My thoughts on the Pechu Kucha presentation style BEFORE the HEA STEM Conference

This week I'm attending the HEA STEM Conference 2014.

+Paul Harper  and I will be presenting some work we undertook with +Louise Orpin and +Noel-Ann Bradshaw (the title of the talk is 'Operational research ambassadors in schools' but that's for another time).

All of the presenters have been given strict constraints to use the 'Pechu Kucha' style.

This involves using 20 slides that are set on a timer so that every slide is shown for 20 seconds with no control from the speaker. (All slides have had to be sent to the organisers quite a while ago and will be ran from a central computer.)

I am writing this post before the conference so perhaps my opinion will change but at present: I don't like it.

There are obvious benefits to using this style:

• It's something different;
• It will be fast paced;
• It is easy to control (I have heard that this format was chosen because multiple talks overran in past conferences).

I'm sure I'm missing other good points (feel free to add them in the comments).

Here comes my negative points:

From a technical point of view it's a shame to not be trusted

We had a virtual meeting yesterday where +Noel-Ann Bradshaw suggested something that really should have been on our slides but we cannot modify them.

Forcing everyone to use a given content delivering format is not appropriate.

This is an education conference with talks entitled: 'Dancing statistics - communicating statistical ideas to non-mathematical students' and 'iLectures - designing and developing interactive lectures using cloud-based broadcasting solutions'. These talks sound like they will be discussing various innovative content delivery formats. There is (in my opinion) no single best content delivery format but usually an ok content-audience-speaker triplet.

Why should everyone have to use the same format? (For some Pechu Kechu might be great but for others it might be terrible).

This is enforcing a lecture style delivery with a disconnection between audience and speaker

I try my best to make my presentations (and lectures) as interactive as possible. I encourage interruptions and if we (the audience and I) go down a particular lane that isn't what I had planned: that's often just fine!

There is time planned for questions at the end of the session but what if I want to ask the audience a question or if I welcomed a discussion midway through the presentation? Without being able to carefully ensure that this fits in the 20 second per slide constraint this is something that I simply won't be able to use.

Why am I here?

When my frustrations with the format first began I thought that perhaps Paul and I should simply screencast our talk which would enable us to edit it carefully and have the 6 minutes and 40 seconds perfectly cut to a high standard. Thus, when it was our turn to 'talk' we could simply press play and sit back.

Sadly this is not an option as everything is being run from a central computer through PowerPoint. In essence though, there is no point in us being here apart from taking the potential questions towards the end of the entire session (by which time the audience as a whole will have completely disconnected from our talk).

Looking forward to the conference

I suppose this post stems from the fact that I'm a spoilt only child and don't like being told what to do. I think that I'm just unsure about everyone having to use the same thing (whatever that thing may be). We are all different with different presentation skills and styles. We should be 'allowed' to express ourselves.

Ultimately I am very much looking forward to the conference and also am (despite what this post might indicate) optimistic about trying a different delivery format. I will try and write a reflective post after the conference: it would be awesome if I'm completely incorrect and Pechu Kechu is actually a great initiative from the organisers (who I'm sure have worked extremely hard to put on what will be a great conference).

I have spoken to Paul about this but in no way mean to bring my co-authors in to this rant: this is my personal opinion :)

Finally, so that there's something nice to look at here is a picture of Machu Picchu (from wikipedia) as that's what I've been calling Pechu Kucha for the past month or so as I've not been able to remember it's correct name:

Thinking about moving my blog...

Over the Christmas break I moved my website that sat on a Google sites page to my own server and did this mainly to learn Django. I'm now really happy with my personal site (modulo css which I'll fix when I have time) and like the workflow involved with updating the underlying database and the templates taking care of everything (a lot of my students in particular have commented on the ease of access to teaching resources on there).

I'm thinking of moving this blog over there too.

The way I see it there are good points and bad points to this.

