An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations

An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a two-stage process in which the approximate solution is computed by existing numerical libraries and is then verified in a moderate computational time. The procedure returns intervals containing one exact eigenvalue in each interval. Test calculations were carried out for organic device materials, and the verification method confirms that all exact eigenvalues are well separated in the obtained intervals. This verification method will be integrated into EigenKernel (https://github.com/eigenkernel/), which is middleware for various parallel solvers for the generalized eigenvalue problem. Such an a posteriori verification method will be important in future computational science.Comment: 15 pages, 7 figure

DGEMM on Integer Matrix Multiplication Unit

Deep learning hardware achieves high throughput and low power consumption by reducing computing precision and specializing in matrix multiplication. For machine learning inference, fixed-point value computation is commonplace, where the input and output values and the model parameters are quantized. Thus, many processors are now equipped with fast integer matrix multiplication units (IMMU). It is of significant interest to find a way to harness these IMMUs to improve the performance of HPC applications while maintaining accuracy. We focus on the Ozaki scheme, which computes a high-precision matrix multiplication by using lower-precision computing units, and show the advantages and disadvantages of using IMMU. The experiment using integer Tensor Cores shows that we can compute double-precision matrix multiplication faster than cuBLAS and an existing Ozaki scheme implementation on FP16 Tensor Cores on NVIDIA consumer GPUs. Furthermore, we demonstrate accelerating a quantum circuit simulation by up to 4.33 while maintaining the FP64 accuracy

Functional characterization of olfactory receptors in three Dacini fruit flies (Diptera: Tephritidae) that respond to 1-nonanol analogs as components in the rectal glands

Dacini fruit flies (Tephritidae: Diptera), including destructive pest species, are strongly affected in their reproductive behaviors by semiochemicals. Notably, male lures have been developed for pest management e.g., aromatic compounds for the Oriental fruit fly Bactrocera dorsalis and the melon fruit fly Zeugodacus cucurbitae; terpenic α-ionone analogs for the solanaceous fruit fly, B. latifrons. Other than those specific male attractants, 1-nonanol analogs have been noticed as major aliphatic components in the male rectal gland, which is considered as a secretory organ of male sex pheromones. Although multiple semiochemicals associated with the life cycle of Dacini fruit flies have been identified, their behavioral role(s) and chemosensory mechanisms by which the perception occurs have not been fully elucidated. In this study, we conducted RNA sequencing analysis of the chemosensory organs of B. latifrons and Z. cucurbitae to identify the genes coding for chemosensory receptors. Because the skeletons of male attractants are different among Dacini fruit fly species, we analyzed phylogenetic relationships of candidate olfactory receptors (ORs) among the three species. We found that the OR phylogeny reflects the taxonomic relationships of the three species. We further characterized functional properties of OR74a in the three Dacini species to the 1-nonanol analogs related to components in the rectal glands. The three OR74a homologs responded to 1-nonanol, but their sensitivities differed from each other. The OR74a homologs identified from B. dorsalis and Z. cucurbitae responded significantly to 6-oxo-1-nonanol, but not to 1, 3-nonanediol and nonyl acetate, indicating similar binding properties of the homologous ORs

RNA interference in Lepidoptera: an overview of successful and unsuccessful studies and implications for experimental design

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Verified numerical computations for large-scale linear systems

summary:This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical solutions. We report the implementation of a verification method for large-scale linear systems and some numerical results using the RIKEN K computer and the Fujitsu PRIMEHPC FX100, which show the high performance of the verified numerical computations

Fast algorithms for floating-point interval matrix multiplication

AbstractWe discuss several methods for real interval matrix multiplication. First, earlier studies of fast algorithms for interval matrix multiplication are introduced: naive interval arithmetic, interval arithmetic by midpoint–radius form by Oishi–Rump and its fast variant by Ogita–Oishi. Next, three new and fast algorithms are developed. The proposed algorithms require one, two or three matrix products, respectively. The point is that our algorithms quickly predict which terms become dominant radii in interval computations. We propose a hybrid method to predict which algorithm is suitable for optimizing performance and width of the result. Numerical examples are presented to show the efficiency of the proposed algorithms

Summary of assembly results.

<p>Summary of assembly results.</p