Good Parallel Research Articles

A parallel exponential integrator scheme for linear differential equations

New approximations of the matrix φ functions are developed. These approximations are rational functions of a specific form allowing simple and accurate schemes for linear systems. Furthermore, these approximations are fully parallelizable. Several tests show the efficiency of the method and its good parallelization properties.

Multilevel Schur-complement algorithms for scalable parallel reservoir simulation with temperature variation

In reservoir simulation, the non-isothermal multiphase flow problem introduces the temperature variable to account for thermal effects, simultaneously posing challenges in efficiently solving the nonlinear systems for large-scale simulations. In this paper, we introduce and investigate a family of Schur-complement-based field-split algorithms designed for addressing non-isothermal multiphase flow problems, particularly those characterized by high heterogeneity. This algorithm involves decomposing a large system into smaller, more manageable sub-systems for solving non-isothermal multiphase flow problems with multiple physical fields, which enables parallel computation and makes it suitable for high-performance computing environments. Furthermore, a multilevel Schur-complement preconditioner, which involves applying the Schur-complement technique at each level of the hierarchy by capturing the coupling between different fields and physics, is proposed to enhance the efficiency and robustness of the parallel simulator. Large-scale simulations for both benchmark and realistic problems are conducted on a supercomputer, showcasing the method's efficacy in managing heat diffusion, significantly reducing linear iterations, and demonstrating a good parallel scalability.

Isaiah 6:1–3 and Angelomorphic Christology. An Approach to Understand Origen’s Isaiah Exegesis

This article deals with Origen’s interpretation of Isaiah’s vision in Isa 6. Origen refers to his Hebrew Master’s statement in Orig. Princ. 1.3.4 where two Seraphim are identified with Christ and the Holy Spirit. The main scope in the article is to put the Hebrew Master’s opinion in balance with Origen’s own Christology. The problem is approached from the method of biblical argumentation by using ancien reception historical ways to understand scripture. The Hebrew Master’s statement is related to three important themes: First, the angelomorphic theophanies in the Old Testament provide a general background for the idea that Christ (and the Holy Spirit) can be identified with Seraphim. Second, Origen relates Isaiah’s Seraphim to Cherubim in the Ark of Covenant and use Hab 3:2 to illustrate his Christology. Third, the Christology of the Ascension of Isaiah provides a good parallel to understand the Hebrew Master’s statement about Seraphim. The main result in the article is that Origen’s own Christology is well balanced with the statement of the Hebrew Master. Origen’s teachings about Christ can be characterized as high and subordinate Christology, and its roots are in early Jewish-Christian circles.

PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation

The aim of this paper is to introduce the PLEIADES framework offering a set of services and numerical tools to model and simulate the behavior of nuclear fuels of different concepts of reactors. The framework provides in particular the following features: interfaces to manipulate meshes and fields, services to deal with different physical solvers, setup of coupling trees to realize multiphysics partitioned (accelerated) fixed point couplings, automated time-marching algorithm, checkpoint/restart strategies, capability to realize on-the-fly multiscale couplings. It is built with a permanent concern for sustainability, scalability and maintainability. PLEIADES framework supports multidimensional simulations, typically 1D, 2D and 3D, possibly multilayered. To date, this framework relies on the generic thermomechanical finite elements solver Cast3M to deal with partial derivative problems (mechanical, thermal or diffusion problems) at the scale of the structure or the (heterogeneous) microstructure. It also makes use of so-called point models (mainly based on ODE — ordinary differential equations) to describe the local (mesoscale) evolution of the material through the physics of irradiation. Several software applications are built on the PLEIADES framework, they can use its parallel features to use multiple processors. The multilayered calculation scheme provides a way to loosen the computations and access to a good parallel performance up to hundred cores. It is also possible to achieve efficient scalable concurrent multiscale simulations through finite element square (FE2) computational homogenization algorithms.