Here is how I see the bad points:

• It'll be 'hard': blogger just takes care of everything for me.
• I have a modest number of readers and it would be a shame to 'lose' them.
• Disqus.com comments are great but I'm a huge +Google+ fan and like the interaction I get on comments with the +Blogger / G+ thing.

Here is how I see the good points:

• It'll be 'hard': I have a slight addiction to putting myself out of my comfort zone so learning how to set up my own RSS feed (which in practice should take 20 minutes of googling) would be good fun. A part from that it will actually be very easy.
• I'll have more control: I've had issues with +MathJax not playing nice with +Blogger so if it's all on my server I won't have these problems.
• I'll prefer the workflow: at the moment I write my posts in markdown, pandoc them and then copy the html and fix it in +Blogger. With my own site, posting will be a simple git push away...

On reflection I think the only real bad side would be through potential loss of interaction / engagement but I also think that by simple sharing on Twitter and G+ not much would be lost.

Perhaps I'm wrong, if anyone has moved their blog and could offer me some advice that would be great. Also, how important is the RSS feed nowadays (personally most of the blogs I read get pushed to me by social networks and/or Google Now - I wonder how many people wouldn't have read this if it hadn't gotten to them via RSS)?

A list of stuff for my student to look at before getting down to some Sage development

+James Campbell will be working with me this Summer on a project aimed at developing game theoretical stuff in to +Sage Mathematical Software System. James just emailed me asking for a list of stuff he could/should read up on before he starts. I thought more knowledgeable people than me might be able to contribute so I've lazily copied my email to him here: 

------------ email ------------

Code:

- git

- github (do +Daniele Procida's tutorial: https://dont-be-afraid-to-commit.readthedocs.org/en/latest/)

- sage development (tickets, documentation etc... This is something I don't know much about myself so read about it on the Safe site and watch videos on youtube there are a bunch of them)

- cython (http://cython.org/ - watch this intro to Sage lecture by +William Stein: https://www.youtube.com/watch?v=fI4NlMfGHC0 that's the first lecture in a class he's currently giving you also could watch the rest)

- C (to help with cython - you don't necessarily need to be an expert I think)

- markdown (https://www.youtube.com/watch?v=6A5EpqqDOdk)

- Test driven development: (watch all this and you will know what I mean: https://www.youtube.com/playlist?list=PL5859017B018F03F4)

- ssh and *nix (so that you're comfortable to jump on to one of my machines if necessary - depending on time we might also get you to tweak the Cardiff server)

- matplotlib (the python library that Sage uses to plot stuff, good to know it from a python pov so as to be able to get Sage to make it do what we want - we might or might not use this)

- How Sage plots graphs (graph theory graphs like I used for this: http://goo.gl/KHGYk7 - we might or might not need this)

Game Theory:

- Matching games (http://www.vincent-knight.com/teaching/gametheory/matchinggames/)

- Cooperative game theory (http://www.vincent-knight.com/teaching/gametheory/cooperativegames/)

We'll talk about this but 1 of the above (easy to code: 30 minutes of work) will be a gentle appetiser to the 'piece de resistance': normal form games,

- Normal form games (first 6 chapters of http://www.vincent-knight.com/teaching/gametheory/)

- The lrs algorithm (there is an implementation of this written in c that we either want to re-write to get working in Sage so you'll need to understand it or get Sage to talk to it / use it, I know Sage kind of has this as an optional library but I'm not entirely sure how to 'get at it' http://cgm.cs.mcgill.ca/~avis/C/lrs.html)

- Polytopes, you want to be comfortable-ish with the vocabulary around polytopes to be able to understand the lrs algorithm a bit. 

Books:

- In general I'd say don't spend much money on Python books. Like most OSS stuff there's an awesome amount of stuff online. Take a look at: http://pythonbooks.revolunet.com/ (a list of free Python books). There are various exceptions to this rule though.

