Scalable Matrix Computations on Large Scale-Free Graphs Using 2D Graph Partitioning.
Abstract not provided.
Boman, Erik G.↗
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Where Lower Calcite Abundance Creates More Alteration: Enhanced Rock Matrix Diffusivity Induced by Preferential Dissolution [Where Lower Calcite Abundance Creates More Alteration: Enhanced Rock Matrix Diffusivity Induced by Preferential Carbonate Dissolution]
Fractured rocks are essential for flow, solute transport and energy production in geosystems. Existing studies on mineral reactions in fractured rocks mostly consider single mineral systems where reactions occur at the fracture wall without changing rock matrix properties. This work presents multicomponent reactive transport numerical experiments in a fractured rock from the Brady’s field, a geothermal reservoir at a depth of 1,396 m in the Hot Springs Mountains, Nevada. Initial porosity, permeability, mineral composition (quartz, clay, and calcite), and fracture geometry are based on microscopy characterization and X-ray tomography. The model was calibrated using a CO 2 -saturated water flooding experiment. Three numerical experiments were carried out with the same initial physical properties however different calcite content. Although total dissolved masses are similar among the three cases, abundant calcite (50% (v/v), calcite50) leads to a localized, thick zone of large porosity increase while low calcite content (10% (v/v), calcite10) creates an extended and narrow zone of small porosity increase resulting in surprisingly larger change in effective transport property. After 300 days of dissolution, effective matrix diffusion coefficients increase by 9.9 and 19.6 times in calcite50 and calcite10, respectively, inducing corresponding 2.1 and 3.2 times rise in the slopes of power law tailing, a measure of transport properties. This counterintuitive results suggest that lower abundance of reactive minerals leads to greater alteration in the fractured media. Detailed analysis show that the effective rates of the fast-dissolving calcite are limited by diffusive transport in the altered matrix and the shape of the altered zone. In contrast, the while effective dissolution of slow-dissolving quartz depends on effective diffusion within the entire rock matrix. Calcite dissolution only occurs at the thin altered–unaltered matrix interface of tens of micrometers thickness occupying less than 1% of the total calcite content. In contrast, all quartz are effectively dissolving. Furthermore, this work highlights the importance of mineralogical complexity in determining mineral dissolution and rock matrix property evolution.
58 GEOSCIENCES↗
Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs
In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S –1 . This factorization of S –1 , written as ZZT = S –1 , is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix–matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.
36 MATERIALS SCIENCE↗
Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach
To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Geometry of matrix product states: Metric, parallel transport, and curvature
We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold, which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Communication-Avoiding Parallel Sparse-Dense Matrix-Matrix Multiplication
Multiplication of a sparse matrix with a dense matrix is a building block of an increasing number of applications in many areas such as machine learning and graph algorithms. However, most previous work on parallel matrix multiplication considered only both dense or both sparse matrix operands. This paper analyzes the communication lower bounds and compares the communication costs of various classic parallel algorithms in the context of sparse-dense matrix-matrix multiplication. We also present new communication-avoiding algorithms based on a 1D decomposition, called 1.5D, which - while suboptimal in dense-dense and sparse-sparse cases - outperform the 2D and 3D variants both theoretically and in practice for sparse-dense multiplication. Our analysis separates one-time costs from per iteration costs in an iterative machine learning context. Experiments demonstrate speedups up to 100x over a baseline 3D SUMMA implementation and show parallel scaling over 10 thousand cores.
Koanantakool, Penporn↗
Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.
97 MATHEMATICS AND COMPUTING↗
Technique for information retrieval using enhanced latent semantic analysis generating rank approximation matrix by factorizing the weighted morpheme-by-document matrix
A technique for information retrieval includes parsing a corpus to identify a number of wordform instances within each document of the corpus. A weighted morpheme-by-document matrix is generated based at least in part on the number of wordform instances within each document of the corpus and based at least in part on a weighting function. The weighted morpheme-by-document matrix separately enumerates instances of stems and affixes. Additionally or alternatively, a term-by-term alignment matrix may be generated based at least in part on the number of wordform instances within each document of the corpus. At least one lower rank approximation matrix is generated by factorizing the weighted morpheme-by-document matrix and/or the term-by-term alignment matrix.
