Format Abstraction for Sparse Tensor Algebra Compilers

This paper shows how to build a sparse tensor algebra compiler that is agnostic to tensor formats (data layouts). We develop an interface that describes formats in terms of their capabilities and properties, and show how to build a modular code generator where new formats can be added as plugins. We then describe six implementations of the interface that compose to form the dense, CSR/CSF, COO, DIA, ELL, and HASH tensor formats and countless variants thereof. With these implementations at hand, our code generator can generate code to compute any tensor algebra expression on any combination of the aforementioned formats. To demonstrate our technique, we have implemented it in the taco tensor algebra compiler. Our modular code generator design makes it simple to add support for new tensor formats, and the performance of the generated code is competitive with hand-optimized implementations. Furthermore, by extending taco to support a wider range of formats specialized for different application and data characteristics, we can improve end-user application performance. For example, if input data is provided in the COO format, our technique allows computing a single matrix-vector multiplication directly with the data in COO, which is up to 3.6$\times$ faster than by first converting the data to CSR.Comment: Presented at OOPSLA 201

Sparse Tensor Transpositions

We present a new algorithm for transposing sparse tensors called Quesadilla. The algorithm converts the sparse tensor data structure to a list of coordinates and sorts it with a fast multi-pass radix algorithm that exploits knowledge of the requested transposition and the tensors input partial coordinate ordering to provably minimize the number of parallel partial sorting passes. We evaluate both a serial and a parallel implementation of Quesadilla on a set of 19 tensors from the FROSTT collection, a set of tensors taken from scientific and data analytic applications. We compare Quesadilla and a generalization, Top-2-sadilla to several state of the art approaches, including the tensor transposition routine used in the SPLATT tensor factorization library. In serial tests, Quesadilla was the best strategy for 60% of all tensor and transposition combinations and improved over SPLATT by at least 19% in half of the combinations. In parallel tests, at least one of Quesadilla or Top-2-sadilla was the best strategy for 52% of all tensor and transposition combinations.Comment: This work will be the subject of a brief announcement at the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '20

Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces

Universal bi-Hamiltonian hierarchies of group-invariant (multicomponent) soliton equations are derived from non-stretching geometric curve flows \map(t,x) in Riemannian symmetric spaces $M=G/H$, including compact semisimple Lie groups $M=K$ for $G=K\times K$, $H={\rm diag} G$. The derivation of these soliton hierarchies utilizes a moving parallel frame and connection 1-form along the curve flows, related to the Klein geometry of the Lie group $G\supset H$ where $H$ is the local frame structure group. The soliton equations arise in explicit form from the induced flow on the frame components of the principal normal vector N=\covder{x}\mapder{x} along each curve, and display invariance under the equivalence subgroup in $H$ that preserves the unit tangent vector T=\mapder{x} in the framing at any point $x$ on a curve. Their bi-Hamiltonian integrability structure is shown to be geometrically encoded in the Cartan structure equations for torsion and curvature of the parallel frame and its connection 1-form in the tangent space T_\map M of the curve flow. The hierarchies include group-invariant versions of sine-Gordon (SG) and modified Korteweg-de Vries (mKdV) soliton equations that are found to be universally given by curve flows describing non-stretching wave maps and mKdV analogs of non-stretching Schrodinger maps on $G/H$. These results provide a geometric interpretation and explicit bi-Hamiltonian formulation for many known multicomponent soliton equations. Moreover, all examples of group-invariant (multicomponent) soliton equations given by the present geometric framework can be constructed in an explicit fashion based on Cartan's classification of symmetric spaces.Comment: Published version, with a clarification to Theorem 4.5 and a correction to the Hamiltonian flow in Proposition 5.1

Force-insensitive optical cavity

We describe a rigidly-mounted optical cavity which is insensitive to inertial forces acting in any direction and to the compressive force used to constrain it. The design is based on a cubic geometry with four supports placed symmetrically about the optical axis in a tetrahedral configuration. To measure the inertial force sensitivity, a laser is locked to the cavity while it is inverted about three orthogonal axes. The maximum acceleration sensitivity is 2.5\times10^-11/g (where g=9.81 ms^-2), the lowest passive sensitivity to be reported for an optical cavity.Comment: 3 pages, 3 figures, journa

Health-related quality of life and depression among participants in the Sjögren's International Collaborative Clinical Alliance registry.