- With regards to Sage I don't think you need a book for this project (as it's about building stuff for Sage so mainly reading about the development process and watching youtube videos is the way to go), I have a kindle copy of http://goo.gl/q9s9da, it's not bad but really everything is online. If you haven't already take a look at http://sagemath.org/help.html and join the relevant discussion groups on there.

- With regards to Game Theory there's a reading list on my website (all that follow are linked to on there). Webb's book is a gentle introduction, Algorithmic Game Theory is great and more about what you will be looking at. Finally there's a newish book by Maschler which looks really nice but I've not had time to work through it yet. In general my course site should suffice (reading/working through those books could take you years) with regards to what you need to know for game theory and I am certainly not asking you to spend money on a book. If there's a book (GT or code) that you really think would be useful let's talk.

------------

James is a pretty good coder with a good knowledge of a git based workflow already as his first year project (during which he actually learnt to code) has led his group to develop: http://thefightclub.herokuapp.com/ which is also on github (if you've made your way this far, please click on that and waste a minute or 2 of your life).

If there's anything missing from this list please add it to the comments :)

I'm looking forward to this project.

Scheduling group presentations using Graph Theory and Sage.

Yesterday (2014-03-26) I spoke at the Embedded Enterprise Exchange about my new first year module. I used a Hangout on air during the talk and you can see it here:

That's not what I'm going to talk about here though. The course I talked baout ends with all the 'companies' (groups of 4 students) giving a $\approx 25$ minute talk.

I need to schedule 40ish talks and this needs to fit around the student availability as well as my own. In this post I'll describe how I did this using a combination of Doodle, +Sage Mathematical Software System and Graph Theory.

The beginning of this post will be some of the boring details but towards the end I start talking about the mathematics (so feel free to skip to there...).

First of all I needed to know my students availability.

For this I simply used Doodle: https://doodle.com. I kind of use Doodle for every meeting I have to schedule (they also offer a cool tool that lets you show your availability so students/colleagues have an indication of when I might be able to meet with them).

Here's a screenshot of the responses:

You can't really see anything there as I had to zoom out a lot to grab the whole picture. Doodle allows you to download the information for any given poll in .xls format so I could relatively easily obtain the biadjacency matrix $M$ for my problem. Where $M_{ij}$ is 1 if group $i$ is available for schedule slot $j$ and 0 otherwise.

The mathematics and code needed.

Once I've got a .csv file (by tweaking the .xls file) of the biadjacency matrix I import that in to +Sage Mathematical Software System  and convert it to an instance of the `Matrix` class using the following:

import csv 
f=open(DATA+'availabilitymatrix','r') 
data = [[int(j) for j in row] for row in csv.reader(f)] 
f.close() 
M = Matrix(data)

I then need to remove any particular scheduled slots that are not picked by any company:

M = matrix([row for row in M.transpose() if max(row) != 0]).transpose()

Once I've done this I can define the bi-partite graph (bi-partite simply means that the vertices can be separated in to 2 non adjacent collections):

g = BipartiteGraph(M)

We can then get a get a picture of this, I do this using a 'partition' (a graph colouring) that will colour the groups (red) and the schedule slots (blue):

g = BipartiteGraph(M)
p = g.coloring()
g.show(layout='circular',dist=1,vertex_size=250, graph_border=True, figsize=[15,15],partition=p)

The various options I pass to the `show` command are simply to get the circular arrangement (and other minor things):

The above looks quite messy and what I essentially want is get as many pairwise matchings between the blue vertices (slots) and red vertices (companies) so that each schedule slot is attributed at most 1 company and every company has at least 1 schedule slot.

On any given graph $G=(V,E)$ this problem is known as looking for a maximal matching and can be written down mathematically:

Max:  $\sum_{e \in E(G)} m_e$

Such that:  $\forall v$ $\sum_{e \in E(G) \atop v \sim e} m_e \leq 1$

We are in essence finding a subset of edges of our original graph in such a way as to maximise the number of edges such that no vertex has more than 1 edge.

