Answer the following questions about Monte Carlo problems and pseudo-randomnumber generators (PRNGs). Pick the best answer for each item.A PRNG will always eventually repeatitself - this is calledA method of creating PRNG for parallelapplications is for each task to takeonly every Pth random number (P is thenumber of processors).A PRNG that has only one work ofstate isA matrix whose diagonal elements srean order of magnitude higher than therestWe want to be able to rerun with theexact same random numbers - we careaboutThe theory behind Monte CarlomethodsReproducibility[Choose ][Choose]Linear CongruentialReproducibilityDiagonally DominantLeapfrog MethodUniform distributioncyclesLagged FibonaciMean Value TheoremSequence Splitting MethodManager Worker MethodUncorrelated[Choose][Choose]

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A PRNG will always eventually repeat itself - this is called A method of creating PRNG for parallel applications is for each task to take only every Pth random number (P is the number of processors). A PRNG that has only one work of state is

A PRNG will always eventually repeat itself - this is called A method of creating PRNG for parallel applications is for each task to take only every Pth random number (P is the number of processors). A PRNG that has only one work of state is

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Computer Science Given an N x N matrix M with binary entries i.e every entry is either 1 or 0. You are told that every row and every column is sorted in increasing order. You are required to output a pair (i,j) with 1 <= i and j <= n corresponding to the entry of the matrix satisfying Mij = 1 and Mrs = 0 for all 1 <= r <= i and 1 <= s <= j except for Mij Informally this includes the entry of M = 1 and is closest to the top left corner. for example: M = [ 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1] output is (2,3) or (1,4) M = [ 0 1 1 1 1 1 1 1 1] output could be (1,2) or (2,1) Design a divide and conquer algorithm, explain correctness and runtime of the algorithm.
Matrix multiplication plays an important role in a number of applications. Two matrices can only be multiplied if the number of columns of the fi rst matrix is equal to the number of rows in the second.Let’s assume we have an m × n matrix A and we want to multiply it by an n × p matrix B. We can express their product as an m × p matrix denoted by AB (or A ⋅ B). If we assign C = AB, and ci,j denotes the entry in C at position (i, j), then for each element i and j with 1 ≤ i ≤ m and 1 ≤ j ≤ p. Now we want to see if we can parallelize the computation of C. Assume that matrices are laid out in memory sequentially as follows: a1,1, a2,1, a3,1, a4,1, ..., etc.Assume that we are going to compute C on both a single core shared memory machine and a 4-core shared-memory machine. Compute the speedup we would expect to obtain on the 4-core machine, ignoring any memory issues.Repeat above Exercise, assuming that updates to C incur a cache miss due to false sharing when consecutive elements are in a…
Solving with Matlab
Recall that np.dot (a,b) performs a matrix multiplication on a and b, whereas ab performs an element-wise multiplication. Consider the two following random arrays "a" and "b": a = np.random.randn (12288, 150) a.shape (12288, 150) b = np.random.randn(150, 45) b.shape= (150, 45) c = np.dot (a, b) What is the shape of c?
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Python code for this one, thanks
The method to compress an image in image processing is using convolution matrix where the number of outputs is reduced by replacing the matrix multiplication with much smaller kernel matrix. This is illustrated on the figure below. In this example a black and white photograph is scanned as a rectangular array of pixels and then stored as image matrix on the left by assigning each pixel a numerical value in accordance with its gray level, (0 = white to 255 = black), then the entries in the matrix are integers between O and 255.Then multiplication is employed with much smaller kernel matrix in the middle. 0|0 21 00 o 106 85 71 1 250 231 127 63 1 250 252 250 209 56 1 250 252 250 250 83 Kernel 0 0 0 Feature map Image Boxes in red and blue frames indicate how the upper left element is formed by applying the kernel to the corresponding upper left region of the input matrix. The elements of much smaller "feature map" matrix on the right can be calculated from: 3.
solve with MatLab
In MATLAB
The goal of this problem is to walk from cell (0, 0) to cell (m, n) of a two-dimensional array. Each step must be either to the right or downward. So you can step from cell (1, 1) to cell (1, 2) or (2, 1). but not from (1, 1) to (0, 1) or (1,0). You are given a toll matrix, where each cell contains a toll that must be paid upon entry into that cell. The goal is to make it from cell (0, 0) to cell (m, n) while paying the smallest possible total toll. Does a greedy algorithm work? Think it out. Write a dynamic programming algorithm that finds the minimum possible total toll. It does not need to do reconstruction and say how to achieve that total toll.
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