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• Implemented K-CliqueWeight into the ProBiS-Dock algorithm, enhancing its capabilities for molecular docking. • Efficiently identifies the top N weighted k-cliques, addressing challenges in molecular docking and diverse problem domains. • Demonstrated superior performance of K-CliqueWeight, surpassing alternatives by several orders of magnitude. • Accessible to academia for free at http://insilab.org/kcliqueweight, facilitating widespread use. Molecular docking, a key process in drug discovery, is often used in the discovery of new bioactive compounds. In this technique, small molecules are systematically placed at a protein binding site to identify the ligands with the highest binding affinity. Here we have developed a new graph-theoretical algorithm called K-CliqueWeight. This algorithm efficiently identifies the top N highest weight k-cliques in different types of vertex-weighted graphs and can serve as a building block for various algorithms addressing different problems, including molecular docking. K-CliqueWeight and its variant K-CliqueDynWeight are extensions of our established and widely used maximum clique algorithm. Our new algorithm uses a novel approach to approximate graph coloring and provides efficient upper bounds on the size and weight of a k-clique within the branch-and-bound algorithm. It outperforms alternative methods and often shows a speedup of several orders of magnitude. Rigorous tests with general random graphs and those specifically designed for docking confirm its exceptional performance. K-CliqueWeight has been integrated into the existing ProBiS-Dock algorithm for molecular docking. The algorithm is freely available to the academic community at http://insilab.org/kcliqueweight. [Display omitted] [ABSTRACT FROM AUTHOR]

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 X N sparse system arising from 3D high-frequency Helmholtz and Maxwell problems. [ABSTRACT FROM AUTHOR]

We present and discuss the advancements made in PyRETIS 3, the third instalment of our Python library for an efficient and user‐friendly rare event simulation, focused to execute molecular simulations with replica exchange transition interface sampling (RETIS) and its variations. Apart from a general rewiring of the internal code towards a more modular structure, several recently developed sampling strategies have been implemented. These include recently developed Monte Carlo moves to increase path decorrelation and convergence rate, and new ensemble definitions to handle the challenges of long‐lived metastable states and transitions with unbounded reactant and product states. Additionally, the post‐analysis software PyVisa is now embedded in the main code, allowing fast use of machine‐learning algorithms for clustering and visualising collective variables in the simulation data. [ABSTRACT FROM AUTHOR]

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to sevenfold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-ofthe-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK (STRUctured Matrices PACKage), which also has a distributed memory component for dense rank-structured matrices. [ABSTRACT FROM AUTHOR]

Highlights: [•] The manuscript presents a highly scalable preconditioned Conjugate Gradient method. [•] It presents a pipelined preconditioned Conjugate Residual method. [•] It shows how global communication can be overlapped with local work. [•] It shows numerical stability of the methods. [•] It shows improved scalability and runtime compared to CG and CR. [ABSTRACT FROM AUTHOR]