## Algebra Miscs

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Misc things that are taught in class but not written in the note of MATH 210.

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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.

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京都大学の応用解析学通論Bのノート