1. Show that the counting numbers defined by equation (11.26) are convex.
2. In this exercise, we will derive another message passing algorithm, called the two-way algorithm, for finding fixed points of region-based energy functionals; this algorithm allows for more general region graphs than in exercise. It uses two messages along each link r → r’: one from r to r’ and one from r’ to r. Consider a region-based free energy as in equation (11.27). For any region r, let pr = |Up(r)| be the number of regions that are directly upward of r. Assume that for any top region (so that pr = 0), we have that κr = 1. We now define qr = (1 − κr)/pregion, taking qr = 1 when pr = 0 (so that κr = 1, as per our assumption). Assume furthermore that qr ≠ 2, and define βr = 1/(2 − qr).
The following equalities define the messages and the potentials in this algorithm:
Note that the messages 
are as we would expect: the message sent from r to r’ is simply the product of r’s initial potential with all of its incoming messages except the one from r’ (and similarly for the message sent from r’ to r). However, as we discussed in our derivation of the region graph algorithm, this computation will double-count the information that arrived at r from r’ via an indirect path. The final computation of the messages δ 
is intended to correct for that double-counting. In this exercise, you will show that the fixed points are precisely the same as the fixed points of the update equations equation (11.71)–equation (11.76).
a. We begin by defining the messages in terms of the beliefs and the Lagrange multipliers:
Show that these messages satisfy the fixed-point equations in equation (11.33).
b. Show that
Conclude that equation (11.76) holds.
c. Show that
Show that the only solution to these equations is given by equation (11.73) and equation (11.74).
d. Show by direct derivation that theorem 11.6 holds for the potentials defined by equation (11.71)–11.76.
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1 Show 8052 Code Which Sets Timer 1 To 16bit Mode Turns It On And Sets It Starting V 2847350
/in Uncategorized /by developer1. Show 8052 code which sets timer 1 to 16bit mode, turns it on and sets it starting value such that it overflows every 100th.
2. You are building an 8052-based device which will use both a 3-axis accelerometer and a temperature sensor. A variety of these are available, would you choose UART or 12C based communications? Why?
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1 Shady Rest Nursing Home Has 100 Private Pay Residents The Administrator Is Concern 3832174
/in Uncategorized /by developer1. Shady Rest Nursing Home has 100 private pay residents. The administrator is concerned about balancing the ratio its private pay to non-private pay patients. Non-private pay sources reimburse an average of $100 per day whereas private pay residents pay average 100 percent of full daily charges. The administrator estimates that variable cost per resident per day is $25 for supplies, food, and contracted services and annual fixed costs are $4,562,500.a) If 25 percent of the residents are non-private pay, what will Shady Rest charge the private pay patients in order to break even?
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1 Show An Example Of A Markov Chain Where The Limiting Distribution Reached Via Repe 2528155
/in Uncategorized /by developer1. Show an example of a Markov chain where the limiting distribution reached via repeated applications of equation (12.20) depends on the initial distribution P(0).
2. Consider the following two conditions on a Markov chain T:
a. It is possible to get from any state to any state using a positive probability path in the state graph.
b. For each state x, there is a positive probability of transitioning directly from x to x (a self-loop).
a. Show that, for a finite-state Markov chain, these two conditions together imply that T is regular.
b. Show that regularity of the Markov chain implies condition 1.
c. Show an example of a regular Markov chain that does not satisfy the condition 2.
d. Now let us weaken condition 2, requiring only that there exists a state x with a positive probability of transitioning directly from x to x. Show that this weaker condition and condition 1 together still su‑ce to ensure regularity.
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1 Show 8052 Code Which Sets Timer 1 To 16bit Mode Turns It On And Sets It Starting V 2847352
/in Uncategorized /by developer1. Show 8052 code which sets timer 1 to 16bit mode, turns it on and sets it starting value such that it overflows every 100th.
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1 Show How Education Can Signal The Worker S Innate Ability In The Labor Market What 2652644
/in Uncategorized /by developer1. Show how education can signal the worker's innate ability in the labor market. What is a pooled equilibrium? What is a perfectly separating signaling equilibrium?
2. How can we differentiate between the hypothesis that education increases productivity and the hypothesis that education is a signal for the worker's innate ability?
3. Discuss the difference between general training and specific training. Who pays for and collects the returns from each type of training?
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1 Show Directly From Equation 12 21 Without Using The Detailed Balance Equation That 2528156
/in Uncategorized /by developer1. Show directly from equation (12.21) (without using the detailed balance equation) that the posterior distribution P(X | e) is a stationary distribution of the Gibbs chain (equation (12.22)).
2. Show that any distribution π that satisfies the detailed balance equation, equation (12.24), must be a stationary distribution of T.
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1 Show How To Use A Systolic Array To Transpose A Matrix 2 How Many Processors And H 2538339
/in Uncategorized /by developer1. Show how to use a systolic array to transpose a matrix.
2. How many processors and how many steps are required for a systolic machine that can multiply an M -by-N matrix by an N -by-1 vector?
3. Give a simple parallel scheme for matrix-vector multiplication using processors which have the capability to “remember” computed values.
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1 Show That A Monotone Real Function Is Measurable 2 2008152
/in Uncategorized /by developer1. Show that a monotone real function is measurable.
2.
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1 Show That If Q I Q X I U I Then 2 Develop A Variational Approximation Using Bayesi 2528134
/in Uncategorized /by developer1. Show that if Q =
i Q(Xi|Ui), then
2. Develop a variational approximation using Bayesian networks. Assume that Q is represented by a Bayesian network of a given structure G. Derive the fixed-point characterization of parameters that maximize the energy functional for this type of approximation.
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1 Show That The Counting Numbers Defined By Equation 11 26 Are Convex 2 In This Exer 2528121
/in Uncategorized /by developer1. Show that the counting numbers defined by equation (11.26) are convex.
2. In this exercise, we will derive another message passing algorithm, called the two-way algorithm, for finding fixed points of region-based energy functionals; this algorithm allows for more general region graphs than in exercise. It uses two messages along each link r → r’: one from r to r’ and one from r’ to r. Consider a region-based free energy as in equation (11.27). For any region r, let pr = |Up(r)| be the number of regions that are directly upward of r. Assume that for any top region (so that pr = 0), we have that κr = 1. We now define qr = (1 − κr)/pregion, taking qr = 1 when pr = 0 (so that κr = 1, as per our assumption). Assume furthermore that qr ≠ 2, and define βr = 1/(2 − qr).
The following equalities define the messages and the potentials in this algorithm:
Note that the messages
are as we would expect: the message sent from r to r’ is simply the product of r’s initial potential with all of its incoming messages except the one from r’ (and similarly for the message sent from r’ to r). However, as we discussed in our derivation of the region graph algorithm, this computation will double-count the information that arrived at r from r’ via an indirect path. The final computation of the messages δ 
is intended to correct for that double-counting. In this exercise, you will show that the fixed points are precisely the same as the fixed points of the update equations equation (11.71)–equation (11.76).
a. We begin by defining the messages in terms of the beliefs and the Lagrange multipliers:
Show that these messages satisfy the fixed-point equations in equation (11.33).
b. Show that
Conclude that equation (11.76) holds.
c. Show that
Show that the only solution to these equations is given by equation (11.73) and equation (11.74).
d. Show by direct derivation that theorem 11.6 holds for the potentials defined by equation (11.71)–11.76.
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