97 MATHEMATICS AND COMPUTING↗
Unitarity and the Holographic S-Matrix
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators O{sub 1} and O{sub 2} to extract the contribution of an individual primary O{sub {Delta},{ell}} in their OPE. This provides a method for isolating the contribution of specific conformal blocks which we use to prove an important relation between certain conformal block coefficients and anomalous dimensions. These techniques make essential use of the simplifications that occur when CFT correlators are expressed in terms of a Mellin amplitude.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Integrin nanoclusters can bridge thin matrix fibres to form cell–matrix adhesions
Integrin-mediated cell-matrix adhesions are key to sensing the geometry and rigidity of extracellular environments and influence vital cellular processes. In vivo, the extracellular matrix is composed of fibrous arrays. To understand the fibre geometries that are required for adhesion formation, we patterned nanolines of various line widths and arrangements in single, crossing or paired arrays with the integrin-binding peptide Arg-Gly-Asp. Single thin lines (width ≤ 30 nm) did not support cell spreading or formation of focal adhesions, despite the presence of a high density of Arg-Gly-Asp, but wide lines (>40 nm) did. Using super-resolution microscopy, we observed stable, dense integrin clusters formed on parallel (within 110 nm) or crossing thin lines (mimicking a matrix mesh) similar to those on continuous substrates. These dense clusters bridged the line pairs by recruiting activated but unliganded integrins, as verified by integrin mutants unable to bind ligands that coclustered with ligand-bound integrins when present in an active extended conformation. Furthermore, in a fibrous extracellular matrix mesh, stable integrin nano-clusters bridge between thin (≤ 30 nm) matrix fibres and bring about downstream consequences of cell motility and growth.
36 MATERIALS SCIENCE↗
Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication
The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computation to improve application-specific algorithms for multiplying sparse matrices.
97 MATHEMATICS AND COMPUTING↗
Mechanical behaviors of ceramic matrix composites with matrix cracking and fiber debonding
The purpose of this paper is to summarize the current research of the authors on the mechanical behaviors of ceramic matrix composites, including (1) the stress distributions in a composite with matrix cracking and interfacial debonding, (2) the critical strain for matrix cracking, and (3) the effects of fiber/matrix debonding and thermal residual stresses on the critical strain. The stress fields in both bonded and debonded regions are evaluated by taking into account thermal effects. An energy balance approach is followed to determine the critical strain for matrix cracking. From the general equation of the critical strain for matrix cracking, close form solutions have been obtained for two limiting cases: perfect bonding and complete debonding. Numerical solutions are given for the cases of partial fiber debonding and nonzero debonding energy. It is found that thermal residual stresses and the debonding energy have significant effects on the critical strain.
Kuo, Wen-Shyong↗
High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.
Goldberg, Robert K.↗
Ceramic matrix composite component and process of producing a ceramic matrix composite component
A process of producing a ceramic matrix composite component. The process includes positioning core plies on a mandrel. At least partially rigidizing the core plies to form a preform ceramic matrix composite arrangement defining a tip cavity and a hollow region. Ceramic matrix composite tip plies are positioned on the preform ceramic matrix composite arrangement and within the tip cavity. The ceramic matrix composite tip plies are densified to form a tip region of the composite component.
36 MATERIALS SCIENCE↗
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix
It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Performance optimization, modeling and analysis of sparse matrix-matrix products on multi-core and many-core processors
Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. In this work, we firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We examine their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. We build the performance model for hash-table and heap-based algorithms, which supports the recipe. A critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix. Finally, we integrate our implementations into a large-scale protein clustering code named HipMCL, accelerating its SpGEMM kernel by up to 10X and achieving an overall performance boost for the whole HipMCL application by 2.6X.
97 MATHEMATICS AND COMPUTING↗
Baryon number violation: from nuclear matrix elements to BSM physics
Processes that violate baryon number, most notably proton decay and $n\bar{n}$ transitions, are promising probes of physics beyond the Standard Model (BSM) needed to understand the lack of antimatter in the Universe. To interpret current and forthcoming experimental limits, theory input from nuclear matrix elements to UV complete models enters. Thus, an interplay of experiment, effective field theory, lattice QCD, and BSM model building is required to develop strategies to accurately extract information from current and future data and maximize the impact and sensitivity of next-generation experiments. Here, we briefly summarize the main results and discussions from the workshop ‘INT-25-91W: Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics,’ held at the Institute for Nuclear Theory, University of Washington, Seattle, WA, 13–17 January 2025.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