ObjectiveTo examine health-related quality of life (HRQoL) and depression among participants in an international Sjögren's syndrome (SS) registry, comparing those with and without SS.MethodsCross-sectional study of participants in the Sjögren's International Collaborative Clinical Alliance (SICCA) registry. The 2016 American College of Rheumatology/European League Against Rheumatism SS classification criteria were used to determine disease status. HRQoL was assessed using the Short Form 12, version 2 Health Survey to derive scores for physical component summary (PCS) and mental component summary (MCS). Depression was assessed using the 9-Item Patient Health Questionnaire. Multivariate linear and logistic regression analyses were performed to identify predictors of HRQoL and depression while controlling for potential confounders.ResultsAmong 2401 SICCA participants who had symptoms of dry eyes and dry mouth, 1051 had SS (44%) and 1350 did not (56%). After controlling for confounders, when compared with non-SS participants, those with SS had better PCS (p<0.001, β=2.43, 95% CI 1.57 to 3.29), MCS (p=0.002, β=1.37, 95% CI 0.50 to 2.23) and lower adjusted odds of depression (p<0.001, OR 0.67, 95% CI 0.55 to 0.81). Other significant predictors of HRQoL and depression included employment, country of residence and use of medication with anticholinergic effect or for management of SS-related signs and symptoms.ConclusionOur results suggest that among symptomatic patients, having a diagnosis of SS may be associated with better emotional and psychological well-being compared with patients without a diagnosis. Having a definitive diagnosis of SS may encourage patients to obtain a better understanding of their disease and have coping mechanisms in place to better manage their symptoms

Protein structure similarity from principle component correlation analysis

BACKGROUND: Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. Currently, the structural similarity between two proteins is measured by the root-mean-square-deviation (RMSD) in their best-superimposed atomic coordinates. RMSD is the golden rule of measuring structural similarity when the structures are nearly identical; it, however, fails to detect the higher order topological similarities in proteins evolved into different shapes. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities. RESULTS: We measure structural similarity between proteins by correlating the principle components of their secondary structure interaction matrix. In our approach, the Principle Component Correlation (PCC) analysis, a symmetric interaction matrix for a protein structure is constructed with relationship parameters between secondary elements that can take the form of distance, orientation, or other relevant structural invariants. When using a distance-based construction in the presence or absence of encoded N to C terminal sense, there are strong correlations between the principle components of interaction matrices of structurally or topologically similar proteins. CONCLUSION: The PCC method is extensively tested for protein structures that belong to the same topological class but are significantly different by RMSD measure. The PCC analysis can also differentiate proteins having similar shapes but different topological arrangements. Additionally, we demonstrate that when using two independently defined interaction matrices, comparison of their maximum eigenvalues can be highly effective in clustering structurally or topologically similar proteins. We believe that the PCC analysis of interaction matrix is highly flexible in adopting various structural parameters for protein structure comparison

Two-Point Focused Laser Differential Interferometry Second-Mode Measurements at Mach 6

A two-point focused laser differential interferometer (FLDI) is used to make measurements of density fluctuations on a 7 degree half-angle cone in a Mach 6 flow. The system was first characterized in the laboratory using laser induced breakdown to provide a well defined density fluctuation. The speed of the shock wave generated by the breakdown is verified using simultaneous high-speed schlieren. The FLDI system is then installed at the NASA Langley 20-Inch Mach 6 air tunnel to make measurements in the boundary layer of the 7 degree half-angle cone model and in the tunnel freestream for a unit Reynolds number range of 3.0 to 8.22 x 10(exp 6)/ft. Second-mode packets are visible in the spectra, with peak frequencies increasing linearly and peak amplitude increasing as a function of unit Reynolds number. The two-point measurement allows for the calculation of the second-mode wavepacket speeds, which propagate between 88% and 92% of the freestream velocity of the tunnel for all Reynolds numbers. The FLDI measurements are compared to surface-mounted fast-response pressure transducer measurements, where second-mode frequencies and wavepacket speeds are in good agreement

The Tensor Algebra Compiler

Tensor and linear algebra is pervasive in data analytics and the physical sciences. Often the tensors, matrices or even vectors are sparse. Computing expressions involving a mix of sparse and dense tensors, matrices and vectors requires writing kernels for every operation and combination of formats of interest. The number of possibilities is infinite, which makes it impossible to write library code for all. This problem cries out for a compiler approach. This paper presents a new technique that compiles compound tensor algebra expressions combined with descriptions of tensor formats into efficient loops. The technique is evaluated in a prototype compiler called taco, demonstrating competitive performance to best-in-class hand-written codes for tensor and matrix operations