Reversed-phase thin-layer chromatography and ultra-performance liquid chromatography/mass spectrometry to estimate the drug likeness of phosphodiesterase 10A inhibitors with phthalimide core

Lipophilicity is a physicochemical parameter well known as a decisive factor for predicting the successful development of a drug. Thus, a balance between potency and physicochemical properties during medicinal chemistry optimization is needed. In this study, the lipophilicity of isoindole-1,3(2H)-dione derivatives designed as phosphodiesterase 10A (PDE10A) inhibitors was determined by chromatographic [reversed-phase thin-layer chromatography (RP-TLC) and ultra-performance liquid chromatography/mass spectrometry (UPLC/MS)] and in silico methods. To assess the correlation between the obtained lipophilicity parameters, principal component analysis (PCA) was performed. logP values obtained by chromatographic (logPRP-TLC and logPUPLC/MS) and in silico methods were compared using the PCA method. The results of PCA revealed that logPUPLC/MS and in silico clogP provided by the ChemDraw program were highly correlated. Compounds’ drug likeness was screened, and the pharmacokinetic properties were predicted. All the investigated compounds displayed drug-likeness properties, and they met the criteria of Lipinski’s rule of five, which predicted the oral bioavailability of drug candidates. Analysis of the influence of physicochemical properties on the biological activity showed that the compounds with increased potency on PDE10A had significantly higher topological polar surface area (TPSA) values. The blood‒brain barrier permeability and the hemolytic activity of model compound 18 were examined. The model compound 18 displayed no toxicity effect on erythrocytes in the hemolytic assay and good parallel artificial membrane permeability. The results showed that phthalimide compounds with benzimidazole moiety are a source of compound-targeted inhibition of PDE10A with balanced physicochemical and drug-likeness properties.

Exploiting inherent elasticity of serverless in algorithms with unbalanced and irregular workloads

Function-as-a-Service execution model in serverless computing has been successful in running large-scale computations like MapReduce, linear algebra, and machine learning. However, little attention has been given to executing highly-dynamic parallel applications with unbalanced and irregular workloads. These algorithms are difficult to execute with good parallel efficiency due to the challenge of provisioning the required computing resources in time, leading to resource over- and under-provisioning in clusters of static size. We propose that the elasticity and fine-grained “pay-as-you-go model” of the FaaS model can be a key enabler for effectively running these algorithms in the cloud. We use a simple serverless executor pool abstraction, and evaluate it using three algorithms with unbalanced and irregular workloads. Results show that their serverless implementation can outperform a static Spark cluster of large virtual machines by up to 55% with the same cost, and can even outperform a single large virtual machine running locally.

Alterite and Magnesioalterite, Two New Oxalate Minerals, from the Vermillion Cliffs, Coconino County, Arizona, USA

Abstract Two new organic minerals, alterite and magnesioalterite, ideally Zn2Fe3+4(SO4)4(C2O4)2(OH)4·17H2O and Mg2Fe3+4(SO4)4(C2O4)2(OH)4·17H2O, respectively, were discovered in carbonaceous petrified wood from an unnamed uranium prospect, the Vermillion Cliffs, Coconino County, Arizona, USA. Associated minerals include gypsum, alunogen, natrojarosite, sulfur, celestine, and quartz. Both alterite and magnesioalterite are yellowish green in transmitted light and transparent with white streak and vitreous luster. They are brittle and have a Mohs hardness of ∼1.5; cleavage is perfect on (001). No parting or twinning was observed. The measured densities are 2.18(4) and 2.17(3) g/cm3 for alterite and magnesioalterite, respectively. Optically, alterite is biaxial (+), with α = 1.545(5), β = 1.565(5), γ = 1.635(5), 2Vmeas. = 56(2)°, 2Vcal. = 58°. Magnesioalterite is also biaxial (+), with α =1.520 (5), β = 1.578 (6), γ = 1.610 (5), 2Vmeas. = 74(2)°, 2Vcal. = 76.5°. Both new minerals are insoluble in water, but slowly dissolve in hydrochloric acid. An electron microprobe analysis, together with data from an Elemental Combustion System for C, yielded the empirical formula (based on 45 O apfu) (Zn0.84Fe2+0.57Mg0.48Mn0.14)Σ2.03Fe3+4.00(S0.99O4)4(C2O4)2(OH)4·17H2O for alterite and (Mg0.74Zn0.60Fe2+0.58Mn0.09)Σ2.01Fe3+4.00(SO4)4.00(C2O4)2(OH)4·17H2O for magnesioalterite, both of which can be simplified to (Zn,Fe,Mg,Mn)2Fe3+4(SO4)4(C2O4)2(OH)4·17H2O and (Mg,Zn,Fe2+,Mn)2Fe3+4(SO4)4(C2O4)2(OH)4·17H2O, respectively. The measured δ13C ‰ value for the carbonaceous petrified wood on which the minerals were found is −23.1 and for alterite and magnesioalterite is 0.2. Alterite and magnesioalterite constitute a complete solid solution. They are monoclinic with the same space group, C2/c. The unit-cell parameters are a = 16.7656(15), b = 9.4074(7), c = 25.351(3) Å, β = 108.258(5)°, V = 3797.1(6) Å3 for alterite and a = 16.7696(5), b = 9.4020(2), c = 25.3466(8) Å, β = 108.2520(10)°, V = 3795.28(18) Å3 for magnesioalterite. The crystal structures of alterite and magnesioalterite are characterized by four-membered clusters of corner-sharing Fe3+(O5OH) octahedra. These clusters are linked by SO4 tetrahedra along the b axis and by the oxalate groups (C2O4)2− along the a axis to form sheets parallel to (001). Between the sheets are layers of M2+(H2O)6 octahedra (M = Zn2+, Mg2+, Fe2+, and Mn2+) and three symmetrically distinct H2O molecules that are not bonded to any non-H cations. The linkage between the sheets and the layers is achieved by hydrogen bonds, accounting for the good cleavage parallel to (001). Alterite and magnesioalterite are two of five double-salt minerals with hydrated sulfate-oxalates, after coskrenite-(Ce), Ce2(SO4)2(C2O4)·8H2O; levinsonite-(Y), YAl(SO4)2(C2O4)·12H2O; and zugshunstite-(Ce), CeAl(SO4)2(C2O4)·12H2O. They are also the most hydrated among the 34 oxalate minerals reported thus far. Noticeably, both alterite and magnesioalterite contain a significant amount of Fe2+ substituting for Mg and Zn, pointing to the likelihood for the existence of a Fe2+-analogue of alterite.

