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At least 1,333 records · Page 74

QUBO formulations for training machine learning models

Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore’s law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

97 MATHEMATICS AND COMPUTING↗

Metastability, spectrum, and eigencurrents of the Lennard-Jones-38 network

We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure and Dynamics of Polysulfide Clusters in a Nonaqueous Solvent Mixture of 1,3-Dioxolane and 1,2-Dimethoxyethane

Molecular clustering and associated dynamic processes of lithium polysulfide species were unraveled using classical molecular dynamics and ab initio metadynamics calculations. The spectroscopic signatures of polysulfide clusters were analyzed using a multimodal analysis including experimental and computational nuclear magnetic resonance (NMR) and X-ray absorption spectroscopies. Lithium polysulfide solutes (Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 ) and their mixtures in a 1,3-dioxolane and 1,2-dimethoxyethane (DOL/DME) solvent undergo aggregation driven by intramolecular lithium–sulfur (Li–S) interactions, leading to distributions of cluster sizes, which could critically influence the functioning of lithium–sulfur batteries. Representative polysulfide clusters with systematic increases in molecular size were extracted from the classical molecular dynamics trajectories for subsequent structural and spectroscopic property calculations using density functional theory analysis. Structural analysis of these clusters reveals progressively decreasing solvent involvement in Li+ coordination varying from Li 2 S 4 to Li 2 S 8 , with more pronounced variation and changes in DME compared with those in DOL. These observations are reflected in the analysis of the experimental and theoretical 7 Li and 17 O NMR chemical shifts and pulsed field gradient-NMR diffusion measurements. A comparison of experimental and theoretical S K-edge X-ray absorption near edge spectra shows that relatively large lithium sulfide chain clusters are likely to occur in the DOL/DME-solvated lithium sulfide systems. Ab initio metadynamics simulations and NMR analysis indicate that Li + solvated by only the solvent can occur through Li + dissociation from sulfide chains. However, the occurrence of “sulfide-free” Li + is a minor mechanism compared with the dynamic aggregation and shuttling processes of polysulfide solvates in DOL/DME-based electrolytes of Li–S batteries. Overall, atomistic insights gained about clustering and lithium exchange dynamics will be critical for the predictive understanding of the polysulfide shuttling and nucleation process that dictates the Li–S battery performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Examination of the Performance of Parallel Calculation of the Radiation Integral on a Beowulf-Class Computer

This paper uses the parallel calculation of the radiation integral for examination of performance and compiler issues on a Beowulf-class computer. This type of computer, built from mass-market, commodity, off-the-shelf components, has limited communications performance and therefore also has a limited regime of codes for which it is suitable.

Beowulf cluster pile of PCs parallel computation p↗

CASM — A software package for first-principles based study of multicomponent crystalline solids

CASM is a software package that enables first-principles based studies of crystalline materials. It has been designed to treat coupled chemical, mechanical, vibrational, and magnetic degrees of freedom to determine ground state and finite temperature properties of crystals. The symmetry of the underlying parent crystal structure is used to enumerate perturbations of the parent crystal structure and generate derivative structures which can be input to first-principles calculations in order to explore the ground state energy landscape. CASM algorithmically constructs cluster expansions that fully couple discrete and continuous degrees of freedom, and generates highly efficient code to evaluate the cluster expansion basis functions. Widely used machine learning methods are integrated for fitting expansion coefficients to first-principle calculations. The fully parameterized cluster expansions can be combined with (kinetic) Monte Carlo methods to calculate finite temperature thermodynamic and kinetic properties. CASM Alloy Manager identifies distinct parent crystal structures in an alloy system, creating individual projects for each, and integrating the results. The integrated infrastructure facilitates the linkage between first-principles statistical mechanics predictions with higher length scale computational methods, such as phase field simulations. In conclusion, CASM projects are designed to be easy to share in repositories, to re-use, and to extend to include additional chemical species or types of degrees of freedom.

