We have the following two prototype vectors:i. Find and sketch a decision boundary for a perceptron network that will recognize these two vectors.ii. Find weights and bias that will produce the...
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We want to design a perceptron network to output a 1 when either of these two vectors are input to the network:and to output a -1 when either of the following vectors are input to the network:i....
Consider the classification problem defined below:i. Draw a diagram of the single-neuron perceptron you would use to solve this problem. How many inputs are required?ii. Draw a graph of the data...
Consider the following perceptron network.i. How many different classes can this network classify?ii. Draw a diagram illustrating the regions corresponding to each class. Label each region with the...
Consider the following prototype patterns.i. Find and sketch a decision boundary for a perceptron network that will recognize these two vectors.ii. Find weights and bias which will produce the...
In this chapter we have designed three different neural networks to distinguish between apples and oranges, based on three sensor measurements (shape, texture and weight). Suppose that we want to...
Consider the following neural network.Sketch the following responses (plot the indicated variable versus p for -3
Consider the following neuron.Sketch the neuron response (plot a versus p for -2
A two-layer neural network is to have four inputs and six outputs. The range of the outputs is to be continuous between 0 and 1. What can you tell about the network architecture? Specifically:i. How...
Given a two-input neuron with the following weight matrix and input vector: we would like to have an output of 0.5. Do you suppose that there is a combination of bias and transfer function that...
Consider a single-input neuron with a bias. We would like the output to be -1 for inputs less than 3 and +1 for inputs greater than or equal to 3.i. What kind of a transfer function is required? ii....
A single input neuron has a weight of 1.3 and a bias of 3.0. What possible kinds of transfer functions, from Table 2.1, could this neuron have, if its output is given below. In each case, give the...
Consider a Hopfield network, with the following weight and bias.i. The following input (initial condition) is applied to the network. Find the network response (show the network output at each...
A single-layer neural network is to have six inputs and two outputs. The outputs are to be limited to and continuous over the range 0 to 1. What can you tell about the network architecture?...
What is the output of the neuron of P2.1 if it has the following transfer functions?i. Hard limitii. Lineariii. Log-sigmoidP2.1The input to a single-input neuron is 2.0, its weight is 2.3 and its...
The input to a single-input neuron is 2.0, its weight is 2.3 and its bias is -3.i. What is the net input to the transfer function?ii. What is the neuron output?
1. Write a Java class that implements all the methods of the sorted map ADT by means of an (a,b) tree, where a and b are integer constants passed as parameters to a constructor. 2. Implement the...
1. Suppose that instead of having the node-search function f(d) = 1 in an order-d B-tree T, we have f(d) = log d. What does the asymptotic running time of performing a search in T now become?2....
1. Describe an efficient external-memory algorithm that determines whether an array of n integers contains a value occurring more than n/2 times.2. Consider the page caching strategy based on the...
Consider the page caching problem where the memory cache can hold m pages, and we are given a sequence P of n requests taken from a pool of m+1 possible pages. Describe the optimal strategy for the...
1. Describe how to use a B-tree to implement the Partition ADT (Section 14.7.3) so that the union and find operations each use at most O(logn/log B) disk transfers.2. Suppose we are given a sequence...
Another possible external-memory map implementation is to use a skip list, but to collect consecutive groups of O(B) nodes, in individual blocks, on any level in the skip list. In particular, we...
Given a two-input neuron with the following parameters: b = 1.2 W = [3 2] and p = [-5 6]T, calculate the neuron output for the following transfer functions:i. A symmetrical hard limit transfer...
Describe a modified version of the B-tree insertion algorithm so that each time we create an overflow because of a split of a node w, we redistribute keys among all of w’s siblings, so that each...
1. Describe an external-memory data structure to implement the stack ADT so that the total number of disk transfers needed to process a sequence of k push and pop operations is O(k/B).2. Describe an...
1. Draw the result of inserting, into an initially empty order-7 B-tree, entries with keys(4,40,23,50,11,34,62,78,66,22,90,59,25,72,64,77,39,12), in this order.2. Describe an efficient...
1. Describe, in detail, algorithms for adding an item to, or deleting an item from, an (a,b) tree.2. Suppose T is a multiway tree in which each internal node has at least five and at most eight...
Consider an initially empty memory cache consisting of four pages. What is the maximum number of page misses that the random algorithm incurs on the following page request sequence:...
1. Consider an initially empty memory cache consisting of four pages. How many page misses does the LRU algorithm incur on the following page request sequence: (2,3,4,1,2,5,1,3,5,4,1,2,3)?2....
Julia just bought a new computer that uses 64-bit integers to address memory cells. Argue why Julia will never in her life be able to upgrade the main memory of her computer so that it is the...
Write a program that builds the routing tables for the nodes in a computer network, based on shortest-path routing, where path distance is measured by hop count, that is, the number of edges in a...
One way to construct a maze starts with an n × n grid such that each grid cell is bounded by four unit-length walls. We then remove two boundary unit-length walls, to represent the start and finish....
1. Describe an external-memory version of the PositionalList ADT (Section 7.3), with block size B, such that an iteration of a list of length n is completed using O(n/B) transfers in the worst case,...
Perform an experimental comparison of two of the minimum spanning tree algorithms discussed in this chapter (Kruskal and Prim-Jarn´ık). Develop an extensive set of experiments to test the running...
Extend the class of Exercise P-14.75 to support the update methods of the graph ADT.Exercise P-14.75Implement the simplified graph ADT described in Exercise P-14.73, using the adjacency list...
Implement the simplified graph ADT described in Exercise P-14.73, using the adjacency list structureExercise P-14.73Use an adjacency matrix to implement a class supporting a simplified graph ADT...
Implement the simplified graph ADT described in Exercise P-14.73, using the edge list structure.Exercise P-14.73Use an adjacency matrix to implement a class supporting a simplified graph ADT that...
Use an adjacency matrix to implement a class supporting a simplified graph ADT that does not include update methods. Your class should include a constructor method that takes two collections—a...
Karen has a new way to do path compression in a tree-based union/find partition data structure starting at a position p. She puts all the positions that are on the path from p to the root in a set...
Suppose we are given a directed graph with n vertices, and let M be the n×n adjacency matrix corresponding to .a. Let the product of M with itself (M2) be defined, for 1 ≤ i, j ≤ n, as...
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