Question 1
5 out of 5 points
If the information coming into your decision-making process is in bad
form, you'll more than likely make a poor decision. This concept is referred
to as _.
Selected Answe
Question 1
5 out of 5 points
If a salesperson attempts to order merchandise for a customer who should
but does not exist in the customer database, the database will typically
generate an error messag
Question 1
5 out of 5 points
_ is a formal document that describes in detail your logical
requirements for a proposed system and invites vendors to submit bids for
its development.
Selected Answer:
R
Question 1
5 out of 5 points
What is the difference between SCM and CRM?
Selected
Answer:
SCM manages production and delivery information; CRM
manages customer information.
Answers:
CRM records infor
Question 1
5 out of 5 points
In the implementation phase of decision making, analytics takes on the
role of quality control, allowing you to gather information regarding your
solution to ensure that
Question 1
2 out of 2 points
Which of the following is true of ethics?
Selected
Answer:
Ethics are more subjective than
laws.
Answers:
Ethics and laws are the
same.
Laws and ethics clearly require or
Question 1
5 out of 5 points
Which of the following is true of commoditylike business environments?
Selected Answer:
They have low barriers to
entry.
Answers:
They are similar to specialty
items.
The
process, then the vector p whose elements are the
probabilities p is precisely the one correctly normalized
eigenvector of the Markov matrix which has eigenvalue
one. Putting this together with Equati
weighted by how long the system spends in that state.
How can we adapt our previous ideas concerning the
transition probabilities for our Markov process to take
this new idea into account? Well, assum
values. Such a rotation is called a limit cycle. In this case
w() would satisfy w() = P n w(), (2.11) where n is
the length of the limit cycle. If we choose our transition
probabilities (or equivalent
majority of its time in a small number of states (such as,
for example, the lowest-lying ones when we are at low
temperatures), since these will be precisely the states
that we pick most often, and th
this chapter has single-spin-flip dynamics, although this is
not what makes it the Metropolis algorithm. (As
discussed below, it is the particular choice of acceptance
ratio that characterizes the Met
down into two parts: P( ) = g( ) A( ). (2.16)
The quantity g( ) is the selection probability, which is
the probability, given an initial state , that our algorithm
will generate a new target state , a
we have QM = hQi. The question we would like to
answer now is how should we choose our M states in
order that QM be an accurate estimate of hQi? In other
words, how should we choose the probability d
new states are selected with exactly the correct transition
probabilities all the time, and the acceptance ratio is
always one. A good algorithm is one in which the
acceptance probability is usually c
the selection probabilities g( ), since the constraint
(2.14) only fixes the ratio P( ) P( ) = g( )A(
) g( )A( ) . (2.17) The ratio A( )/A(
) can take any value we choose between zero and
infinity,
studied in Problem 1.3 and hence calculate the internal
energy as a function of temperature. 2 The principles of
equilibrium thermal Monte Carlo simulation In Section
1.3.1 we looked briefly at the ge
giving a little extra thought to choosing the best set of
transition probabilities to construct an algorithm that will
answer the particular questions that you are interested
in. A purpose-built algor
the sums are dominated by the contribution from this
state. On the other hand, if we had some way of knowing
which states made the important contributions to the
sums in Equation (2.1) and if we could
sphere gases, and any algorithm, applied to any model,
which chooses selection probabilities according to a rule
like (3.7) can be said to be a Metropolis algorithm. At
first, this rule may seem a lit
Boltzmann probability distribution which we generate
after our system has come to equilibrium, rather than any
other distribution. Its derivation is quite subtle. Consider
first what it means to say t
scheme of sampling states at random; we would end up
rejecting virtually all states, since the probabilities for
their acceptance would be exponentially small. Instead,
almost all Monte Carlo schemes
rest of this book, we measure temperature in energy
units, so that k = 1. Thus when we say T = 2.0 we mean
that 1 = 2.0.) Then we might start off by performing a
simulation at T = 1.0 using the zero-t
proportion to P( ). Thus our continuous time Monte
Carlo algorithm consists of the following steps: 42
Chapter 2: Equilibrium thermal Monte Carlo simulations
1. We calculate the probabilities P( ) for
Markov process generating the state on being fed the
state is the same every time it is fed the state ,
irrespective of anything else that has happened. The
transition probabilities P( ) must also sat
has you realize that this would never be possible. For
instance, consider again the example we took in the last
chapter of a litre container of gas at room temperature
and atmospheric pressure. Such a
= 1, which means that the condition of detailed balance is
always satisfied for P( ), no matter what value we
choose for it. This gives us some flexibility about how we
choose the other transition pro
Markov process corresponding to these transition
probabilities so as to generate a chain of states. After
waiting a suitable length of time7 to allow the probability
distribution of states w(t) to get
ratio given in Equation (3.6) (solid line). This acceptance
ratio gives rise to an algorithm which samples the
Boltzmann distribution correctly, but is very inefficient,
since it rejects the vast majo
exploit these narrow ranges of energy and other
quantities to make our estimates of such quantities very
accurate. For this reason, we normally try to take a
sample of the states of the system in whic