36 MATERIALS SCIENCE↗

Quasichemical analysis of the cluster-pair approximation for the thermodynamics of proton hydration

A theoretical analysis of the cluster-pair approximation (CPA) is presented based on the quasichemical theory of solutions. The sought single-ion hydration free energy of the proton includes an interfacial potential contribution by definition. It is shown, however, that the CPA involves an extra-thermodynamic assumption that does not guarantee uniform convergence to a bulk free energy value with increasing cluster size. A numerical test of the CPA is performed using the classical polarizable AMOEBA force field and supporting quantum chemical calculations. The enthalpy and free energy differences are computed for the kosmotropic Na{sup +}/F{sup −} ion pair in water clusters of size n = 5, 25, 105. Additional calculations are performed for the chaotropic Rb{sup +}/I{sup −} ion pair. A small shift in the proton hydration free energy and a larger shift in the hydration enthalpy, relative to the CPA values, are predicted based on the n = 105 simulations. The shifts arise from a combination of sequential hydration and interfacial potential effects. The AMOEBA and quantum chemical results suggest an electrochemical surface potential of water in the range −0.4 to −0.5 V. The physical content of single-ion free energies and implications for ion-water force field development are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development and optimization of SPECT gated blood pool cluster analysis for the prediction of CRT outcome

Purpose: Phase analysis of single photon emission computed tomography (SPECT) radionuclide angiography (RNA) has been investigated for its potential to predict the outcome of cardiac resynchronization therapy (CRT). However, phase analysis may be limited in its potential at predicting CRT outcome as valuable information may be lost by assuming that time-activity curves (TAC) follow a simple sinusoidal shape. A new method, cluster analysis, is proposed which directly evaluates the TACs and may lead to a better understanding of dyssynchrony patterns and CRT outcome. Cluster analysis algorithms were developed and optimized to maximize their ability to predict CRT response. Methods: About 49 patients (N = 27 ischemic etiology) received a SPECT RNA scan as well as positron emission tomography (PET) perfusion and viability scans prior to undergoing CRT. A semiautomated algorithm sampled the left ventricle wall to produce 568 TACs from SPECT RNA data. The TACs were then subjected to two different cluster analysis techniques, K-means, and normal average, where several input metrics were also varied to determine the optimal settings for the prediction of CRT outcome. Each TAC was assigned to a cluster group based on the comparison criteria and global and segmental cluster size and scores were used as measures of dyssynchrony and used to predict response to CRT. A repeated random twofold cross-validation technique was used to train and validate the cluster algorithm. Receiver operating characteristic (ROC) analysis was used to calculate the area under the curve (AUC) and compare results to those obtained for SPECT RNA phase analysis and PET scar size analysis methods. Results: Using the normal average cluster analysis approach, the septal wall produced statistically significant results for predicting CRT results in the ischemic population (ROC AUC = 0.73;p < 0.05 vs. equal chance ROC AUC = 0.50) with an optimal operating point of 71% sensitivity and 60% specificity. Cluster analysis results were similar to SPECT RNA phase analysis (ROC AUC = 0.78, p = 0.73 vs cluster AUC; sensitivity/specificity = 59%/89%) and PET scar size analysis (ROC AUC = 0.73, p = 1.0 vs cluster AUC; sensitivity/specificity = 76%/67%). Conclusions: A SPECT RNA cluster analysis algorithm was developed for the prediction of CRT outcome. Cluster analysis results produced results equivalent to those obtained from Fourier and scar analysis.

60 APPLIED LIFE SCIENCES↗

ACDT: Architected Composite Data Types Trading-in Unfettered Data Access for Improved Execution

