From 9645b74827a4ebcdee78914cfbd68839c8288afe Mon Sep 17 00:00:00 2001 From: Andrew Brown Date: Fri, 24 Aug 2018 13:44:02 +0100 Subject: [PATCH] Fixed non-ascii chars and latex deprecations make errors resulting from non-ascii characters in python files in ./Scripts were corrected by adding encoding information to the heads of the files. make errors arising from non-ascii characters in latex and xml files were corrected by using correct ascii quote marks and the latex command \pounds. make errors arising from deprecated latex commands `\rm` and `\bf` were corrected by replacement with `\textrm`, `\mathrm` or `\bfseries` as appropriate --- Modules/SOR3012 | 2 +- Resources/2-level-exercise.tex | 4 ++-- Resources/bayes-theorem-problems.xml | 4 ++-- Resources/betrand-paradox-project.tex | 2 +- Resources/binomial-random-variable-project.tex | 4 ++-- Resources/central-limit-theorem-problems.xml | 2 +- Resources/central-limit-theorem-proof.tex | 2 +- Resources/closed-1D-ising-model.tex | 4 ++-- Resources/conditional-probability-problems.xml | 2 +- Resources/ehrenfest-urns-program.tex | 2 +- Resources/ensembles-exercise.tex | 4 ++-- Resources/estimating-pi-project.tex | 2 +- Resources/exponential-random-variable-problems.xml | 6 +++--- Resources/exponential-random-variable-project.tex | 4 ++-- Resources/gamblers-ruin-expectation.tex | 2 +- Resources/gamblers-ruin-probability.tex | 12 ++++++------ Resources/gamblers-ruin-program.tex | 2 +- Resources/geometric-random-variable-project.tex | 4 ++-- Resources/info-theory-video1.xml | 2 +- Resources/lagrange-multipliers-video.xml | 4 ++-- Resources/limit-squeeze-problems.xml | 2 +- .../markov-stationary-distribution-problems.xml | 2 +- Resources/mean-field-2-ising-model.tex | 4 ++-- Resources/mean-field-ising-model.tex | 4 ++-- Resources/medical-markov-chains-project.tex | 6 +++--- Resources/molecular-partition-function.tex | 6 +++--- Resources/normal-random-variable-project.tex | 4 ++-- Resources/open-1D-ising-model.tex | 4 ++-- Resources/poisson-process-project.tex | 6 +++--- Resources/poisson-random-variable-project.tex | 4 ++-- Resources/potts-model.tex | 4 ++-- Resources/queues-project.tex | 6 +++--- Resources/uniform-random-variable-project.tex | 4 ++-- SOR3012-tutorials/Week04/tutorial.tex | 2 +- SOR3012-tutorials/Week08/tutorial.tex | 2 +- Scripts/basicgraph.py | 4 ++-- Scripts/classifyResourceGui.py | 1 + Scripts/createHTMLFromXML.py | 1 + Scripts/createModulePages.py | 1 + Scripts/createTopicPage.py | 1 + Scripts/fullgui.py | 1 + 41 files changed, 72 insertions(+), 67 deletions(-) diff --git a/Modules/SOR3012 b/Modules/SOR3012 index 76fa21a..616b150 100644 --- a/Modules/SOR3012 +++ b/Modules/SOR3012 @@ -15,7 +15,7 @@ LEARNINGOUTCOMES: - You should be able to calculate expectations and variances directly, using the moment generating function and by using the conditional expectation theorem. You should also be able to explain what predictions can be made given the expectation and/or the variance. -- You should be able to recognise which type of random variable is appropriate for modelling a given phenomenon, identify the assumptions that they have made in constructing this model and critically assess their validity.