A parallel finite element post-processing algorithm for the damped Stokes equations

This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method and post-processing technique. The most valuable highlights of the present algorithm are that (1) a global continuous approximate solution is generated via the partition of unity method; (2) by adding an extra coarse grid correction step, the smoothness of the approximate solution is improved; (3) it has a good parallel performance since there requires little communication in solving a series of residual problems in the subdomain of interest. We theoretically derive the L2-error estimates both for the approximate velocity and pressure and H1-error estimate for the velocity under some necessary conditions. Meanwhile, we numerically perform various test examples to validate the theoretically predicted convergence rate and illustrate the high efficiency of the proposed algorithm.

Large‐scale homo‐ and heterogeneous parallel paradigm design based on CFD application PHengLEI

SummaryThe development of computational fluid dynamics (CFD) highly depends on high‐performance computers. Computer hardware has evolved rapidly, yet scalable CFD parallel software remains scarce. In this article, we design a highly scalable CFD parallel paradigm for both homogeneous and heterogeneous supercomputers. The paradigm achieves the separation of communication and computation and automatically adapts to various solvers and hardware environments, thus reducing programming difficulties and increasing automatic parallelization. Meanwhile, the number of communications is greatly reduced and the scalability of the program is improved through implementing centralized communication and two‐level partitioning techniques. Complex flow problems for real aircraft were then computed on different hardware platforms with a grid size of ten billion. The homogeneous computer hardware includes Intel Xeon Gold 6258R and Phytium 2000+ processors, and the heterogeneous computer platforms include NVIDIA Tesla V100 and SW26010 processors. High parallel efficiency was obtained on all computer platforms, verifying that the paradigm has good automatic parallelization, scalability, and stability. The paradigm in this article has an important reference value for CFD massively parallel computing and can promote the development and application of CFD technology.

An improved dynamical Poisson equation solver for self-gravity

ABSTRACT Since self-gravity is crucial in the structure formation of the Universe, many hydrodynamics simulations with the effect of self-gravity have been conducted. The multigrid method is widely used as a solver for the Poisson equation of the self-gravity; however, the parallelization efficiency of the multigrid method becomes worse when we use a massively parallel computer, and it becomes inefficient with more than 104 cores, even for highly tuned codes. To perform large-scale parallel simulations (>104 cores), developing a new gravity solver with good parallelization efficiency is beneficial. In this article, we develop a new self-gravity solver using the telegraph equation with a damping coefficient, κ. Parallelization is much easier than the case of the elliptic Poisson equation since the telegraph equation is a hyperbolic partial differential equation. We analyse convergence tests of our telegraph equations solver and determine that the best non-dimensional damping coefficient of the telegraph equations is $\tilde{\kappa } \simeq 2.5$. We also show that our method can maintain high parallelization efficiency even for massively parallel computations due to the hyperbolic nature of the telegraphic equation by weak-scaling tests. If the time-step of the calculation is determined by heating/cooling or chemical reactions, rather than the Courant–Friedrichs–Lewy (CFL) condition, our method may provide the method for calculating self-gravity faster than other previously known methods such as the fast Fourier transform and multigrid iteration solvers because gravitational phase velocity determined by the CFL condition using these time-scales is much larger than the fluid velocity plus sound speed.

