What feels like a lifetime ago (before some other genetics happened) I listened to Adam Rutherford's book of the week "How to Argue With a Racist" on Radio 4. It's now been so long that the Radio 4 link is dead, but you can buy the book or read the book review. The radio series was interesting, but one particular (slightly off topic) point I remember. Adam claimed (I mean, I *think*, it was a while ago) something like

Go back around 11 generations, and you will have ancestors who share none of your genetic material.

What argument might lead to this conclusion? My main initial conclusion was that I did not really know how inheritance works at the genetic level.

Read More →Some notes to myself on working with DJVU and PDF.

To convert a DJVU file to PDF:

- Download djvulibre for windows.
- Use
`ddjvu.eve -format=pdf -page=1-10 infile.djvu outfile.pdf`

- Manual: http://djvu.sourceforge.net/doc/man/ddjvu.html Notice in particular docs about quality, using JPEG compression etc.
- Source: https://superuser.com/a/571787/503838

Well, not new really, just I forgot to blog about it. "Ring-theoretic (in)finiteness in reduced products of Banach algebras" with Bence Horváth (currently a postdoc at the Czech academy of sciences). Available at arXiv:1912.07108 [math.FA]

We look at ultrapowers and the asymptotic sequence algebra of Banach algebras. There has been some interest recently in using tools from Model Theory (specifically, the recent area of "Continuous model theory") to study such objects for \( C^* \) and von Neumann algebras. One of our research themes is that things do not work so nicely for Banach algebras, and in particular, one often has to get one's hands dirty (and not use Model Theory results) because Banach algebras are not very "metrical" objects, unlike operator algebras. We construct various counter-examples, and also leave open some tantalizing questions about renormings of some rather concrete algebras.

I worked (in a very "bare hands" way) on ultraproducts in my thesis, and shortly afterwards, and it was fun to return to this topic, but to take a slightly more abstract approach. Something we wrote in the introduction is that we wonder if the asymptotic sequence algebra of a Banach algebra could be an interesting source of (counter-)examples for other problems?

Read More →The 2nd part of my talk to postgraduate students is all about statistics, particularly hypothesis testing, and why I like Bayesian approaches. As the room allocated was long and thin with whiteboards only on the long walls, I decided that a chalk-and-talk would just lead to neck ache in my audience.

So I want with a beamer talk (pdf of slides) which inevitably lead to me finishing early. I guess no-one minded this.

A mini-bibliography:

- I still really enjoy my undergraduate lecture notes curtesy of Prof. Richard Weber (I feel old to see that Prof Weber is now retired...)
- Rice, "Mathematical Statistics And Data Analysis" which said lecture notes follow moderately closely. Amazon link. Also available in the UCLAN library.
- A wonderful book is MacKay, Information Theory, Inference, and Learning Algorithms. Available in electronic format for free.
- A more straight-up introduction to Bayesian thought is Sivia and Skilling, "Data Analysis: A Bayesian Tutorial". Amazon link. This book blends some philosophical thoughts (but not overly heavy) with practical and interesting advanced statistics. I believe it's available online from one of the online libraries UCLAN subscribes to (and/or is in the library).
- A more heavy-weight alternative is Bayesian Data Analysis, Third Edition by the gang of six. Amazon link.
- A bed-time book is the excellent Nate Silver's book "The signal and the noise". Amazon link. Everyone should read this.

As part of my job, I have to give two lectures to postgraduate students, as part of a "training programme" for them. As we have no Mathematics PhD students, I will be speaking to (Astro-)Physicists and Astronomers. This leave me with three choices, as I see it:

- Give an actual research talk, and loose everyone in 3 minutes (hands up who knows what a Hilbert Space is. Oh.)
- Give a "public science" like talk on e.g. non-commutative geometry. Hard to see how this contributes to "training".
- Speak about something Mathematical, but not related to my current research. Something on basic statistics it is then.

So, my talks will be "A Mathematician looks at statistics". These are some brief working notes: for the first talk at least I plan to give a "chalk-and-talk" with maybe some brief Python demonstrations.

Read More →The final part of building a voice-activated Christmas tree light is the actual lights. Following the instructions in PiMag 88 I bought 2 meters of NeoPixels from Pimoroni and, erm, little else!

Read More →This is a follow-on post about speech recognition on a Raspberry Pi. Of course, Christmas and come and gone; perhaps I will finish this project for Christmas 2020! The original project was to make some voice activated Christmas tree lights. The original project had a push-button activation, but to compete with my son's new Alexa, I wanted to use a hotword wake-up instead.

The first attempt was to use Snowboy which is an open source, but slightly morribund project. The previous blog post details (with links) how to build a Python 3 compatible library.

Read More →My son and I are attempting to follow the instructions in Pi Mag 88 to build a voice activated LED-powered Christmas tree decoration. This is part of what I suspect shall be many posts documenting my attempts to actually use the couple of Raspberry Pis which we own.

Up first is recording audio on the Pi. I purchased this cheap USB microphone. It works, but it's rather poor quality. With a bit more research, I might have bought a Playstation Eye which is nearly as cheap, and apparently pretty much works out the box with the Pi. We played with the Microphone on our Pi 3 connected up to monitor, keyboard etc. but eventually we want to use my Pi 0 in headless mode.

Read More →