This is all explained extremely well at the +Sage Mathematical Software System documentation pages here.

Furthermore at the documentation the code needed to solve the problem is also given:

p = MixedIntegerLinearProgram()  
matching = p.new_variable(binary=True)
p.set_objective(sum(matching[e] for e in g.edges(labels=False)))
for v in g:
      p.add_constraint(sum(matching[e]
          for e in g.edges_incident(v, labels=False)) <= 1)
p.solve()

When I run the above, `p` is now a solved Mixed Integer Linear Program (corresponding to the matching problem described). To obtain the solution:

matching = p.get_values(matching)
schedule = [e for e,b in matching.iteritems() if b == 1]

Calling `schedule` gives a set of edges (denoted by the corresponding vertex numbers):

[(5, 57), (0, 45), (23, 50), (4, 42), (38, 60), (26, 56), (34, 62), (16,

68), (1, 43), (7, 40), (9, 44), (36, 58), (12, 49), (35, 71), (28, 66),
(25, 47), (24, 53), (6, 46), (3, 64), (39, 67), (17, 69), (22, 55), (13,
48), (33, 41), (10, 63), (21, 61), (30, 52), (29, 65), (37, 70), (15,
54), (19, 51), (11, 59)]

It is then really easy to draw another graph:

B=Graph(schedule)
p = B.coloring()
B.show(layout='circular',dist=1,vertex_size=250, graph_border=True, figsize=[15,15],partition=p)

Which gives:

You can see that the obtained graph has all the required properties and most importantly is a lot less congested.

Some details.

I'm leaving out some details, for example I kept track of the names of the companies and also the slots so that the final output of all this looked like this:

4InARow: Fri1100

Abacus: Tue0930

Alpha1: Thu1130

Alpha2: Mon0930

AusfallLtd: Fri1230

AxiomEnterprise: Thu1000

Batduck: Thu1430

CharliesAngles: Thu1500

CwmniRhifau: Mon1330

EasyasPi: Fri1130

Evolve: Thu1300

HSPLLtd.: Mon1030

JECT: Tue1200

JJSL: Thu1030

JNTL: Mon1400

JennyCash: Tue1630

KADE: Fri1330

MIAS: Fri1300

MIPE: Thu1100

MLC: Tue1600

Nineties: Mon0900

Promis: Fri1400

R.A.C.H: Tue1530

RYLR: Tue1230

SBTP: Fri1030

Serendipity: Mon1230

UniMath: Tue1300

VectorEnterprises: Tue1330

Venus: Thu1400

codeX: Mon1300

dydx: Wed1630

eduMath: Thu0930

(BatDuck is my favourite company name by far...)

Why did I do this this way?

There are 3 reasons:

1. I shared the schedule with my students through a published Sage sheet on our server. That way they can see a direct applied piece of mathematics and can also understand some of the code if they wanted to.

2. "Point and click doesn't scale" - I'm sure I could have solved this one instance of my problem with pen and paper and some common sense faster than it took me to write the code to solve the problem. The thing is next year when I need to schedule these talks again it will at most take me 3 minutes as the code is all here and ready to go. (Most readers of this blog won't need that explained but if any of my students find their way here: that's an important message for you).

3. It was fun.

Basketball and cooperative games in class

Here is the state of my class after my students learnt about cooperative game theory (Chapter 16 of my course):

Cooperative game theory is concerned with situations where coalitions are allowed to form in game theoretic situations. In my class the particular aspect we consider is the Shapley value which is of interest when sharing a particular commodity amongst a group of player who each contribute to the commodity differently.

I use this in practice when dealing with attributing individual marks to a group project: you can read about that here.

To introduce this I asked 3 students to come down and play a game: $S$, $L$ and $C$ volunteered (or at least gave a lazy nod when I asked if anyone had played basketball before) to come down.