Bidynamical all-optical reservoir computing for parallel task processing.

A bidynamical all-optical reservoir computing (RC) system for parallel task processing is proposed based on a unidirectional semiconductor optical amplifier optical fiber loop. The polarization dynamics and intensity dynamics are excited by the input signals injected into the reservoir via phase modulation and intensity modulation, respectively. Simultaneous computation of two independent tasks is implemented based on the dynamical responses in polarization and intensity of the optical fiber loop. To our knowledge, this is the first time that two kinds of dynamical responses of an all-optical RC system are used as independent task processing channels to implement parallel task processing. The proposed RC system can achieve good parallel task processing performance with low system cost.

Morpheme-Based Neural Machine Translation Models for Low-Resource Fusion Languages

Neural approaches, which are currently state-of-the-art in many areas, have contributed significantly to the exciting advancements in machine translation. However, Neural Machine Translation (NMT) requires a substantial quantity and good quality parallel training data to train the best model. A large amount of training data, in turn, increases the underlying vocabulary exponentially. Therefore, several proposed methods have been devised for relatively limited vocabulary due to constraints of computing resources such as system memory. Encoding words as sequences of subword units for so-called open-vocabulary translation is an effective strategy for solving this problem. However, the conventional methods for splitting words into subwords focus on statistics-based approaches that mainly conform to agglutinative languages. In these languages, the morphemes have relatively clean boundaries. These methods still need to be thoroughly investigated for their applicability to fusion languages, which is the main focus of this article. Phonological and orthographic processes alter the borders of constituent morphemes of a word in fusion languages. Therefore, it makes it difficult to distinguish the actual morphemes that carry syntactic or semantic information from the word’s surface form, the form of the word as it appears in the text. We, thus, resorted to a word segmentation method that segments words by restoring the altered morphemes. We also compared conventional and morpheme-based NMT subword models. We could prove that morpheme-based models outperform conventional subword models on a benchmark dataset.

Automatic Resource Augmentation for Machine Translation in Low Resource Language: EnIndic Corpus

Parallel corpus is the primary ingredient of machine translation. It is required to train the statistical machine translation (SMT) and neural machine translation (NMT) systems. There is a lack of good quality parallel corpus for Hindi to English. Comparable corpora for a given language pair are comparatively easy to find, but this cannot be used directly in SMT or NMT systems. As a result, we generate a parallel corpus from the comparable corpus. For this purpose, the sentences (which are translations of each other) are mined from the comparable corpus to prepare the parallel corpus. The proposed algorithm uses the length of the sentence and word translation model to align sentence pairs that are translations of each other. Then, the sentence pairs that are poor translations of each other (measured by a similarity score based on IBM model 1 translation probability) are filtered out. We apply this algorithm to comparable corpora, which are crawled from speeches of the President and Vice-President of India, and mined parallel corpora out of them. The prepared parallel corpus contains good quality aligned sentences (with 96.338% f-score). Subsequently, incorrect sentence pairs are filtered out manually to make the corpus in qualitative practical use. Finally, we gather various sentences from different sources to prepare the EnIndic corpus, which comprises 1,656,207 English-Hindi sentence pairs (miscellaneous domain). We have deployed this prepared largest English-Hindi parallel corpus at https://github.com/debajyoty/EnIndic.git and the source code at https://github.com/debajyoty/EnIndicSourceCode.git.

