## Meet the Researcher – Haixuan Yang

Where do you work?
School of Mathematics, Statistics and Applied Mathematics.

B.S. in Mathematics (Lanzhou University), M.S. in Mathematics (Qufu Normal University), Ph.D. in Mathematics (Lanzhou University), Ph.D. in Computer Science and Engineering (The Chinese University of Hong Kong).

Where do you come from in the world?
Hebei, China.

What is your area of research?
Bioinformatics & Statistical Modelling, especially of network data such as PPI, co-expression, and functional similarity.

How would you describe it to a five year old?
In a kindergarten, there are five boys and five girls. They are dancing hand in hand – this is a network because they are linked by their hands. Tired of dancing, they begin to listen to stories. Dr.  Deirdre Ní Chonghaile is telling a story about a killer whale and will play music about it. In the meantime, Dr. Yang is telling a story about Mickey and his three partners. Boys like the story about a killer whale while girls like Mickey, so they are divided into two groups – this is another network because they are linked by listening to the same story. By a magic number, I can say that these two networks are very different. When you grow up, and still want to listen to my stories, I will reveal this magic number to you from a secret box.

Describe one of your Eureka moments?
I was not taking a bath when I thought of a link between a cyclic matrix and the Fermat Last Theorem for the case n = 3, so my discovery is a small one – I failed to apply it to the case of any n. It was on a train in 1990 which was moving slowly through the famous Shapotoua desert. My exploration on the Fermat Last Theorem had been lasting for at least 3 years – slowly as the train – there was still little progress like a desert. But I did not give up. I believe that a difficult problem has its own special gate, through which one can enter. Everyone may walk through a different path that crowded ingenious guys happen to miss, and such a special path may lead to the special gate. The slow train, the slow progress, the desert outside the train, and the crowded people in the train gave me a hint – a special path – a link between a cyclic matrix and the Fermat Last Theorem for the case n = 3. Imagine what would happen if I was taking a bath!

How did you first get interested in this research space?
My philosophy described above is correct, I believe. Thus I continued to use this strategy, and I received some more: a short paper in one of two best journals in China, and a long paper that is my representative work in my pure Mathematics career. Suddenly I realized one day that my work may have important impacts 100 year later, but I cannot see them before I retire. This was not what I want, so I changed my philosophy as “special paths + real world challenging problems”.

A biologist happened to talk to me that human genomes had been sequenced; it was a book written in secret codes; it was difficult to read such a book – this challenging problem inspired my interest in Bioinformatics. Sometime around, I rediscovered the Nadaraya-Watson formula – this gave me the confidence that I can do something in Statistics. A friend told me later that Google’s Pagerank algorithm in Computer Science was powerful; Besides PageRank, I found that the decision trees algorithms CART and C4.5 were ranked in top 10 data mining algorithms – problems with wide applications also inspired me – I wanted to develop a better one.

After many years’ work, my interests get converged:  I am continuing my academic efforts on designing/applying statistical methods to tackle some biological problems – to which, I feel that, I am fully exploiting my abilities in Mathematics, Machine Learning, and Computer Science, and – for which, my curiosity about living beings is substantially satisfied.

Why is NUI Galway a good place to be a researcher?
Well-organized research groups: I attend Prof. John Hinde’s statistics group and Prof. Cathal Seoighe’s Bioinformatics group, from which I benefit a lot.

Friendly colleagues: they help me a lot.

Good academic environment: weekly seminar, problems of the week, and a collection of excellent people in pure mathematics, statistics, Bioinformatics, applied mathematics, and computer science – my academic background links to all of them – I am afraid that there are not many departments/schools in the world where I can link every piece of work to.

What discovery in history do you wish you’d made?
A method that is mathematically simple and beautiful, has wide applications, and contains insights.

What’s the most rewarding thing about working in research?
Eureka moments.

What’s the biggest challenge in the work that you do?
Find a significant research problem, towards which ingenious guys are not crowded.

What would you like to be the legacy of your career in research?
It is hopefully that my early representative work “Two operators on the lattice of completely regular semigroup varieties” will be a legacy 100 years later if there are important theoretical/practical applications found. There should be few citations because that I closed the door in this work and that real-world applications are unknown.

I expect that my unpublished work “Random graph dependency” will be a legacy because I open the door to researchers. In this work, I introduce the concept, algebraic links to existing measures in degraded cases, a significance test, and three application examples in Biology, World Wide Web, and Social Network. By “open the door to researcher”, I mean, if they want, they can do:

1. Pure mathematicians can generalize this work to hypergraphs, matrices, and even semigroups/groups; 2. Statisticians can prove the Central Limit Theory;

3. People including me in Bioinformatics can use it to compare two biological networks;

4. Anyone can use it because there are numerous networks (see what I have described to a five year old).