 +- You should be able to recognise which type of random variable is appropriate for modelling a given phenomenon, identify the assumptions that they have made in constructing this model and critically assess their validity. - You should be able to explain what it means when we state that a time dependent process has independent and stationary increments and how this differs from a Markov process. By using your understanding of this distinction you should be able to construct probabilistic models for time dependent phenomena, explain the assumptions that have been made in the constructing these models and critically assess their validity. diff --git a/Resources/2-level-exercise.tex b/Resources/2-level-exercise.tex index 7215793..a2c3f3c 100644 --- a/Resources/2-level-exercise.tex +++ b/Resources/2-level-exercise.tex @@ -22,7 +22,7 @@ %\begin{tcolorbox}[colback=blue!05,width=\textwidth] % #3 %\end{tcolorbox} -\Huge {\bf #2} +\Huge {\bfseries #2} \tcblower #3 \end{tcolorbox} @@ -71,4 +71,4 @@ \item You should discuss how one could construct a Hamiltonian for a system in which the particles sit on a lattice and in which the particles do not interact. At variance with the normal lattice gas system, however, this system should not adopt a configuration with a high symmetry when the temperature is low. \end{enumerate} -\end{document} \ No newline at end of file +\end{document} diff --git a/Resources/bayes-theorem-problems.xml b/Resources/bayes-theorem-problems.xml index 52eb8e7..bdd2195 100644 --- a/Resources/bayes-theorem-problems.xml +++ b/Resources/bayes-theorem-problems.xml @@ -58,8 +58,8 @@ $$ Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90 % of the time. -When it doesn’t rain, he incorrectly forecasts rain 10 % of the time. What is the probability that -it will rain on the day of Marie’s wedding? (Assume that there are no leap years) +When it doesn't rain, he incorrectly forecasts rain 10 % of the time. What is the probability that +it will rain on the day of Marie's wedding? (Assume that there are no leap years) $$ diff --git a/Resources/betrand-paradox-project.tex b/Resources/betrand-paradox-project.tex index ec23776..fcbb8d2 100644 --- a/Resources/betrand-paradox-project.tex +++ b/Resources/betrand-paradox-project.tex @@ -50,7 +50,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] diff --git a/Resources/binomial-random-variable-project.tex b/Resources/binomial-random-variable-project.tex index 9dcf7fc..6c7ff99 100644 --- a/Resources/binomial-random-variable-project.tex +++ b/Resources/binomial-random-variable-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on binomial random variables. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on binomial random variables. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item An explanation on the type of experiments that this random variable can be used to model. diff --git a/Resources/central-limit-theorem-problems.xml b/Resources/central-limit-theorem-problems.xml index 141098b..baa504e 100644 --- a/Resources/central-limit-theorem-problems.xml +++ b/Resources/central-limit-theorem-problems.xml @@ -55,7 +55,7 @@ f_{X}(x) = \right. $$ Calculate $\mathbb{E}(X)=\mu$ and $\sqrt{\textrm{var}(X)}=\sigma$ and hence use the central limit -theorem to estimate the probability that the price will increase by £1.20 , or more, after 3 hours. +theorem to estimate the probability that the price will increase by \pounds~1.20 , or more, after 3 hours. WE are given information on a random variable in the question. We can use this information to diff --git a/Resources/central-limit-theorem-proof.tex b/Resources/central-limit-theorem-proof.tex index d2ca8bd..fdf97a3 100644 --- a/Resources/central-limit-theorem-proof.tex +++ b/Resources/central-limit-theorem-proof.tex @@ -53,7 +53,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] diff --git a/Resources/closed-1D-ising-model.tex b/Resources/closed-1D-ising-model.tex index 3e58c48..3c46ceb 100644 --- a/Resources/closed-1D-ising-model.tex +++ b/Resources/closed-1D-ising-model.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{AMA4004: Statistical Mechanics} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on the 1D-closed Ising model. You should prepare your report as an ipython notebook and within +For this project you must produce a {\bfseries three page} set of notes on the 1D-closed Ising model. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} diff --git a/Resources/conditional-probability-problems.xml b/Resources/conditional-probability-problems.xml index c3de65a..3042d4b 100644 --- a/Resources/conditional-probability-problems.xml +++ b/Resources/conditional-probability-problems.xml @@ -11,7 +11,7 @@ $$ -There are $n$ boxes, one with a prize of £100, the others are empty. +There are $n$ boxes, one with a prize of \pounds~100, the others are empty. A group of $n$ people are asked to form a queue and choose a box (at random) each in turn. Bob complains that this gives an unfair advantage to those first in the queue. diff --git a/Resources/ehrenfest-urns-program.tex b/Resources/ehrenfest-urns-program.tex index 8b132bb..b35f9ee 100644 --- a/Resources/ehrenfest-urns-program.tex +++ b/Resources/ehrenfest-urns-program.tex @@ -50,7 +50,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] diff --git a/Resources/ensembles-exercise.tex b/Resources/ensembles-exercise.tex index d1814a4..fdcc507 100644 --- a/Resources/ensembles-exercise.tex +++ b/Resources/ensembles-exercise.tex @@ -22,7 +22,7 @@ %\begin{tcolorbox}[colback=blue!05,width=\textwidth] % #3 %\end{tcolorbox} -\Huge {\bf #2} +\Huge {\bfseries #2} \tcblower #3 \end{tcolorbox} @@ -95,4 +95,4 @@ \item Explain the meaning of the term ``Potential of mean force" \end{itemize} -\end{document} \ No newline at end of file +\end{document} diff --git a/Resources/estimating-pi-project.tex b/Resources/estimating-pi-project.tex index bee892a..bebee35 100644 --- a/Resources/estimating-pi-project.tex +++ b/Resources/estimating-pi-project.tex @@ -50,7 +50,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] diff --git a/Resources/exponential-random-variable-problems.xml b/Resources/exponential-random-variable-problems.xml index d230d10..fb352b2 100644 --- a/Resources/exponential-random-variable-problems.xml +++ b/Resources/exponential-random-variable-problems.xml @@ -207,7 +207,7 @@ Once you realise this the solution is the same as that for the above problem wit A company offers to fix the mobile phones bought by its customers. These phones break in one of two ways: either the battery fails, which costs -£20 to fix, or the screen breaks, which costs £30 to +\pounds~20 to fix, or the screen breaks, which costs \pounds~30 to fix. If the time taken for the battery to fail is given by an exponentially distributed random variable with parameter $\lambda$ and the time taken for the screen to break is given by an exponentially distributed random variable with @@ -222,11 +222,11 @@ The key to solving this problem is recognizing three things:
  • The amount of time taken for the screen to break is a random variable, $X$, with cumulative probability distribution function: $P(X \le x) = 1 - e^{-\lambda x}$
  • The amount of time taken for the battery to fail is a random variable, $Y$, with cumulative probability distribution function: $P(Y \le y) = 1 - e^{-\mu y}$
    • -
  • If $P(Y \lt X)$ then the company has to pay out £20 and if $P(X \lt Y)$ the company has to pay out £30.
    • +
  • If $P(Y \lt X)$ then the company has to pay out \pounds~20 and if $P(X \lt Y)$ the company has to pay out \pounds~30.
You can determine the two probabilities in the third item above using the same method that was used to solve the problem with Alice and Bob above. These two probabilities will add up to one as such you can think of this pair of probabilities as the probability mass function for a discrete -random variable with two possible outcomes - a cost of £30 to the company or a cost of £20 to the company. Calculating the expectation of this +random variable with two possible outcomes - a cost of \pounds~30 to the company or a cost of \pounds~20 to the company. Calculating the expectation of this random variable is straightforward. diff --git a/Resources/exponential-random-variable-project.tex b/Resources/exponential-random-variable-project.tex index c20ed1c..b845234 100644 --- a/Resources/exponential-random-variable-project.tex +++ b/Resources/exponential-random-variable-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on exponential random variables. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on exponential random variables. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item An explanation on the type of experiments that this random variable can be used to model. diff --git a/Resources/gamblers-ruin-expectation.tex b/Resources/gamblers-ruin-expectation.tex index 0f9e5ab..f7b71c1 100644 --- a/Resources/gamblers-ruin-expectation.tex +++ b/Resources/gamblers-ruin-expectation.tex @@ -47,7 +47,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] diff --git a/Resources/gamblers-ruin-probability.tex b/Resources/gamblers-ruin-probability.tex index 586079b..e12399f 100644 --- a/Resources/gamblers-ruin-probability.tex +++ b/Resources/gamblers-ruin-probability.tex @@ -47,7 +47,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -69,7 +69,7 @@ holding. If it does not transpire you loose your stake and are thus left with $a - x$ pounds. The ideas in this first paragraph have been covered in the videos on the gamblers video and in the programming exercise. We have shown how we can describe the above process using a Markov chain, -what the transition graph is for this chain and what the associated one-step transition probability matrix is for this discrete Markov chain. {\bf Before attempting this exercise make sure you are +what the transition graph is for this chain and what the associated one-step transition probability matrix is for this discrete Markov chain. {\bfseries Before attempting this exercise make sure you are familiar with these ideas and that you can thus do the following items:} \begin{enumerate} @@ -80,7 +80,7 @@ you start with $k$ pounds and where $p$ and $q$ are the probabiltiy of winning when you place each stake. \end{enumerate} -{\bf If you cannot do all of the above things watch the video on gamblers ruin again. If you are unable to do the above you will not understand the remainder of this exercise.