With Exascale performance and its challenges in mind, one ubiquitous concern among architects is energy efficiency. Petascale systems projected to Exascale systems are unsustainable at current power consumption rates. One major contributor to system-wide power consumption is the number of memory operations leading to data movement and management techniques applied by the runtime system. To address this problem, we present the concept of the Architected Composite Data Types (ACDT) framework. The framework is made aware of data composites, assigning them a specific layout, transformations and operators. Data manipulation overhead is amortized over a larger number of elements and program performance and power efficiency can be significantly improved. We developed the fundamentals of an ACDT framework on a massively multithreaded adaptive runtime system geared towards Exascale clusters. Showcasing the capability of ACDT, we exercised the framework with two representative processing kernels - Matrix Vector Multiply and the Cholesky Decomposition – applied to sparse matrices. As transformation modules, we applied optimized compress/decompress engines and configured invariant operators for maximum energy/performance efficiency. Additionally, we explored two different approaches based on transformation opaqueness in relation to the application. Under the first approach, the application is agnostic to compression and decompression activity. Such approach entails minimal changes to the original application code, but leaves out potential applicationspecific optimizations. The second approach exposes the decompression process to the application, hereby exposing optimization opportunities that can only be exploited with application knowledge. The experimental results show that the two approaches have their strengths in HW and SW respectively, where the SW approach can yield performance and power improvements that are an order of magnitude better than ACDT-oblivious, hand-optimized implementations.We consider the ACDT runtime framework an important component of compute nodes that will lead towards power efficient Exascale clusters.

exascale↗

Hetero-site Double Core Ionization Energies with Sub-electronvolt Accuracy from Delta-Coupled-Cluster Calculations

Benchmark scalar-relativistic delta-coupled-cluster calculations of hetero-site double core ionization energies of small molecules containing second-row elements are reported. The present study has focused on the high-spin triplet components of two-site double core-ionized states, which are single reference in character and consistent with the use of standard coupledcluster methods. Contributions to computed double core ionization energies from electron-correlation and basis-set effects as well as corrections to the core-valence separation approximation have been analyzed. Furthermore, on the basis of systematic convergence of computational results with respect to these effects, delta-coupled-cluster calculations have been shown to be capable of providing accurate double core ionization energies with remaining errors estimated to be below 0.3 eV, and thus they are recommended for use to facilitate experimental studies of two-site double core-ionized states that are involved in X-ray pump/X-ray probe studies of electronic and molecular dynamics following inner shell ionization or excitation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

HiSpatialCluster: A novel high‐performance software tool for clustering massive spatial points

Abstract In the era of big data, spatial clustering is a very important means for geo‐data analysis. When clustering big geo‐data such as social media check‐in data, geotagged photos, and taxi trajectory points, traditional spatial clustering algorithms are facing more challenges. On the one hand, existing spatial clustering tools cannot support the clustering of massive point sets; on the other hand, there is no perfect solution for self‐adaptive spatial clustering. In order to achieve clustering of millions or even billions of points adaptively, a new spatial clustering tool—HiSpatialCluster—was proposed, in which the CFSFDP (clustering by fast search and finding density peaks) idea to find cluster centers and the DBSCAN (density‐based spatial clustering of applications with noise) idea of density‐connect filtering for classification are introduced. The tool’s source codes and other resources have been released on Github, and experimental evaluation was performed through clustering massive taxi trajectory points and Flickr geotagged photos in Beijing, China. The spatial clustering results were compared with those through K‐means and DBSCAN as well. As a spatial clustering tool, HiSpatialCluster is expected to play a fundamental role in big geo‐data research. First, this tool enables clustering adaptively on massive point datasets with uneven spatial density distribution. Second, the density‐connect filter method is applied to generate homogeneous analysis units from geotagged data. Third, the tool is accelerated by both parallel CPU and GPU computing so that millions or even billions of points can be clustered efficiently.

