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Local vs Global seems to be one of the most important philosophies behind math. People in some fields call it “compactness”, others don’t. In short, it says that the property of an object is related to the property of every smaller subobject.
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This post briefly proves why the rational points of an elliptic curve is a group. The proof idea comes from MATH 214B, but I tried to use classical language.
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This posts briefly introduced what I learned on C++ 20 coroutine mechanism after I used it to imitate Python generator and ayncio. REPO
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This posts discusses the relation between two’s complement and 2-adic integer in math. I want to show what operations we can have if we ignore overflow.
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George is a fantastic teacher with very attractive lectures. I think his secret sauces include the following:
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Authentication (AuthN, 認証) and authorization (AuthZ, 承認) are important pieces in system security. In one word, AuthN verifies the identity of the requester, and AuthZ decides whether a specific operation is allowed.
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This is a review and summary for course MATH 220BC, given by Professor Artem Chernikov and Andrew Marks.
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This is a review and summary for course MATH 206A Combinatorics at UCLA, given by Prof. Igor Pak.
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This post introduces some tricks on polynomials widely used in ICPC. I will try to practice algebraic knowledge as well.
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Rephrase the chess picking problem in a more formal way.
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Misc things that are taught in class but not written in the note of MATH 210.
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Discuss POJ3557 Map Generator and its variants.
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This post makes notes on residue theorem and its application, since most non-mathematicians only need to remember this after learning complex analysis. Some definitions may be not defined very rigorously from a complex analysis view.
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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.
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In this post I want to analyze the stability of Dledger, a DAG-based distributed logging system.
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Service invocation is tricky. The protocol itself seems to be super simple: we call a function, and it returns. But the problem is, when the function is on another machine, how we know the state of that machine / the whole system. The developers of the caller do not want to care, so we protocol designers should care for them. But trying to make everyone happy is so tough here.
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There is always a need for service discovery and load balancing, but no universal solution. Sometimes naive ways may satisfy most needs.
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I find that some terms are confusing.
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TL; DR: Reflection should be used for encoding or serilization.
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When solving a problem, it is common that we have two different strategies that fit in different cases. For example, one algorithm may have a better time complexity but uses more memory than the other. Or, one is fast when there are only a few of large objects, but the other works better when there are many small objects. However, I found that there usually exists a solution which is a naive mixture of the two strategies, and its performance will be the sqrt of the two.