} +{\bfseries If you cannot do all of the above things watch the video on gamblers ruin again. If you are unable to do the above you will not understand the remainder of this exercise.} The purpose of this exercise is to find an exact expression for the conditional probability of ruin given that you start with exactly $k$ pounds, $\pi_k$. @@ -103,7 +103,7 @@ \section*{Solution guidelines} \[ \phi_k = A \theta_1^k + B \theta_2^k \] -{\bf Insert the trial solution $\pi_k = \theta^k$ into the homogenous difference equation above remebering that $\phi_{k+1}=\theta^{k+1}$. Factorise the resulting equation and hence show that: +{\bfseries Insert the trial solution $\pi_k = \theta^k$ into the homogenous difference equation above remebering that $\phi_{k+1}=\theta^{k+1}$. Factorise the resulting equation and hence show that: \begin{equation} \pi_k = A + B \left( \frac{q}{p}\right)^k @@ -112,11 +112,11 @@ \section*{Solution guidelines} where $A$ and $B$ are as yet unknown parameters.} -\item Think about what the quantity $\pi_k$ represents. This is the probability of ruin given that you start with exactly $k$ pounds to your name. Given the meaning of this quantity, $\pi_k$, {\bf +\item Think about what the quantity $\pi_k$ represents. This is the probability of ruin given that you start with exactly $k$ pounds to your name. Given the meaning of this quantity, $\pi_k$, {\bfseries what are the values of $\pi_0$ and $\pi_n$.} Notice that here $n$ is the target amount of money the gambler wants to win. \item If you insert the values of $\pi_0$ and $\pi_n$ into the left hand side of equation \ref{eqn:soln} and the corresponding values of $k$ into the right hand side you get two simulaltaneous -equation with two unknowns $A$ and $B$. {\bf Solve this set of simultaneous equations and find values for $A$ and $B$.} Hence, show that: +equation with two unknowns $A$ and $B$. {\bfseries Solve this set of simultaneous equations and find values for $A$ and $B$.} Hence, show that: \[ \pi_k = \frac{ \left( \frac{q}{p} \right)^k - \left( \frac{q}{p} \right)^n }{ 1 - \left( \frac{q}{p} \right)^n } \] diff --git a/Resources/gamblers-ruin-program.tex b/Resources/gamblers-ruin-program.tex index e4978be..d1eacc3 100644 --- a/Resources/gamblers-ruin-program.tex +++ b/Resources/gamblers-ruin-program.tex @@ -50,7 +50,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] diff --git a/Resources/geometric-random-variable-project.tex b/Resources/geometric-random-variable-project.tex index 13537d1..51c6e9c 100644 --- a/Resources/geometric-random-variable-project.tex +++ b/Resources/geometric-random-variable-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on geometric random variables. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on geometric random variables. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item An explanation on the type of experiments that this random variable can be used to model. diff --git a/Resources/info-theory-video1.xml b/Resources/info-theory-video1.xml index d272949..95d18fa 100644 --- a/Resources/info-theory-video1.xml +++ b/Resources/info-theory-video1.xml @@ -3,7 +3,7 @@ diff --git a/Resources/limit-squeeze-problems.xml b/Resources/limit-squeeze-problems.xml index 639ece2..aae2039 100644 --- a/Resources/limit-squeeze-problems.xml +++ b/Resources/limit-squeeze-problems.xml @@ -15,7 +15,7 @@ $$ $$ -If we put the equation in the question into words we are being asked to ``find the limit of $\sin(x)$ over $x$ as $x$ tends to infinity.” +If we put the equation in the question into words we are being asked to ``find the limit of $\sin(x)$ over $x$ as $x$ tends to infinity.'' In more prosaic terms substitute $\infty$ into the equation after the limit sign and see what happens. Obviously, this is not a problem we can solve with a calculator as (a) we cannot put infinity into a calculator and (b) even if we could the value of $\frac{\infty}{\infty}$ is undefined. We thus have to use some other scheme. For this particular problem we solve the limit as follows: diff --git a/Resources/markov-stationary-distribution-problems.xml b/Resources/markov-stationary-distribution-problems.xml index 5198544..a81dde1 100644 --- a/Resources/markov-stationary-distribution-problems.xml +++ b/Resources/markov-stationary-distribution-problems.xml @@ -190,7 +190,7 @@ $$ A double glazing firm employs staff to cold call clients and try to sell them new windows for their home. There are three levels of staff pay: Level 1 -(£50), Level 2 (£75) or Level 3 (£100). The amount a +(\pounds~50), Level 2 (\pounds~75) or Level 3 (\pounds~100). The amount a person is paid in a given evening is determined by their performance that evening and their performance on the previous evening. A staff member who was paid at level 1 on the previous day is moved to level 2 if they are diff --git a/Resources/mean-field-2-ising-model.tex b/Resources/mean-field-2-ising-model.tex index 684cb15..80561d3 100644 --- a/Resources/mean-field-2-ising-model.tex +++ b/Resources/mean-field-2-ising-model.