They had 20 seconds to get as many crumpled up pieces of paper as possible in the bin above (it was on the table). The paper was stapled and it needed to be separated and crumpled so I suggested that perhaps 1 or 2 of them could spend some of the 20 seconds separating and crumpling.

We played this 3 times and it was all good fun. After $S$, $L$ and $C$ had their go 3 other students thought they could do better (no comment).

After that I asked the class how we could share out the 10 chocolates between $S$, $L$ and $C$: what would be the fair way? After some discussion it was clear that L had made the biggest contribution to the group for example and so this was not a trivial question.

After a little while I started to ask 'how many do you think $L$ and $C$ would have had together? etc... We wrote down the characteristic function for our game:

$$v(C)=\begin{cases}4, & C=\{S\}\\2, & C=\{C\}\\6, & C=\{L\}\\4, & C=\{S,C\}\\8, & C=\{S,L\}\\10, & C=\{C,L\}\\10, & C=\Omega\end{cases}$$

where $\Omega$ denotes the grand coalition.

At this point one student suggested that we somehow needed to take all this information in to account. He couldn't quite articulate how to do that but he's completely correct.

The way to share the chocolates 'fairly' is to consider all permutations of the players and consider marginal contributions for each permutation (take a look at my notes to read about that some more).

Let me try and explain with an example:

For the first permutation $\pi=(S,C,L)$ we calculate the contribution of $S$ first: $4$. We then calculate the marginal contribution of $C$ to the coalition $\{S,C\}$, which from above has value $4$ so $C$ needs to contribute 0. Finally $L$ needs to contribute $6$.

For the second permutation $\pi=(S,L,C)$ we calculate the contribution of $S$ first: $4$ (again). We then calculate the marginal contribution of $L$ to the coalition $\{S,L\}$, which from above has value $8$ so $L$ needs to contribute 4. Finally $C$ needs to contribute $2$.

Here's all the marginal contributions for each permutation:

• $(S,C,L)$ gives: $(4,0,6)$
• $(S,L,C)$ gives: $(4,2,4)$
• $(C,S,L)$ gives: $(2,2,6)$
• $(C,L,S)$ gives: $(0,2,8)$
• $(L,S,C)$ gives: $(2,2,6)$
• $(L,C,S)$ gives: $(0,4,6)$

We calculate the average values of the contribution vector (indexed by the players) to give the Shapley value:

$$\phi=(2,2,6)$$

This was good fun and I'm really happy with the discussion that lead us to the calculations and it was also fun to get students to mess around in class.

Here's one (of my most viewed!) +YouTube videos that I put together on it:

Matching games in class

Last week after looking at stochastic games we looked at matching games (corresponding to Chapter 15 of my course). There's an awesome video on +YouTube describing the problem:

I thought about possibly getting 6 students to form two groups (a set of reviewers and a set of suitors); ranking each other and then getting the class to put together a stable matching. I thought twice about this though as I'm sure it's the kind of thing that could get me fired so instead I brought 3 toys along to class with me:

• A tech deck (finger skateboard: http://www.techdeck.com/)
• The best teenage mutant ninja turtle: Donatello

Both of those you can see in this picture:

• The third toy I brought was my favourite nerf gun (the 'Praxis'):

I actually named 'her' Zoe; after my wife (+Zoë Prytherch).

Three students ('A', 'S' and 'R') came down and agreed to put together their ranking of which toy they preferred:

- A: Donatello, Zoe, Deck
- S: Zoe, Donatello, Deck
- R: Donatello, Zoe, Deck

I came up with a pretty random preference for the toys:

- Donatello: R, S, A
- Deck: A, R, S
- Zoe: R, S, A


We then discussed possible matchings and allocations of the toys (if we came to a stable one A, R and S could stick with that toy for the rest of the lesson). Here is one example that's close to what was suggested (I didn't record it and I don't quite remember it):

- A gets Donatello;
- S gets Zoe;
- R gets Deck

The thing with this is that Donatello prefers R and R prefers Donatello to their current match so the above is not stable.

