About Mathematics

More than 20 years ago, in a calculus class, the lecturer told us during the last lesson of the semester: "Now we've learned a year of calculus. But in the real world, you will probably not do it the way we do our homework anymore, as there are lots of software products such as MATLAB to perform these tasks. But I think it is still necessary to understand the theories and concepts in order to use those software tools properly."

Then he paused for a moment and said, "It is also important to note that thesesoftware tools do not work the same way you do for homework or examinations. They don't use formulas for differentiation or integration. Instead, the programs simulate the fundamental core of calculus by approximating the area under an irregular curve with a large number of rectangular bars. The result will be more accurate if you cut it into more pieces, with the trade-off of a higher computational cost."

I am grateful to have had such a young and excellent mathematics teacher during my first year of university. I still consider him to be one of the best teachers I've ever had. He focused on explaining the concepts and theirmotivation in a very intuitive way.

Whenever I contacted him to ask questions, he always tried his best to explain everything patiently. He reassured me that no matter how poor my foundation was at the beginning, given that I had passed the entrance exams to enroll in the university, my classmates who seemed to achieve much better marks did not actually have a distinctive advantage. "Four years is not a short time. By continuously studying hard, you can reach a level equal to anyone in your class."

He highlighted the generality of an approach rather than focusing on methods that only applied to very specific situations, which are unlikely to occur in the real world.

I didn't fully understand his words back then. Several years later, when I read the mathematical analysis textbook authored by Professor Terence Tao, I was drawn to the in-depth discussion of how definitions are constructed and how to derive theories from them, as well as how the system would change if we defined a concept differently. After reading his textbook and many posts on his blog, I think I've gained a basic idea of how to construct mathematical models by abstracting physical reality.

Then I wondered why one plus one equaled two. It doesn't have to be that way! In a binary system, one plus one equals "10"!

Then I kept thinking: why do we need a binary system**?** It is because an electrical switch is a robust way to represent data in a digital system. Can we find a way nowadays to represent data directly in a more complex manner? Would it be beneficial because we could skip many intermediate steps in computations? Yes, that is the motivation behind quantum computers!

Outside the Window

Spring has finally arrived in Brisbane, and the daytime is becoming much longer. Early in the morning, I can hear birds singing in the trees nearby. There are usually a few daisies waving on the curbside lawn. Spring is definitely the most pleasant season in Brisbane.

Last week I drew a watercolor picture titled "Outside the Window." On the left side of the picture is a soft curtain, indicating a warm and cozy room where the painter was. The right side of the paper shows the window, through which we can see a nice sunset street view. The central idea of the painting is that, despite the room where the painter was being warm and comfortable, they were longing for the freedom outside. The outside world is much bigger, more splendid, and more diverse.

To understand the picture, we can think of the many contrasts between the inside and the outside of the room. The inside of the room may represent a career you have been in for a long time and are very familiar with; consequently,you may be eager to switch to another career path. The inside of the room can also be a place you've lived in for a long time, and you now want to migrate elsewhere. Any of these interpretations are rational.

My research in process mining

 When I rejoined the BPM team at QUT in 2014, many changes had taken place. The team had been relocated to the newly built P-Block. Arthur was still the leader of the team, but Marcello had been promoted to become QUT's youngest professor in computer science, managing a large group of human resources. Research within the team had switched its focus from process automation to process mining—a discipline created by Professor Wil van der Aalst, whom I have always respected as a mentor, friend, and rival. Moe was my direct supervisor, but frankly, I did not appreciate her research that much.

"Why do you want to return to BPM?" Arthur asked me during the job interview.

"I want to do open-source projects," I replied. "The SAIVT group where I worked previously does not allow me to share source code with others, which negatively impacts the promotion of my research outputs. Everything I did at SAIVT was sound, accurate, and objective; there is nothing I wish to hide. I want people to understand my publications fully. I admire your effort to host open-source projects and create websites for each small research area."