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{AMA4004: Statistical Mechanics} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on modelling the Ising model within a mean field theory where the interactions between neighboring spins is modelled exactly and where each pair of spins then interacts with the mean field. You should prepare your report as +For this project you must produce a {\bfseries three page} set of notes on modelling the Ising model within a mean field theory where the interactions between neighboring spins is modelled exactly and where each pair of spins then interacts with the mean field. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} diff --git a/Resources/mean-field-ising-model.tex b/Resources/mean-field-ising-model.tex index 203b842..85f0d6a 100644 --- a/Resources/mean-field-ising-model.tex +++ b/Resources/mean-field-ising-model.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{AMA4004: Statistical Mechanics} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on modelling the Ising model within a mean field theory where each spin interacts with the mean field. You should prepare your report as an ipython notebook and within +For this project you must produce a {\bfseries three page} set of notes on modelling the Ising model within a mean field theory where each spin interacts with the mean field. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} diff --git a/Resources/medical-markov-chains-project.tex b/Resources/medical-markov-chains-project.tex index 53aea55..bfb9dab 100644 --- a/Resources/medical-markov-chains-project.tex +++ b/Resources/medical-markov-chains-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on how the progression of diseases can be modelled using continuous time Markov chains. You should prepare your report as an +For this project you must produce a {\bfseries three page} set of notes on how the progression of diseases can be modelled using continuous time Markov chains. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} @@ -83,7 +83,7 @@ \end{itemize} You should also explain any results you have used on series expansions or special integrals within your notes and provide the reader with links explaining where they can find material that explains -these ideas. These links might be pointers to particular websites, pointers to notes from modules that you have studied at Queen's or pointers to websites. You {\bf should not} get bogged down in +these ideas. These links might be pointers to particular websites, pointers to notes from modules that you have studied at Queen's or pointers to websites. You {\bfseries should not} get bogged down in explaining what a Markov chain is, how the Kolmogorov equations are derived and so on. You can assume that the readers of your report will have studied what you have in SOR3012 and that they will thus be familiar with these details. diff --git a/Resources/molecular-partition-function.tex b/Resources/molecular-partition-function.tex index 08762a3..9631ca3 100644 --- a/Resources/molecular-partition-function.tex +++ b/Resources/molecular-partition-function.tex @@ -22,7 +22,7 @@ %\begin{tcolorbox}[colback=blue!05,width=\textwidth] % #3 %\end{tcolorbox} -\Huge {\bf #2} +\Huge {\bfseries #2} \tcblower #3 \end{tcolorbox} @@ -82,7 +82,7 @@ \item Discuss the behaviour of the heat capacity of the harmonic oscillator and the particle in a box in the low temperature limit. In which of these two systems does the behaviour of the heat capacity deviate from the predictions of equipartition? Why does this deviation occur for this particular system and why does it not occur for the other system you studied? -\item Lets now consider a system of $N$ uncoupled harmonic oscillators with characteristic frequencies $\{ \omega_1, \omega_2, \dots \omega_N\}$. Explain what the heat capacity for this system will equal in the high temperature limit {\bf without} doing any derivations. +\item Lets now consider a system of $N$ uncoupled harmonic oscillators with characteristic frequencies $\{ \omega_1, \omega_2, \dots \omega_N\}$. Explain what the heat capacity for this system will equal in the high temperature limit {\bfseries without} doing any derivations. \item Explain why the canonical partition function for this system of $N$ uncoupled harmonic oscillators is given by: $$ @@ -97,4 +97,4 @@ -\end{document} \ No newline at end of file +\end{document} diff --git a/Resources/normal-random-variable-project.tex b/Resources/normal-random-variable-project.tex index 9155c7f..1782716 100644 --- a/Resources/normal-random-variable-project.tex +++ b/Resources/normal-random-variable-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on normal random variables. