In this white paper, the warm water direct liquid cooling solution implementation in the CCS cluster solution is described. First, literature review of a range of direct liquid cooling solutions implemented in various competing vendors and their pros and cons are briefly presented. Design choices of datacenter cooling water distribution mechanisms (single loop vs primary/secondary loops), types...

abstract This note is concerned with the accuracy of the solution of nearly uncoupled Markov chains by a direct method based on the LU decomposition. It is shown that plain Gaussian elimination may fail in the presence of rounding errors. A modiication of Gaussian elimination with diagonal pivoting as well as corrections of small pivots by sums of oo-diagonal elements in the pivoting columns is...

We propose a novel solution for reconstructing planar surface patches. The theoretical foundation relies on variational calculus, which yields a closed form solution for the normal and distance of a 3D planar surface patch, when an affine transformation is known between the corresponding image region pairs. Although we apply the proposed method to projective cameras, the theoretical derivation ...

Key Laboratories of Bioorganic Chemistry and Molecular Engineering and of Polymer Chemistry and Physics of Ministry of Education, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry, Peking UniVersity, Beijing 100871, China, and Institute of Polymer Optoelectronic Materials and DeVices, South China UniVersity of Technology, and Key Lab of Specially...

In this paper, we present a direct solution method based neural network for image compression. The proposed technique includes steps to break down large images into smaller windows and to eliminate redundant information. Furthermore, the technique employs a neural network trained by a non-iterative, direct solution method. An error backpropagation algorithm is also used to train the neural netw...

The perspective-three-point problem (P3P) is a classical problem in computer vision. The existing direct solutions of P3P have at least 3 limitations: (1) the numerical instability when using different vertex permutations, (2) the degeneration in the geometric singularity case, and (3) the dependence on particular equation solvers. A new direct solution of P3P is presented to deal with these li...

A standard technique for solving three-dimensional momentum-space integral equations in scattering theory is their transformation into one-dimensional equations in terms of partial waves. However, for some scattering systems where a large number of partial waves contribute this technique is not efficient. In this work we explore the alternative approach of solving these equations directly witho...

We explore a method to compute invariant tori in phase space for classical non-integrable Hamiltonian systems. The procedure is to solve the HamiltonJacobi equation stated as a system of equations for Fourier coefficients of the generating function. The system is truncated to a finite number of Fourier modes and solved numerically by Newton’s method. The resulting canonical transformation serve...

The efficient solution of large systems of linear equations represented by sparse matrices appears in many tasks. LU factorization followed by backward and forward substitutions is widely used for this purpose. Parallel implementations of this computation-intensive process are limited primarily to supercomputers. New generations of Field-Programmable Gate Array (FPGA) technologies enable the im...

A general method for solving surface structures in three dimensions using surface x-ray-diffraction data coupled with direct methods is outlined. The method exploits the existence of a support constraint normal to the surface, and couples the concepts of projections, operators, and sets used in the image reconstruction literature with statistical operators used in direct methods. The approach p...