At the end of the interview, Arthur welcomed my return warmly. He mentioned that he had not received any notifications of bugs in C-YAWL, indicating it was developed to a very high quality. I was pleased to learn that YAWL had been installed on the Tianhe-II supercomputer in China.

Process mining is a research area that investigates event logs from information systems using AI techniques. In control flow, I view it as a machine learning area that focuses on data with timestamps as attributes. Within control flow, the core task is to automatically generate a workflow model from transactional logs stored in the databases of information systems. Typically, this workflow is represented as a Petri net.

Wil's team in the Netherlands operates a large open-source project called ProM. It uses a highly innovative method to incorporate new algorithms in this area as plug-ins, a strategy I consider to be very advanced. Wil's contributions to this field are by no doubt the largest in the world. However, at the beginning, I did not think he was exceptionally brilliant because, in my view, all the technical foundations were based on a single model: the Petri net. Later, I reflected on this and realized that in speech recognition, the primary model used was always the Hidden Markov Model (HMM) and its variations. We should not expect every model to be applied across a number of domains of applications. Artem, a young but excellent researcher from Ukraine, told me he heard Wil worked 12 hours a day. Then if that is the case, Wil is still very common! I thought to myself, though I did not dare to speak this out publicly.

The first time I felt Wil was truly unusual was during the writing of a paper on 3D visualization. I wrote the literature review section, and Arthur praised me extensively, saying it was exactly the correct style for a literature review, though he provided a few suggestions. While I agreed with him, I also thought his suggestions were merely theoretical, as I had never read a paper written in that manner. Wil later rewrote the final version. Ah! I fully admitted that Wil's version was much better. This made my own contribution to the paper feel minor.

However, Arthur suggested that I should be the first author, and he noted that Erik had agreed with this arrangement. I kept silent, and from then on I understood why the authorship of the C-YAWL paper would have problems. Then, Moe snatched the first author position. Arthur was confused and asked me why I did not compete for it.

"It's Erik's business," I told him. "Only he is qualified to compete for first authorship."

One day, Moe instructed me to draft the evaluation session for a paper on resource queueing, stating that we needed to finish it that same day. I worked incredibly hard but still could not finish it on time. I ultimately submitted the paper to them the next day.

Soon after, the annual performance review arrived just before the Christmas holidays. Moe blamed me for not finishing the paper on time.

"But I only delayed for a day," I argued.

"You delayed for a day, but Wil went on holiday immediately after," Arthur said. "Your one-day delay pushed back the submission of the paper by at least two months."

After the New Year, the paper underwent a few revisions before final submission. When Wil read the paper, he sent us an email saying that he liked it a lot, especially the evaluation section. Consequently, my draft remained unchanged in the final published version.

I was deeply grateful for Wil's confirmation. From then on, I believed Wil was truly a better leader than Arthur, even though I remained unsatisfied with how the C-YAWL paper was handled.

MAY SPRING COME

A few days ago, when I was jogging in Bernie Brae Park nearby, I was startled by a swooping magpie, which has allowed me to suddenly realise that it was already September and winter has quietly given way to spring here in Brisbane. As is my yearly springtime tradition, I played the Japanese song "May Spring Come”, and this year on the dizi (Chinese bamboo flute).

From a very young age, I have read countless poems and prose pieces praising the beauty of spring. Ironically, spring used to be my least favorite season. Growing up in my hometown, I remembered spring as being constantly wet, misty, and drizzly. The dampness often made me feel gloomy. "This is so different from the scenes described in poems!" I used to wonder. 

Later, I moved to Xi'an for university. Winter in Xi'an is bitter cold, causing all the trees and bushes—except for the pine trees—to lose their leaves. But when spring arrives, the foliage sprouts anew, bursting into a green so vibrant that you can hardly spot a trace of yellow or brown. Blossoms bloom, flowers flourish, and birds sing around the city.

Spring is always the best season in Brisbane. The days grow longer than the nights. The sunshine is bright but not yet too harsh. If you can dodge the swooping magpies, it is the most pleasant time to play on the park lawns, admire the colorful flowers, and enjoy picnics under the shade of the trees.