Chen, Yiran↗

Explicit correlation treatment of the potential energy surface of CO{sub 2} dimer

We present an extensive study of the four-dimensional potential energy surface (4D-PES) of the carbon dioxide dimer, (CO{sub 2}){sub 2}. This PES is developed over the set of intermolecular coordinates. The electronic computations are carried out at the explicitly correlated coupled cluster method with single, double, and perturbative triple excitations [CCSD(T)-F12] level of theory in connection with the augmented correlation-consistent aug-cc-pVTZ basis set. An analytic representation of the 4D-PES is derived. Our extensive calculations confirm that “Slipped Parallel” is the most stable form and that the T-shaped structure corresponds to a transition state. Later on, this PES is employed for the calculations of the vibrational energy levels of the dimer. Moreover, the temperature dependence of the dimer second virial coefficient and of the first spectral moment of rototranslational collision-induced absorption spectrum is derived. For both quantities, a good agreement is found between our values and the experimental data for a wide range of temperatures. This attests to the high quality of our PES. Generally, our PES and results can be used for modeling CO{sub 2} supercritical fluidity and examination of its role in planetary atmospheres. It can be also incorporated into dynamical computations of CO{sub 2} capture and sequestration. This allows deep understanding, at the microscopic level, of these processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

International Symposium on Remote Sensing of Environment, 9th, University of Michigan, Ann Arbor, Mich., April 15-19, 1974, Proceedings. Volumes 1, 2 & 3

The present work gathers together numerous papers describing the use of remote sensing technology for mapping, monitoring, and management of earth resources and man's environment. Studies using various types of sensing equipment are described, including multispectral scanners, radar imagery, spectrometers, lidar, and aerial photography, and both manual and computer-aided data processing techniques are described. Some of the topics covered include: estimation of population density in Tokyo districts from ERTS-1 data, a clustering algorithm for unsupervised crop classification, passive microwave sensing of moist soils, interactive computer processing for land use planning, the use of remote sensing to delineate floodplains, moisture detection from Skylab, scanning thermal plumes, electrically scanning microwave radiometers, oil slick detection by X-band synthetic aperture radar, and the use of space photos for search of oil and gas fields. Individual items are announced in this issue.

Source record↗

Galaxy clusters in the SDSS Stripe 82 based on photometric redshifts

Based on a recent photometric redshift galaxy catalogue, we have searched for galaxy clusters in the Stripe ~82 region of the Sloan Digital Sky Survey by applying the Adami & MAzure Cluster FInder (AMACFI). Extensive tests were made to fine-tune the AMACFI parameters and make the cluster detection as reliable as possible. The same method was applied to the Millennium simulation to estimate our detection efficiency and the approximate masses of the detected clusters. Considering all the cluster galaxies (i.e. within a 1 Mpc radius of the cluster to which they belong and with a photoz differing by less than 0.05 from that of the cluster), we stacked clusters in various redshift bins to derive colour-magnitude diagrams and galaxy luminosity functions (GLFs). For each galaxy with absolute magnitude brighter than -19.0 in the r band, we computed the disk and spheroid components by applying SExtractor, and by stacking clusters we determined how the disk-to-spheroid flux ratio varies with cluster redshift and mass. We also detected 3663 clusters in the redshift range 0.15 13 and a few 10 14 solar masses. Furthermore, by stacking the cluster galaxies in various redshift bins, we find a clear red sequence in the (g'-r') versus r' colour-magnitude diagrams, and the GLFs are typical of clusters, though with a possible contamination from field galaxies. The morphological analysis of the cluster galaxies shows that the fraction of late-type to early-type galaxies shows an increase with redshift (particularly in high mass clusters) and a decrease with detection level, i.e. cluster mass. From the properties of the cluster galaxies, the majority of the candidate clusters detected here seem to be real clusters with typical cluster properties.

79 ASTRONOMY AND ASTROPHYSICS↗

The benzene radical anion: A computationally demanding prototype for aromatic anions

The benzene radical anion is studied with ab initio coupled-cluster theory in large basis sets. Unlike the usual assumption, we find that, at the level of theory investigated, the minimum energy geometry is non-planar with tetrahedral distortion at two opposite carbon atoms. The anion is well known for its instability to auto-ionization which poses computational challenges to determine its properties. Despite the importance of the benzene radical anion, the considerable attention it has received in the literature so far has failed to address the details of its structure and shape-resonance character at a high level of theory. Here, we examine the dynamic Jahn-Teller effect and its impact on the anion potential energy surface. We find that a minimum energy geometry of C{sub 2} symmetry is located below one D{sub 2h} stationary point on a C{sub 2h} pseudo-rotation surface. The applicability of standard wave function methods to an unbound anion is assessed with the stabilization method. The isotropic hyperfine splitting constants (A{sub iso}) are computed and compared to data obtained from experimental electron spin resonance experiments. Satisfactory agreement with experiment is obtained with coupled-cluster theory and large basis sets such as cc-pCVQZ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Numerical investigation of vorticity and bubble clustering in an air entraining hydraulic jump

