terminal spacer B/N3 domain mediates formation of a homotetramer. Using hydrogen-deuterium exchange mass spectrometry, we find evidence that at least part of this putatively disordered domain is structured, potentially forming an α-helix that self-associates and cooperates with the N2b domain to mediate tetramer formation. Finally, we map the locations of amino acid substitutions in the N protein from over 38,000 SARS-CoV-2 genome sequences. We find that these substitutions are strongly clustered in the protein's N2a linker domain, and that substitutions within the N1b and N2b domains cluster away from their functional RNA binding and dimerization interfaces. Overall, this work reveals the architecture and self-assembly properties of a key protein in the SARS-CoV-2 life cycle, with implications for both drug design and antibody-based testing.

While safe chemical storage and disposal are simple in principle-users should read safety specifications and place chemicals in appropriate cabinets or collection points-high-profile incidents involving improper storage and disposal of chemicals continue to occur. This paper introduces ChemStor, an open-source, automated computational system that can guarantee (mathematically verify a system is correct with respect to its specification), with regard to prescribed constraints, safe storage and disposal of chemicals used in academic, industrial, and domestic settings. ChemStor borrows concepts from formal methods-a branch of computer science capable of mathematically proving a specification or software is correct-to safely store or dispose of chemicals. If two or more chemicals can be combined in the same cabinet without forming possibly dangerous combinations of chemicals (while observing cabinet/shelf space constraints), then ChemStor determines that the storage configuration is safe. Likewise, if chemicals can be added to an existing disposal container without forming possibly dangerous combinations of chemicals (or exceeding the volume of the container), then ChemStor determines that the disposal configuration is safe. ChemStor accomplishes this by first building a chemical interaction graph, a graph that describes which chemicals may interact with each other based on their reactivity groups as determined by the United States Environmental Protection Agency. Next, ChemStor computes the chromatic number of the graph, the smallest number of colors used to color the graph such that no two vertices (chemicals) that share an edge (an interaction) share the same color. ChemStor then assigns all the chemicals of each color to a storage or disposal container after confirming that there is enough space in the container. These steps are encoded into a series of satisfiability modulo theory equations, and ChemStor uses an industry-standard tool to try to find a valid solution to these equations. The result is either a solution which dictates exactly where to store or dispose of each chemical, or an indication that no safe storage or disposal configuration could be found. To demonstrate the feasibility of ChemStor, we used the tool to analyze ten real-world chemical storage and disposal incidents that led to injuries or destruction of property. In each case, ChemStor quickly and successfully identified a proper chemical disposal or storage configuration that would have prevented the incident. In the future, ChemStor may be integrated with electronic laboratory notebooks, voice assistants, and other emerging technology to protect users of chemicals in labs, workplaces, and homes.