To carry out this decomposition, we choose the diurnal component d and the weather-related component w i. The data is a set of frequency response measurements, with some measurement errors. The direction of each edge is the reference flow direction in the branch: You are welcome even encouraged to express your solution in terms of block matrices, formed from the given data. Plot the traffic level Ti t for each link on the same plot versus t, for each of the initial source rates. Show that the converse holds: We consider an integrated circuit IC that contains N cells or modules that are connected by K wires.

The goal in congestion control is to adjust the source rates in such a way that the traffic levels converge to the target levels if possible, or close to the target levels otherwise. For each symbol we give a set of symbols which are allowed to follow the symbol. If vj is negative, then metabolite Mi is produced at the rate 2 vj. If the matrix is onto, then so are the matrices A and B. Give the optimal transaction cost. Note that each component of f consists of a linear part, and also a quadratic part. We consider the usual estimation setup:

Here is the problem: When there is no right inverse with the given property, briefly explain why there is no such B.

You are welcome to use any of the operations, matrices, and vectors defined above in your solution e. The data is real, not that it would affect how you solve the problem. Draw a graph of this Markov chain as in the lecture notes.

Explain clearly how you solve the problem, as well as giving the specific answer. The total pollutant measured at spot i is the sum of the contributions from the n sources. Show that the set of points in Rn that are closer to a than b is a halfspace, i.

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In this data set the locations are arranged on a grid, with edges between adjacent locations except when there is an obstruction. Homeworj we do have some possible values of A, A 1. A simple example illustrating this notation is shown below. If your solution is valid provided some matrix is or some matrices are full rank, say so. We do have information about sums of some subsets of the numbers.

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If you find such a B, you must explain how you found it, and verify say, in matlab that it satisfies the required properties. In such cases, least-squares estimation of x works well. You will do that here. Each new line should start with the first letter not listed above. In this problem, we will consider model estimation for vehicles in a fleet. He does this by adjusting one lamp power at a solutiona and observing the resulting temperature profile.

Thus, the goal is to fill in or interpolate missing data in a 2D array an image, sayso the reconstructed array is as smooth as possible.

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After this processing, it is acted on by another channel, given by A. Now, finally, we come to the problem. Points will be deducted from correct answers that are substantially longer than they need to be, or are confusing to us. If you need to assume that one or more matrices that arise in your solution are invertible, homewkrk rank, etc.

The quantities B, b1. The vector x gives the solution of the norm minimization problem above. We should simultaneously estimate both the signal x and the interference v, based on y, using a standard least-squares method to estimate [xT v T ]T given y. Be sure to tell us which spot measurement you believe to be faulty, and what your guess of the emission rates is.

The fixed cells correspond to cells that are already placed, or external pins on the IC. Find the fastest way to get a message that starts at node 5, to node This signal is received at n base stations, located at locations s1. We will assign an orientation to each wire even though wires are physically symmetric.

If you can relate this condition to a simple one involving the lines, please do so. For each hlmework the following questions, you must give the answer explicitly for example, enclosed in a box. We start with the discrete-time model of the system used in lecture 1: The data file contains commented-out code for producing your plots.