However, inside the house, you sometimes start spotting insects, ants, and cockroaches. The most annoying nuisance of all is the sheer number of houseflies. I remember when I was living with my grandma in Indooroopilly, many a morning a bowl of noodles that was prepared by grandma had already been waiting for me before I even got out of bed.

"I’ve cooked some noodles for you!" Grandma said.

"But wait!" she suddenly exclaimed.

She quickly grabbed a fly swatter and smacked a housefly resting on the edge of the bowl.

"Ah, I got rid of the fly!" she said proudly.

Uh, I really wish you hadn't done that! I thought to myself. I felt sick to my stomach, imagining the dirt from the swatter falling straight into my breakfast. But unwilling  to voice my thoughts to her, I ate the whole bowl anyway, pretending I didn't mind it at all.

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From video to Wi-Fi sensing

Ten years ago, one of my classmates, Kien, who came from Vietnam and later worked at QUT, invited me to help him support his student’s project on multi-spectrum survellance event detection. This was because I had undertaken a student project on video surveillance event detection when we studied together on the same course. The term "multi-spectrum" means the integration of cameras, infrared sensors, and radar, as visible light, infrared light, and microwaves are all electromagnetic waves in different spectrums.

"Are you kidding?" I said to Kien. "Do you believe your student can understand that much within a course? Radar is a fierce animal that is hard to tame!"

"Well, we may not have time to do radar. But we've discussed starting with the camera, and using your previous project as the baseline. However, we need to use deep learning techniques..." he said.

"But I don't think the datasets in this area are big enough for deep learning models, which contain too many layers and parameters. I'm sure your model will be overfitted," I said to him frankly.

"At first, we will just use a model with pre-trained parameters," he said.

"You can do things this way if you merely want to have good experimental results to publish papers by using an overfitted model."

I said, "But the results are only beautiful on paper, and cannot be used in applications. Ah, there are too many papers on this topic without any quantitative evaluations. Those even include those published in top journals from prestigious universities like MIT."

I continued, "When I was a student, my supervisor, Simon, asked his supervisor Sridha whether we could do the project without evaluations. He said MIT's papers didn't have any experimental results but they still could be published in IEEE-T-PAMI. But it was said Sridha couldn't accept anything without quantitative evaluations, no matter how others did it and who they were."

Then Kien's boss, Professor Clinton Fookes, came to greet me. He said the motivation for him to apply radar was to tackle occlusions in visual cameras. "There are some papers with algorithms that can detect an event outside a wall!"

I was shocked to see Clinton so confident in radar technology, as I had never heard of him investigating electromagnetic waves. "Nevertheless, I'm interested in it," I told Clinton, adding that I liked physical subjects such as electromagnetism and antenna theory very much when I was in my undergraduate course.

A few years later, I found the student had graduated with a master's degree, while not making much progress in either radar sensing or deep learning.

During those years, I also spent a couple of years in Shenzhen working on a project about Wi-Fi sensing. No outputs were achieved when I finished the job. I then returned to Brisbane.

In my opinion, this area is still too challenging to have any sensible research outputs. I don't believe the results in any paper in this field, as there are too many fundamental settings that haven't been solved.

Currently, classical machine learning models are primarily for text, images, and audio. As all those models are constructed based on assumptions, and because the characteristics of different data media differ significantly, the models cannot be shared without a high degree of adaptation. In fact, there is still a lack of an effective model for surveillance videos. I don't believe existing models can be directly applied to communication channel data.

The methods to collect data, annotate ground truths, and evaluate performance are far from being solved. Researchers often highlight the motivation of tackling occlusions, but no one in the literature I've read highlights the discussion about how to avoid influences from outside the room.

When I was studying in Xi'an, our university had some labs for electromagnetic wave research. I often heard people blaming the previous university chancellor Professor Liang Changhong for disagreeing with the building of an overpass near the campus.

This was said to lead to a poor relationship with the local authority in Xi'an City. But I think there must be a reason for the university leadership team to object to the idea. Most likely, the vehicles on the overpass would interfere with the experimental results of the labs.