A multithreaded CUDA and OpenMP based power‐aware programming framework for multi‐node GPU systems

SummaryIn the article, we have proposed a framework that allows programming a parallel application for a multi‐node system, with one or more graphical processing units (GPUs) per node, using an OpenMP+extended CUDA API. OpenMP is used for launching threads responsible for management of particular GPUs and extended CUDA calls allow to transfer data and launch kernels on local and remote GPUs. The framework hides inter‐node MPI communication from the programmer. For optimization, the implementation takes advantage of the MPI_THREAD_MULTIPLE mode allowing: multiple threads handling distinct GPUs as well as overlapping communication and computations transparently using multiple CUDA streams. The solution allows data parallelization across available GPUs in order to minimize execution time and supports a power‐aware mode in which GPUs are automatically selected for computations using a greedy approach in order not to exceed an imposed power limit. We have implemented and benchmarked three parallel applications including: finding the largest divisors; verification of the Collatz conjecture; finding patterns in vectors. These were tested on three various systems: a GPU cluster with 16 nodes, each with NVIDIA GTX 1060 GPU; a powerful 2‐node system—one node with 8 NVIDIA Quadro RTX 6000 GPUs, the second with 4 NVIDIA Quadro RTX 5000 GPUs; a heterogeneous environment with one node with 2 NVIDIA RTX 2080 and 2 nodes with NVIDIA GTX 1060 GPUs. We demonstrated effectiveness of the framework through execution times versus power caps within ranges of 100–1400 W, 250–3000 W, and 125–600 W for these systems respectively as well as gains from using two versus one CUDA streams per GPU. Finally, we have shown that for the testbed applications the solution allows to obtain high speed‐ups between 89.3% and 97.4% of the theoretically assessed ideal ones, for 16 nodes and 2 CUDA streams, demonstrating very good parallel efficiency.

3D strongly anisotropic intrinsic thermal conductivity of polypropylene separator

In this work, the thermal conductivity in every direction is reported for the first time for the dry separator component made out of polypropylene (PP) that is used in lithium-ion batteries. Herein, a PP separator film is studied dry and in vacuum, as an example of polyolefins separators. These separators are crucial for performance parameters, including cycle life, thermal management, energy and power density, and safety. Hence, a better understanding of the thermal conductivity k in different in-plane directions (parallel and normal direction to the stretching direction in fabrication) as well as the out-of-plane direction is crucial to the overall performance. k of dry PP separator, measured in vacuum, is found four times bigger in the parallel direction (0.217 W⋅m−1⋅K−1) than that in the normal direction (0.043 W⋅m−1⋅K−1), all for the in-plane direction. This strong anisotropy can be explained by the macroscopic and microscopic anisotropic structure and intrinsic anisotropic thermal conductivity of aligned PP. Moreover, the out-of-plane k of the dry PP separator is measured to be 0.036 and 0.025 W⋅m−1⋅K−1 in the air and vacuum, respectively, suggesting good parallel structure of PP in the thickness direction.

A Distributed-GPU Deep Reinforcement Learning System for Solving Large Graph Optimization Problems

Graph optimization problems (such as minimum vertex cover, maximum cut, traveling salesman problems) appear in many fields including social sciences, power systems, chemistry, and bioinformatics. Recently, deep reinforcement learning (DRL) has shown success in automatically learning good heuristics to solve graph optimization problems. However, the existing RL systems either do not support graph RL environments or do not support multiple or many GPUs in a distributed setting. This has compromised the ability of reinforcement learning in solving large-scale graph optimization problems due to lack of parallelization and high scalability. To address the challenges of parallelization and scalability, we develop RL4GO , a high-performance distributed-GPU DRL framework for solving graph optimization problems. RL4GO focuses on a class of computationally demanding RL problems, where both the RL environment and policy model are highly computation intensive. Traditional reinforcement learning systems often assume either the RL environment is of low time complexity or the policy model is small. In this work, we distribute large-scale graphs across distributed GPUs and use the spatial parallelism and data parallelism to achieve scalable performance. We compare and analyze the performance of the spatial parallelism and data parallelism and show their differences. To support graph neural network (GNN) layers that take as input data samples partitioned across distributed GPUs, we design parallel mathematical kernels to perform operations on distributed 3D sparse and 3D dense tensors. To handle costly RL environments, we design a parallel graph environment to scale up all RL-environment-related operations. By combining the scalable GNN layers with the scalable RL environment, we are able to develop high-performance RL4GO training and inference algorithms in parallel. Furthermore, we propose two optimization techniques—replay buffer on-the-fly graph generation and adaptive multiple-node selection—to minimize the spatial cost and accelerate reinforcement learning. This work also conducts in-depth analyses of parallel efficiency and memory cost and shows that the designed RL4GO algorithms are scalable on numerous distributed GPUs. Evaluations on large-scale graphs show that (1) RL4GO training and inference can achieve good parallel efficiency on 192 GPUs, (2) its training time can be 18 times faster than the state-of-the-art Gorila distributed RL framework [ 34 ], and (3) its inference performance achieves a 26 times improvement over Gorila.