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on normal random variables. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item An explanation on the type of experiments that this random variable can be used to model. diff --git a/Resources/open-1D-ising-model.tex b/Resources/open-1D-ising-model.tex index 1ae162b..8df9f82 100644 --- a/Resources/open-1D-ising-model.tex +++ b/Resources/open-1D-ising-model.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{AMA4004: Statistical Mechanics} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on the 1D-open Ising model. You should prepare your report as an ipython notebook and within +For this project you must produce a {\bfseries three page} set of notes on the 1D-open Ising model. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} diff --git a/Resources/poisson-process-project.tex b/Resources/poisson-process-project.tex index 5fa9d18..8ee04ac 100644 --- a/Resources/poisson-process-project.tex +++ b/Resources/poisson-process-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on the Poisson Process. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on the Poisson Process. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item You should discuss phenomena that can be modelled using a Poisson process and you should discuss the assumptions that are made when this model is used to model these phenomena @@ -81,7 +81,7 @@ \end{itemize} You should also explain any results you have used on series expansions or special integrals within your notes and provide the reader with links explaining where they can find material that explains -these ideas. These links might be pointers to particular websites, pointers to notes from modules that you have studied at Queen's or pointers to websites. You {\bf should not} get bogged down in +these ideas. These links might be pointers to particular websites, pointers to notes from modules that you have studied at Queen's or pointers to websites. You {\bfseries should not} get bogged down in explaining what a Markov chain is, how the Kolmogorov equations are derived and so on. You can assume that the readers of your report will have studied what you have in SOR3012 and that they will thus be familiar with these details. diff --git a/Resources/poisson-random-variable-project.tex b/Resources/poisson-random-variable-project.tex index b5bf64d..3d0bdd4 100644 --- a/Resources/poisson-random-variable-project.tex +++ b/Resources/poisson-random-variable-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on poisson random variables. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on poisson random variables. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item An explanation on the type of experiments that this random variable can be used to model. diff --git a/Resources/potts-model.tex b/Resources/potts-model.tex index d45b2e7..1e8ddac 100644 --- a/Resources/potts-model.tex +++ b/Resources/potts-model.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{AMA4004: Statistical Mechanics} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on the Potts model. You should prepare your report as an ipython notebook and within +For this project you must produce a {\bfseries three page} set of notes on the Potts model. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} diff --git a/Resources/queues-project.tex b/Resources/queues-project.tex index 45de91d..8558145 100644 --- a/Resources/queues-project.tex +++ b/Resources/queues-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on the M/M/1 queue. You should prepare your report as an ipython notebook and within it you should present: +For this project you must produce a {\bfseries three page} set of notes on the M/M/1 queue. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} \item You should discuss how a model can be constructed by using the theory of continuous time Markov chains. In this discussion you should talk about the distinction between infinite @@ -85,7 +85,7 @@ \end{itemize} You should also explain any results you have used on series expansions or special integrals within your notes and provide the reader with links explaining where they can find material that explains -these ideas. These links might be pointers to particular websites, pointers to notes from modules that you have studied at Queen's or pointers to websites. You {\bf should not} get bogged down in +these ideas. These links might be pointers to particular websites, pointers to notes from modules that you have studied