In this paper, a high resolution computational fluid dynamics model is used to simulate a steady air entraining laboratory scale hydraulic jump. A detailed examination of shear layer instabilities reveals the dynamic relationship between spanwise vortices, free surface fluctuations, and air–water spatial patterns. Spanwise vortices generated at the toe roll-up under a variable depth roller, creating large free surface fluctuations through high velocity water ejections in the roller. The mean shear layer elevation and free surface elevations periodically alternate between positive and negative correlation throughout the roller, driven by dynamic vortex transport. Vortices descending towards the lower wall create an upwelling of non-bubbly fluid into the shear layer that contributes to regions of decreased bubble concentration between vortices. The position of a strong shear layer at the location of maximum air entrainment, directly above the jump toe, leads to highly aerated vortices that influence bubble behavior. Bubbles breakup quickly after entrainment at the toe and bubble clusters are observed most frequently below and at the end of the roller where bubble breakup and energy dissipation are diminished. Finally, the dominant separation angle of clustered bubbles is independent of downstream distance and aligns closely with the direction of initial shear, suggesting bubble clustering is a remnant of bubble breakup.

13 HYDRO ENERGY↗

Hierarchical Truncations for Many-Body Expansion Potentials

In this work, a new strategy to truncate high-order terms in the many-body expansion (MBE) is proposed. This new approach, which we call a hierarchical many-body expansion (HMBE), is based on a hierarchical partition of the system into multitier fragments and can in principle be applied to any large molecular system. Numerical tests on a series of (H 2 O) 64 structures are presented, demonstrating satisfactory relative energies between the clusters and binding energies of individual clusters compared with full-cluster calculations, with significantly fewer high-order terms computed than conventional MBE. The hierarchical truncation can be augmented by certain many-body terms for fragments at the interface between the partitions (called “Schengen terms”) to further improve accuracy. This work establishes the HMBE scheme as a promising framework to model very large systems (e.g., proteins), which are naturally built on a hierarchical structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A comparison of thermal zone aggregation methods

The impact of increasing energy prices on building operation budgets has fueled demand for more energy-efficient structures. Existing building energy simulation tools generate an immense amount of data yet comparatively little knowledge. This paper introduces a framework that allows aggregation-based model reduction to operate on geometric building information models. The resulting aggregation sequence provides designers with faster simulations and affords insight into complex multi-scale thermal interactions. A comparison of the trade-off between simulation speed and accuracy for three hierarchical cluster partitioning methods concludes the discussion.

97 MATHEMATICS AND COMPUTING↗

Taking a quantum leap in time to solution for simulations of high-Tc superconductors

We present a new quantum cluster algorithm to simulate models of high-Tc superconductors. This algorithm extends current methods with continuous lattice self-energies, thereby removing artificial long-range correlations. This cures the fermionic sign problem in the underlying quantum Monte Carlo solver for large clusters and realistic values of the Coulomb interaction in the entire temperature range of interest. We find that the new algorithm improves time-to-solution by nine orders of magnitude compared to current, state of the art quantum cluster simulations. An efficient implementation is given, which ports to multi-core as well as hybrid CPU-GPU systems. Running on 18,600 nodes on ORNL's Titan supercomputer enables us to compute a converged value of Tc/t = 0.053 ± 0.0014 for a 28 site cluster in the 2D Hubbard model with U/t = 7 at 10% hole doping. Typical simulations on Titan sustain between 9.2 and 15.4 petaflops (double precision measured over full run), depending on configuration and parameters used.

42 ENGINEERING↗