Fuzzy Influenced Process to Generate Comparable to Parallel Corpora

Data-driven supervised approaches rely on the parallel corpus. Due to lack of data and resources availability, it has become more difficult to achieve accurate outputs. In addition, the efficiency of the machine translation system depends on the quality of the used corpora. Hindi still lacks good quality parallel corpora and needs more resources for accurate machine translation. Comparable corpora are easily available compared to parallel corpora, but they cannot be used directly in machine translation. In our present research, we propose an algorithm to mine these comparable corpora from the web, and generate the parallel corpora automatically. Machine translation systems, system combination approach, and IR-based technique join their hands together to choose the set of sentence pairs. Then the sentence pairs having the best score are chosen to prepare the final parallel corpora. The primary modules of this architecture are fuzzy logic-based evaluation metric, information retrieval module, statistical machine translation system, Google neural machine translation system, Microsoft machine translation system, and system combination module for machine translation. For case study, we prepare the Hindi-English parallel corpora of (30825 + 51235) = 82060 sentence pairs. Evaluation results show that the F-Score measurement varies from 95.73 to 96.98 for various data sets. The source code and prepared dataset (comparable and parallel corpus) can be found at https://github.com/debajyoty/Comparable-partallel-Algo2.git.

Prachařite, CaSb5+2(As3+2O5)2O2·10H2O, a new mineral from Lavrion, Greece

Prachařite, ideally CaSb5+2(As3+2O5)2O2·10H2O, is a new mineral found in underground workings of the Plaka Mine No. 80, Plaka, Lavrion Mining District, Attica, Greece. It occurs as colourless to white, thin tabular hexagonal, in general sharp crystals up to 2.5 mm in diameter, and is associated with pharmacolite, sulphur and very rare smamite {Ca2Sb(OH)4[H(AsO4)2]·6H2O} on a matrix composed of sphalerite, galena and carbonate gangue. Prachařite is translucent to transparent, with a glassy lustre, white streak, a good cleavage parallel to {0001} and a distinct cleavage parallel to {10overline{1 }0}. It is non-luminescent, brittle, and has an uneven fracture, a Mohs hardness of 2–2.5 and X-ray density Dx = 2.848 g/cm3, Dcalc. = 2.836–2.853 g/cm3 (for two measured compositions). Optically, it is uniaxial negative, with ω = 1.619(1) and ε = 1.553(1). Prachařite is trigonal, space group Poverline{3 }c1 (no. 165), with a = 13.951(2), c = 19.899(2) Å, V = 3354.1(10) Å3 and Z = 6. Strongest lines in the X-ray powder diffraction pattern are [d in Å (I) hkl]: 9.894 (100) 002; 6.045 (8) 200; 5.156 (10) 202; 4.946 (11) 004; 3.297 (19) 311, 006, 222; 2.988 (22) 400, 313, 116. Two sets of independent electron probe micro-analyses yielded (wt%): CaO 6.28/7.12, MgO 0.09/-, Zn -/0.01, Sb2O5 39.22/40.19, As2O3 47.59/47.39, SO3 -/0.02, H2O 21.65/22.04 (calculated on the basis of ideal composition derived from crystal-structure determination), total 114.83/116.77; the total is reproducibly high due to a loss of a third of all water molecules under the electron beam. The empirical formulae, based on O = 22 atoms per formula unit, for the two datasets are very similar, (Ca0.93Mg0.02)Σ0.95Sb2.02(AsO3)4.00·10H2O and Ca1.04Sb2.03(AsO3)3.92·10H2O. The ideal formula is CaSb5+2(As3+2O5)2O2·10H2O, determined with the help of a crystal-structure determination based on single-crystal X-ray diffraction datasets collected at room temperature (R1 = 2.3%). The atomic arrangement of prachařite is unusual; it is based on two different layers containing a six-membered ring of corner-sharing SbO6 octahedra, an eight-coordinated Ca1 atom in the centre of the ring, two non-equivalent AsO3 groups corner-linked to form a (As2O5)4− diarsenite group, and, on interlayer sites, a seven-coordination Ca2 atom and three water molecules (all only weakly hydrogen-bonded), one of which is only partially occupied (split position). The mineral is named in honour of Dr Ivan Prachař, a long-term researcher of the mineralogy and underground workings of Lavrion.

Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel’s MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.

Codebase release 1.3 for SymTensor

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel’s MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.