After some more discussion we came up with the following stable matching:

We see that whilst A is with his 'least preferred' option (the Deck): no one prefers A to their current matching so A does not have an incentive to change his current matching.

The entire matching is stable because we can't find any pair that has an incentive to move.

In class we then went over the Gale-Shapley algorithm which is an algorithm that guarantees a stable matching. A cool thing is that this algorithm gives (out of all possible stable matchings) the one that is optimal from the suitors point of view and also the worst possible one from the reviewers point of view.

In our case above the matching found is also the matching found through the Gale-Shapley algorithm so sadly for 'A' there is no stable way of matching him to anything but his worst preferred toy and 'S' gets my wife no matter what.

Playing Stochastic/Markov games in class

In class on Monday my students and I looked at Stochastic games (Chapter 14 of my course notes). I decided to play a tournament similar to the iterated games that we played previously (corresponding to Chapters 9 and 10). I've blogged about them here and here.

In short, a stochastic game is a collection of states that themselves correspond to games. After players select strategies at a given state/game the next game they play (or state they are in) is given by a probability distribution.

This is a bit like playing in a casino where the table you play at depends on what happened at the previous table you played.

*The game we played in class corresponds to a casino with two tables:*

- At the first table we play a simple prisoner's dilemma (players aiming to maximise) their utility:

$$\begin{pmatrix}
(2,2)&(0,3)\\
(3,0)&(1,1)
\end{pmatrix}$$

The probability distribution at this table (indicating what game we played next) is given by:

$$\begin{pmatrix}
(.75,.25)&(0,1)\\
(0,1)&(.5,.5)
\end{pmatrix}$$

    - If both players cooperate (getting a utility of $2$ each) then there is a 75% chance that they play at this same table again.
    - If only one player cooperates and the other defects (the defector getting a utility of $3$ and the cooperator a utility of $0$) then the players move to the other game with 100% probability.
    - If both players defect (each getting a utility of $1$) then they will play the same game with 50% chance.

- The second table was a dummy game that basically ended the game:

$$\begin{pmatrix}
(0&0)
\end{pmatrix}$$

The probability distribution for this game is $(0,1)$.

The assumption made in this class is that the games are played infinitely and as such a discounting factor $\delta$ is used. When playing this in class we interpreted the discounting factor as the probability of the game continuing. So the game ended when the probabilities indicated that we were in the second game or when the discounting factor said so (we used $\delta=1/2$).

The class formed 4 teams and we played a round robin.

The first round had Tom's Team go up against Team Roy and Barmy go up against 4:

We see that Tom's team and Team Roy cooperated both times before the game ended whilst 4 defected from the start against Barmy.

The next round had Barmy go up against Tom's Team and Team Roy go up against 4:

We see that Barmy and Team Roy both cooperated before the game ended and Team Roy and 4 both defected before the game ended.

The last game had Tom's Team go up against 4 and Team Roy go up against Barmy. Below you can also see the final cumulative scores:

As you can see Tom's Team won (the name is after +Paul Harper son Tom joined the class during which we played the iterated prisonder's dilemma).

To decide who came second (they could choose the second prize to either be apples or party rings) a best of three game of Rock, Paper, Scissors, Lizard, Spock was played with Joe winning the party rings for Team Roy ('Scissors decapitates lizard').

I think this was good fun and hopefully enabled the students to have a sound grasp of what is meant by a state, a transition, etc..

Interestingly all teams happened to play Markov Strategies (i.e. in any given game they all did the same thing in each state) although this might have been different if the probabilities allowed the game to last longer. In the course we are restricting ourselves to Markov strategies.

After playing this we went through obtaining 2 equilibria for this game (both players defecting and both players cooperating).

Here are some photos that a student grabbed during the class and also a re-share of the gif of +Paul Harper's son Tom using a Nerf gun on those who defected against his team during the Prisoner's dilemma tournament: