(a) Find the fuzzy Cartesian product P = V x I. Now let us define a fuzzy set for the cost C, in dollars, of a transistor, for example, 0.4 0.8 0.5 0.6 0.7 (b) Using a fuzzy Cartesian product, find T =I x C. What would this relation, T, represent physically? (c) Using max-min composition, find E= PoT. What would this relation, E, represent physically? (d) Using max-product composition, find E = PoT.
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- 5.2.2 The Van der Pol oscillator The Van der Pol oscillator is a nonlinear dynamical system with many applications, e.g., in physics, biology, sociology and economics. It is a non-conservative oscillator with nonlinear damping, modelled by the differential equation x” − µ(1 − x²)x′ + x = 0, where the parameter μ measures the strength of the nonlinear damping. (5.9) (1) Rewrite Equation (5.9) as a system of two first-order ODEs for x and x'. Then, write a Python function vdp(x) which returns the vector f(x), as defined in (5.1), for the Van der Pol system. Here, x must be an array of "shape" [1,2]. (2) Solve the Van der Pol system with µ = 1/2, using your Python functions rk4 and vdp, for t = [0, 30], starting with initial conditions (i) x(0) = x'(0) = 0.1; and (ii) x(0) = −2,x'(0) = 2. (You should fix a suitable step size, h.) Then, plot time series, x(t), of the solutions (i) and (ii) in one figure, and plot phase portraits, (x(t), y(t)), for the two solutions, in another figure.…Plot the orbit in 3D using a suitably dimensioned sphere for the Earth. [6]: # YOUR CODE HERE raise NotImplementedError() Not Implemented Error Cell In [6], line 2 1 # YOUR CODE HERE ----> 2 raise NotImplementedError() Not ImplementedError: Problem 1.6 Plot the Specific Energies (i.e., all three Kinetic, Potential and Total Energy) in the same plot as a function of time. The x-axis must show time (in hours) and y axis must show the Energy (in km² /s²). [7] # YOUR CODE HERE Traceback (most recent call last) raise NotImplementedError()Page There is a famous railway station in PopPush City. Country there is incredibly hilly. The station was built in last century. Unfortunately, funds wwere extremely limited that time. It was possible to establish only a surface track. Moreover, it turned out that the station could be only a dead-end one (see picture) and due to lack of available space it could have only one track. 5, 4, 3, 2, 1 1, 2, 3, 4, 5 Station The local tradition is that every train arriving from the direction A continues in the direction B with coaches reorganized in some way. • Assume that the train arriving from the direction A has NS 1000 coaches numbered in increasing order 1, 2, . N. • The chieffor train reorganizations must know whether it is possible to marshal coaches continuing in the direction B so that their order will be a, a2. . aN. Help him and write a program that decides whether it is possible to get the required order of coaches. • You can assume that single coaches can be disconnected from…
- The language must be in python. Neural Network Units two training examples:Example 1: [0.9, 10.0, 3.1, 1]Example 2: [0.9, 2.1, 3.7, 1] Note that you don't have to explicitly include a threshold or bias since the examples include a last element of 1 which means that the last weight effectively operates as a threshold. Create a single ReLU unit and provide the outputs for those examples. Calculate the derivative of the ReLU with respect to net input for both examplesECE 436 Artificial Intelligence - Q9 Y={0/165, 1/175, 0.5/180, 0.25/182.5, 0/185, 0/190}. Given X={0/165, 0/175, 0/180, 0.25/182.5, 0.5/185, 1/190}, Then, X n Y = (0/165, 0/175, 0/180, 0.25/182.5, 0/185, 0/190} O (0/165, 1/175, 0.5/180, 0.25/182.5, 0.5/185, 1/190}TM M = (Q, E, I, 6, 90, 9a, qr), where Q = {90, 91, 92, 9a, 9r}, Σ = {0, 1}, r = {0, 1, L}, and 8 is: 8(qo, U) = (qr, U, R) 8(90, 0) = 8(go, 1) (91, 0, R) (qo, 1, R) = 8(g1, L) = (ga, U, R) 8(91,0) = (91, 0, R) 8(91, 1) = (92, 1, R) = (92, U, R) 8(92, U) 8(92, 0) = (90, 0, R) 8(92, 1) = (92, 1, R) i. Prove that M is NOT a decider. ii. Mathematically describe the language A that M recognises. Prove that A ≤ L(M). iii. Prove A = L(M). iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]
- The language for coding must be in python Neural Network Units Implement a single sigmoid neural network unit with weights of [-1.2, -1.1, 3.3, -2.1] Calculate the outputs for two training examples:Example 1: [0.9, 10.0, 3.1, 1]Example 2: [0.9, 2.1, 3.7, 1] Note that you don't have to explicitly include a threshold or bias since the examples include a last element of 1 which means that the last weight effectively operates as a threshold. Assuming that a sigmoid unit response >0.5 denotes a positive class and <0.5 is negative class, is example 1 positive or negative? is example 2 positive or negative? Create a single ReLU unit and provide the outputs for those examples. Calculate the derivative of the sigmoid with respect to net input for both examples Calculate the derivative of the ReLU with respect to net input for both examplesAbstract: the main purpose of this experiment is build real time system using PPI 8255 to control devices connected to. Problem description: assume that there are two devices are connected to port A and two sensors are connected to port B of PPI 8255. They work according to the following table Sensors (S1S2) Devices (DID2) 00 01 01 10 10 11 11 00 Write a program to control these two devices according to the values of sensors.Consider the statements below and choose the corect option T: Mathematical functions are used to draw an image in random scan system. Il: Screen points/pixels are used to draw an image in raster scan system. Both are false I is false and II is true I is true and Il is false Both are true
- Translate the following specifications into English where F(p) is“Printer p is outof service”, B(p) is “Printer p is busy”, L(j) is “Print job j is lost”, and Q(j) is “Print job j isqueued”. a) ∃p(F(p) ∧ B(p)) → ∃jL(j)b) ∀pB(p) → ∃jQ(j)c) ∃j(Q(j) ∧ L(j)) → ∃pF(p)d) (∀pB(p) ∧ ∀jQ(j)) → ∃jL(j)Question 3: On planet Z, a hybrid cooling system is to be built consisting of a cooling fan unit (F) and an air conditioning unit (C). You need to create a system that controls these two features depending on certain conditions. Assume that there are four sensors: Input (4 variables) T= 1 indicates that the temperature is high, 0 if not H= 1 indicates it is humid, O if not D= 1 indicates that it is day, O if night w = 1 indicates it is winter, O if not [Note: You need to maintain the input order as THDW with T as the MSB and W as the LSB] Output (2 variables) F = 1 indicates that the cooling fan unit is ON C= 1 indicates that the Air Conditioning Unit is ON. You have to consider the following conditions: The operation of the Air Conditioner requires a high temperature but the cooling fan works at all temperatures. The Air Conditioner will ONLY work at night and the cooling fan will work during both day and night.A produce dealer has a warehouse that stores a variety of fruits. He wants a machine capable of sorting the fruit according to the type. There is a conveyor belt on which the fruit is loaded. It is then passed through a set of sensors which measure 3 properties of the fruit: shape, texture, and weight. The sensor system is somehow rather primitive: • Shape sensor : -1 if the fruit is round and 1 if it is more elliptical• Texture sensor : -1 if the surface is smooth, 1 if it is rough• Weight sensor : -1 if the fruit is > 500g, 1 if is < 500g The sensor output will then be input to a Neural Networks based classifying system. As an AI Engineer you are supposed to design (draw the architecture and determine the optimal weight W and bias b) a simple neural network (could be a single perceptron) that can be used to recognize the fruit so that it can be directed to the correct storage bin. As a startup case, the simple network will only be used for two type of fruit i.e. banana and…