Xueba's life simulator

Chapter 65 Laplacian Matrix and Artificial Intelligence

The content on the screenshot is probably the promise Zhou Ming made to Bi Wanfang, that is, Zhou Ming said that he would produce two research results that could be published in Nuture within one month after the start of school.

In addition, Zhou Ming also learned from this answer what Li Yanghua did not tell him, that is, Bi Wanfang's postgraduate students will be sent by Zhou Ming within that month.

"That's right, I did say that, what's wrong?" Zhou Ming admitted it openly.

"One month, two research results, you can still go to Nuture. Brother Zhou, are you sure you're not joking?" It is estimated that Zhao Letian has been holding the phone all the time. Zhou Ming's message has just been sent, and Zhao Letian Bian returned the message.

"Do you think I'll joke about this kind of thing?" Zhou Ming asked instead.

"It's all right, when are you coming back?" Hearing Zhou Ming's words, Zhao Letian knew what he meant, and after getting Zhou Ming's confirmation, he simply replied and asked.

"I'm afraid it will be after midnight when I go back to school at night. I'll find a hotel in front of the school to sleep overnight and go back to school tomorrow." Zhou Ming said.

Besides, today is the last day of the May [-]th holiday. If it had been the first two nights, Zhou Ming might not have been able to find an empty hotel room at the school gate.

The prices of hotels next to the university are not much different from hotels in other places, and there are many vacant rooms.

However, once it comes to weekends or other legal holidays, the price will skyrocket. It is trivial to increase by two or three times, and that's it, if you don't book early, it will be difficult to get a room.

As for why this happens, I can only say that I understand everything.

Zhou Ming only knew this information from Liu Tianlu. After all, Liu Tianlu had a partner in their dormitory, and he had never stayed in a hotel near the school.

Zhao Letian did not reply to Zhou Ming's news again, because he had already returned to pretending to be aggressive.

"That's right, I can confirm that the answers of this answerer who only dares to remain anonymous and dare not disclose information are almost all true." Zhao Letian replied under the anonymous answer, pretending to be coercive.

Zhao Letian is almost famous now, especially about Zhou Ming's answer.

And under the anonymous answer, the previous comments are almost all in disbelief.

But now after Zhao Letian replied, those who saw this answer and clicked on the comments all left a sentence of "my grass" under Zhao Letian's comment.

However, since it was almost late at night, this answer did not attract much attention.

After tonight and tomorrow's fermentation, I'm afraid this matter will soon attract a lot of people's attention.

……

number four.

That day happened to be Monday, and classes were full in the morning. After Zhou Ming returned to school, he returned to the dormitory after completing his daily exercise. The kids in the dormitory had just gotten up.

"Brother Zhou, what were you doing last night? I heard that Shen Xueba was still in school yesterday?" Liu Tianlu saw that Zhou Ming didn't come back last night, so he walked to him and looked at him with a smirk on his face. He asked him in a low voice.

"What are you thinking? Do you think I'm the same as you? I really had something to do yesterday." Zhou took a look at Liu Tianlu and sneered back.

"What do you mean being the same as me? Don't talk nonsense, I'm a gentleman." Liu Tianlu defended himself.

Seeing that Zhou Ming came back, Zhao Letian whispered to Liu Tianlu, and also came up to him, saying, "You two are muttering here, what are you talking about? What kind of gentleman?"

"Liu Tianlu said that he has never stayed out at night. He is a gentleman." Zhou Ming said first.

"Hey~~~, Liu Tianlu, you still want to say that you are often not seen on Friday and Saturday nights, and you still say that you have never been away at night?" Zhao Letian looked at Liu Tianlu and said disdainfully.

Everyone in the dormitory knew why Liu Tianlu stayed up all night. When Liu Tianlu saw that he was being rebelled by Zhou Ming, he became angry and got entangled with Zhou Ming.

"Okay, okay, I still have to go to class. If Zhou Ming doesn't go, then he doesn't have to go. If you are late, you will have to deduct your usual points." Liu Xiao saw that Liu Tianlu had just woken up and hadn't even brushed his teeth yet. Just started playing around with Zhou Ming, and urged.

After being reminded by Liu Xiao, Liu Tianlu remembered that he still had to attend class.

"Damn, I almost forgot after taking a few days off. It's all Zhou Ming's fault." Liu Tianlu went to get his toothbrush while still blaming Zhou Ming.

Zhou Ming didn't go to the classroom with Shen Qingqiu today, and he went back to the dormitory just to get his laptop.

Not long after Zhao Letian and the others left the dormitory, Zhou Ming also left the dormitory with his laptop and went to the library.

Zhou Ming’s last contribution to the "Mathematics Yearbook" "The node set of the Laplace characteristic function: the proof of the lower limit of the Nadilashvili conjecture and Qiu's conjecture" is only about "the nodes of the Laplace characteristic function set" part.

This time, Zhou Ming came to the library with his laptop, just to publish another part of "The Node Set of Laplace Characteristic Function".

That's right, Zhou Ming is still preparing to write a paper this time, and it is also a mathematics paper. This is his third mathematics paper.

Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure.
This is the title, and the Chinese meaning is "Node Sets of Laplacian Eigenfunctions: Polynomial Upper Limit Estimation of Hausdorff Measures."

“Abstract. Let M be a compact C^∞-smooth Riemannian manifold of dimension n, n ≥ 3, and let φλ:M φλ+λφλ= 0 denote the Laplace eigenfunction on M corresponding to the eigenvalue λ. We show that…

As soon as Zhou Ming arrived at the library, he turned on the computer, and after writing the title, he began to write the abstract.

In this paper, it is proved that the Hausdorff measure estimates the set of zeros of the Laplacian eigenfunction defined by a compact smooth manifold.

This paper, and the previous one, are able to advance the use of Laplace's spectrum and node sets.

Spectral graph theory is an important field of graph theory and combinatorics. Its main research includes three major matrices: adjacency matrix, Laplacian matrix and unsigned Laplacian matrix.

We also call the set of matrix eigenvalues ​​the spectrum of a graph, and the study of the corresponding spectrum is: adjacency spectrum, Laplacian spectrum, and unsigned Laplacian spectrum.

The two mathematical papers submitted by Zhou Ming to the "Mathematics Yearbook" are both related to Laplace spectrum. One of the main reasons why he chose these two papers is that Laplace matrix is ​​the core and basic concept in spectral graph theory. , which has important applications in machine learning and deep learning.

Machine learning and deep learning are crucial in artificial intelligence.

Including but not limited to Laplacian eigenmaps and locality-preserving projections in manifold learning data dimensionality reduction algorithms, spectral clustering algorithms in unsupervised learning, graph-based algorithms in semi-supervised learning, and graph neural networks, etc.

There are also many problems in image processing and computer graphics.

Understanding the definition and properties of the Laplacian matrix is ​​the basis for mastering these algorithms. Zhou Ming's research on this aspect will also benefit his future research on artificial intelligence.

It can be said that mathematics is the foundation of most science and engineering subjects, even some majors in biology have relatively high requirements for mathematics.

(End of this chapter)