Minimizing Communication in Linear Algebra

In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and extended it to the parallel case. In both cases the lower bound may be expressed as $\Omega$(#arithmetic operations / $\sqrt{M}$), where M is the size of the fast memory (or local memory in the parallel case). Here we generalize these results to a much wider variety of algorithms, including LU factorization, Cholesky factorization, $LDL^T$ factorization, QR factorization, algorithms for eigenvalues and singular values, i.e., essentially all direct methods of linear algebra. The proof works for dense or sparse matrices, and for sequential or parallel algorithms. In addition to lower bounds on the amount of data moved (bandwidth) we get lower bounds on the number of messages required to move it (latency). We illustrate how to extend our lower bound technique to compositions of linear algebra operations (like computing powers of a matrix), to decide whether it is enough to call a sequence of simpler optimal algorithms (like matrix multiplication) to minimize communication, or if we can do better. We give examples of both. We also show how to extend our lower bounds to certain graph theoretic problems. We point out recently designed algorithms for dense LU, Cholesky, QR, eigenvalue and the SVD problems that attain these lower bounds; implementations of LU and QR show large speedups over conventional linear algebra algorithms in standard libraries like LAPACK and ScaLAPACK. Many open problems remain.Comment: 27 pages, 2 table

Guidance, flight mechanics and trajectory optimization. Volume 6 - The N-body problem and special perturbation techniques

Analytical formulations and numerical integration methods for many body problem and special perturbative technique

Guidance, Flight Mechanics and Trajectory Optimization. Volume 15 - Application of Optimization Techniques

Pontryagin maximum principle, calculus of variations, and dynamic programming optimization techniques applied to trajectory and guidance problem

Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory (DFT) in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics, and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALBs requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic

Element orbitals for Kohn-Sham density functional theory

We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized around an element, which is a small part of the global domain containing multiple atoms. We demonstrate that the resulting basis set achieves meV accuracy for 3D densely packed systems with a small number of basis functions per atom. The procedure is applicable to insulating and metallic systems

Agricultural Field Robotics for Plant Data Acquisition

As the demand for food increases, we are presented with the challenge of producing food more efficiently. With the help of agricultural robots it will be possible to achieve greater yields by the application of seeds, fertilizers and chemicals in the most efficient way possible. With more advanced robotic systems accurate crop data can be obtained to improve farming products and techniques. Flex-Row is a medium sized agricultural robotic platform built for autonomously traversing through rough fields during multiple crop growing stages. This platform consisting of a flexible frame with the ability to vary both width and height will initially be implemented with sensors to monitor production plants throughout the growing season. Furthermore, the robot will perform low draft applications such as spraying. The intended goal for this project is to develop a tele-operated platform that can be automated in the future. Inter-Row is a much smaller robot designed specifically for plant data acquisition. Tall height is not needed as it individually scans each plant a few cm from the base of the plant. The robot will help eliminate the need for manual labor when counting number of plants per row, which is beneficial on a large acreage field. Advisor: Dr. Santosh K. Pitl

STAMP alters the growth of transformed and ovarian cancer cells

<p>Abstract</p> <p>Background</p> <p>Steroid receptors play major roles in the development, differentiation, and homeostasis of normal and malignant tissue. STAMP is a novel coregulator that not only enhances the ability of p160 coactivator family members TIF2 and SRC-1 to increase gene induction by many of the classical steroid receptors but also modulates the potency (or EC₅₀) of agonists and the partial agonist activity of antisteroids. These modulatory activities of STAMP are not limited to gene induction but are also observed for receptor-mediated gene repression. However, a physiological role for STAMP remains unclear.</p> <p>Methods</p> <p>The growth rate of HEK293 cells stably transfected with STAMP plasmid and overexpressing STAMP protein is found to be decreased. We therefore asked whether different STAMP levels might also contribute to the abnormal growth rates of cancer cells. Panels of different stage human cancers were screened for altered levels of STAMP mRNA. Those cancers with the greatest apparent changes in STAMP mRNA were pursued in cultured cancer cell lines.</p> <p>Results</p> <p>Higher levels of STAMP are shown to have the physiologically relevant function of reducing the growth of HEK293 cells but, unexpectedly, in a steroid-independent manner. STAMP expression was examined in eight human cancer panels. More extensive studies of ovarian cancers suggested the presence of higher levels of STAMP mRNA. Lowering STAMP mRNA levels with siRNAs alters the proliferation of several ovarian cancer tissue culture lines in a cell line-specific manner. This cell line-specific effect of STAMP is not unique and is also seen for the conventional effects of STAMP on glucocorticoid receptor-regulated gene transactivation.</p> <p>Conclusions</p> <p>This study indicates that a physiological function of STAMP in several settings is to modify cell growth rates in a manner that can be independent of steroid hormones. Studies with eleven tissue culture cell lines of ovarian cancer revealed a cell line-dependent effect of reduced STAMP mRNA on cell growth rates. This cell-line dependency is also seen for STAMP effects on glucocorticoid receptor-mediated transactivation. These preliminary findings suggest that further studies of STAMP in ovarian cancer may yield insight into ovarian cancer proliferation and may be useful in the development of biomarker panels.</p

STM study of multiband superconductivity in NbSe2 using a superconducting tip

We present a method to produce superconducting tips to be used in Scanning Tunneling Microscopy/Spectroscopy experiments. We use these tips to investigate the evolution of the electronic density of states of NbSe2 from 0.3K up to its critical temperature (7.2K). The use of a superconducting tip (Pb) as ounterelectrode provides an enhancement of the different features related to the DOS of NbSe2 in the tunneling conductance curves, along all the studied thermal range. The analysis of the experimental results gives evidence of the presence of multiband superconductivity in NbSe2.Comment: 5 pages, 5 figures, PDF fil

How young people from culturally and linguistically diverse backgrounds experience mental health: some insights for mental health nurses

This article reports on a part of a study which looked at the mental health of culturally and linguistically diverse (CALD) young people. The research sought to learn from CALD young people, carers, and service providers experiences relevant to the mental health of this group of young people. The ultimate goal was to gain insights that would inform government policy, service providers, ethnic communities and most importantly the young people themselves. To this end, qualitative interviews were undertaken with 123 CALD young people, 41 carers and 14 mental health service providers in Queensland, Western Australia and South Australia. Only one aspect of the study will be dealt with here, namely the views of the young CALD participants, which included risk factors, coping strategies and recommendations about how they could be supported in their struggle to maintain mental health. One of the most important findings of the study relates to the resilience of these young people and an insight into the strategies that they used to cope. The efforts of these young people to assist us in our attempts to understand their situation deserve to be rewarded by improvements in the care that we provide. To this end this article sets out to inform mental health nurses of the results of the study so that they will be in a position to better understand the needs and strengths of their CALD clients and be in a better position to work effectively with them