at Queen's or pointers to websites. You {\bfseries should not} get bogged down in explaining what a Markov chain is, how the Kolmogorov equations are derived and so on. You can assume that the readers of your report will have studied what you have in SOR3012 and that they will thus be familiar with these details. diff --git a/Resources/uniform-random-variable-project.tex b/Resources/uniform-random-variable-project.tex index 758dfb3..bbd17ac 100644 --- a/Resources/uniform-random-variable-project.tex +++ b/Resources/uniform-random-variable-project.tex @@ -49,7 +49,7 @@ \newcommand{\horrule}[1]{\rule{\linewidth}{#1}} \newcommand{\vek}[1]{\mbox{\boldmath $ #1$}} \newcommand{\ex}[1]{\ensuremath {\mathbb{E}} \left[ #1 \right]} -\newcommand{\var}[1]{\ensuremath{{\rm var}\left[ #1 \right]}} +\newcommand{\var}[1]{\ensuremath{{\mathrm var}\left[ #1 \right]}} \title{\usefont{OT1}{bch}{b}{n} \normalfont \normalsize \textsc{SOR3012: Stochastic Processes} \\ [25pt] \horrule{0.5pt} \\[0.4cm] @@ -66,7 +66,7 @@ \begin{document} \maketitle -For this project you must produce a {\bf three page} set of notes on both discrete uniform and continuous uniform random variables. You should prepare your report as an ipython notebook and within +For this project you must produce a {\bfseries three page} set of notes on both discrete uniform and continuous uniform random variables. You should prepare your report as an ipython notebook and within it you should present: \begin{itemize} diff --git a/SOR3012-tutorials/Week04/tutorial.tex b/SOR3012-tutorials/Week04/tutorial.tex index 3f3a09a..8883d7a 100644 --- a/SOR3012-tutorials/Week04/tutorial.tex +++ b/SOR3012-tutorials/Week04/tutorial.tex @@ -54,7 +54,7 @@ \section{Question 2} \right. $$ Calculate $\mathbb{E}(X)=\mu$ and $\sqrt{\textrm{var}(X)}=\sigma$ and hence use the central limit -theorem to estimate the probability that the price will increase by £1.20 , or more, after 3 hours. +theorem to estimate the probability that the price will increase by \pounds~1.20 , or more, after 3 hours. \section{Question 3} diff --git a/SOR3012-tutorials/Week08/tutorial.tex b/SOR3012-tutorials/Week08/tutorial.tex index 447d962..0101eb0 100644 --- a/SOR3012-tutorials/Week08/tutorial.tex +++ b/SOR3012-tutorials/Week08/tutorial.tex @@ -76,7 +76,7 @@ \subsection{Question 3} A double glazing firm employs staff to cold call clients and try to sell them new windows for their home. There are three levels of staff pay: Level 1 -(£50), Level 2 (£75) or Level 3 (£100). The amount a +(\pounds~50), Level 2 (\pounds~75) or Level 3 (\pounds~100). The amount a person is paid in a given evening is determined by their performance that evening and their performance on the previous evening. A staff member who was paid at level 1 on the previous day is moved to level 2 if they are diff --git a/Scripts/basicgraph.py b/Scripts/basicgraph.py index 53685ff..e9e0c78 100644 --- a/Scripts/basicgraph.py +++ b/Scripts/basicgraph.py @@ -88,10 +88,10 @@ def printNodeGraph(self,node): graphstr += "edge[style=invis];\n" graphstr += backnodes[len(backnodes)-2] + " -> " + self.nodes[j] + '\n' backnodes.append(self.nodes[j]) - for i in range(0,math.floor(len(forwardnodes)/2)+1) : + for i in range(0,int(math.floor(len(forwardnodes)/2)+1)) : if len(forwardnodes)>2*i+2 : graphstr += "{ rank=same; " + forwardnodes[2*i] + ";" + forwardnodes[2*i+1] + "; } \n" - for i in range(0,math.floor(len(backnodes)/2)+1) : + for i in range(0,int(math.floor(len(backnodes)/2)+1)) : if len(backnodes)>2*i+2 : graphstr += "{ rank=same; " + backnodes[2*i] + ";" + backnodes[2*i+1] + "; } \n" graphstr += "}" diff --git a/Scripts/classifyResourceGui.py b/Scripts/classifyResourceGui.py index ef3fb66..8becba7 100644 --- a/Scripts/classifyResourceGui.py +++ b/Scripts/classifyResourceGui.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- from topic import topiclist import os from PyQt4.QtGui import * diff --git a/Scripts/createHTMLFromXML.py b/Scripts/createHTMLFromXML.py index 40dcc6d..598c86d 100644 --- a/Scripts/createHTMLFromXML.py +++ b/Scripts/createHTMLFromXML.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- import os import sys import shutil diff --git a/Scripts/createModulePages.py b/Scripts/createModulePages.py index 0b41933..da4debf 100644 --- a/Scripts/createModulePages.py +++ b/Scripts/createModulePages.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- import shutil import topic import basicgraph diff --git a/Scripts/createTopicPage.py b/Scripts/createTopicPage.py index 1fe8e63..7b639e7 100644 --- a/Scripts/createTopicPage.py +++ b/Scripts/createTopicPage.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- import shutil import topic import basicgraph diff --git a/Scripts/fullgui.py b/Scripts/fullgui.py index eb3d1f6..f8c1afb 100644 --- a/Scripts/fullgui.py +++ b/Scripts/fullgui.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- import shutil import webbrowser import basicgraph