*Reflections*

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## September 13, 2012

### Second reflection on Urss project

After the draft of my Urss project was finished, I explained it to several friends of mine. Most of them could at least get a basic understanding of what is going on and some of them could see how the mathematics work in my project. However, some of them were not interested in it or confused by the aim of my project. This may be because there was not enough time to give a detailed explantion. In addition, I designed my poster through latex poster template.

### Change of previous plan

Our previous plan included a further investigation of a more general model. However, due to a unforeseen complexity of our first model and the time limitation, we decided to concentrate on our first model so that we can at least obtain some useful results.

### Learning from mistakes and bugs

###### 1. Matlab functions

I used some Matlab functions on symbols. It saved me some time. Then under the pressure of a rise in the amount of calculations, I explored the functions further and found more useful functions which saved me more time. However, there was some limitation in the input of the functions, which I did not notice at the first time. Later it gave out some error since I input some too complicated formula.

Therefore, to test functions before using and get to know the limitation of the functions are important.

###### 2. Bugs.

When I did the simulation, there were annoying errors reported. The problem was that the error reported was not the actual error. It was caused by another error. This mislead me and cost much time to understand the problem.

###### 3. Replacing files wrongly.

I worked both on computers on campus and on my own laptop. I replaced some files wrongly, which cost me one night to recover what I had done. So remember to be careful when replacing files.

### Learning from my supervisor

Analysis on how the cover time changes asymptotically and plots against some parameters give me a more clear picture of what we are investigating and what the results are. My supervisor also explained to me how the underlying theory supports our results. This makes our results more rigorous.

### Learning from P@W workshop

First the lectures were attractive, compact and highly related to my project. Although I can only get a general idea without knowing some details in calculations and proofs, I did feel that I learned a lot from the lectures.

The talks from the young researchers gave me a pretty straight forward picture about what PhD students were doing. And they showed me how to present your own work to the audience. Some of them gave really good presentations. Even I could understand some of the technical details.

My supervisor helped me to solve the problem set and he encouraged to try to think about the problems, though the problems may be a bit hard for my level.

I am really glad to have such an opportunity to attend this workshop. It was extremely beneficial. I hope I can attend such workshops again next time.

### Progress of the project

Since I had a disagreement with my supervisor, I thought the problem deeply. Finally I found that my answer was only correct for the symmetric case. It indeed could not be interpreted meaningfully. On the other hand, my supervisor's method which involved a so-called Doob-h-transformation worked well on the calculation. The only drawback of this method was that it required a massive amount of calculations for large chains. Hence, the simulation could only be done for chains of size about 100. But this is the best we could do.

The other term which was difficult to calculated was simplified and solved by me through several attempts. Then my supervisor gave a very precise deduction which verified my result.

The methods above worked well, but there was a failure in our first method which involved Green's function. It was almost correct except that some terms appeared twice in the calculations. And we could not find the problem.

There were fluctuations in some of the simulations of the cover times, which was counterintuitive. This is because of my method of generating random variables. I generate new random variables each time. So if the random variables vary dramatically, the cover time of large chain can be smaller than that of small chain. I decide to generate random variables gradually. This will make sure the cover time is strictly increasing as the size increase.

### Improvement in typesetting(Latex)

Besides the powerful referencing functions of Latex, I learned how to draw simple graphs and create different types of texts, such as proposition, proof, remark.

### Learning poster design through examples

I learned poster design through examples using Latex poster template. It looked odd at first glimpse. The guide was short so I worked on an example to understand the settings of the package. Then I found it actually very easy to use and lots of options could be set to adjust the poster.

My problem about my poster was that it was hard to fit everything into a A1 paper, though I already gave very brief summaries. I was worried about that the pictures and texts would be blurry if they were set to be too small.

### Reflections on other things

More time should be left to finish the project at the end, since there are lots of trivial and time-consuming stuffs need to be done. Basically, the time management should be improved.

## July 10, 2012

### First reflection on Urss project

My Urss project has gone more than half way through. I think it is the time for me to have a little pause and review what I have done. Moreover, I shall record what I gained and where I need to improve.

**Background reading **

I spent about one week on reading background material, which included three papers and three chapters in a textbook. The difficulty of the reading was about all right, but it did require lots of efforts to concentrate to understand. For a few hard proofs, I can only scratch the main idea. Compared with attending lectures, this self-studying process is more independent with a bit more stress.

**Communication with my supervisor**

I feel that I can understand most of my supervisor's explanations and provide responses related to the topic to show my understanding. I am not afraid to ask questions even if it is sometimes basic. My supervisor explains to me with details, so everything looks very clear.

**Learning from my supervisor**

After obtaining some results, he will check it with a general estimate. If they are different, then he will look up the previous deduction for mistakes. It helps when the final result is a combination of several basic results. It narrows down the range of the mistakes if the final result is incorrect.

Due to lack of understanding of random walks, I often decompose the chain wrongly by removing some edges. This condition sometimes is so strong that the walks are pushed into one direction. Hence the later calculation go wrong. A more careful investigation of the Markov chain can help to solve ths problem.

**Progress of the project**

After learning the background knowledge about the relationship between random walks and electri networks, the analysis of random conductance model on probabilities went smooth. But the analysis on expectations did offer us some challenges. The formula became complicated and messy. We analysed the chain and calculated the formula for several times. Finally we get most of it done except one term in the formula. The simulations for the probabilities run well.

However, I had a disgreement with my supervisor. Based on my calculation, the term we want to find coincides with another term I find. So I guess they are the same, but we need more explanations. but my supervisor thinks they cannot be equal theoretically. Hence he provides me another method to find the term. I will try to investigate this term further to see the result and organise all the drafts.

**Improvement in typesetting(learning latex and bibtex)**

Previously I know TeX, which a basic typesetting program for mathematics. Due to a problem of inserting graphs, I learn latex, which is a more powerful one. It enables me to do something I cannot do before, e.g. the cross referencing within a paper.

I learned how to make a proper reference to a mathematical article. This involves saving the references in a seperate file through bibtex.

**Reflections on other things**

Most of the time, I can meet the goal set by our meeting. But when there is a long break between our meetings, I tends to be inefficient, especially when I am stuck in some mistake. Perhaps I should set a daily goal to improve self-motivation and leave extra time for the goals.