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Everett Miller
Everett Miller


3.1 Find the Vertex of y = -16x2+116x+75Parabolas have a highest or a lowest point called the Vertex . Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting "y" because the coefficient of the first term, -16 , is negative (smaller than zero). Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.6250 Plugging into the parabola formula 3.6250 for x we can calculate the y -coordinate : y = -16.0 * 3.62 * 3.62 + 116.0 * 3.62 + 75.0 or y = 285.250


Genome sequence analysis has enabled significant advancements in medical and scientific areas such as personalized medicine, outbreak tracing, and the understanding of evolution. Unfortunately, it is currently bottlenecked by the computational power and memory bandwidth limitations of existing systems, as many of the steps in genome sequence analysis must process a large amount of data. A major contributor to this bottleneck is approximate string matching (ASM). We propose GenASM, the first ASM acceleration framework for genome sequence analysis. We modify the underlying ASM algorithm (Bitap) to significantly increase its parallelism and reduce its memory footprint, and we design the first hardware accelerator for Bitap. Our hardware accelerator consists of specialized compute units and on-chip SRAMs that are designed to match the rate of computation with memory capacity and bandwidth. We demonstrate that GenASM is a flexible, high-performance, and low-power framework, which provides significant performance and power benefits for three different use cases in genome sequence analysis: 1) GenASM accelerates read alignment for both long reads and short reads. For long reads, GenASM outperforms state-of-the-art software and hardware accelerators by 116x and 3.9x, respectively, while consuming 37x and 2.7x less power. For short reads, GenASM outperforms state-of-the-art software and hardware accelerators by 111x and 1.9x. 2) GenASM accelerates pre-alignment filtering for short reads, with 3.7x the performance of a state-of-the-art pre-alignment filter, while consuming 1.7x less power and significantly improving the filtering accuracy. 3) GenASM accelerates edit distance calculation, with 22-12501x and 9.3-400x speedups over the state-of-the-art software library and FPGA-based accelerator, respectively, while consuming 548-582x and 67x less power. 041b061a72


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