Compare this definition to 1-1 tensor Outer product

The uniqueness of adjoint operator lies in that inner product is non-degenerate

image segmentation By max flow

Obtain a max-flow and consider the residual graph

My Proof: Based on conservation law, split the network into s, L, R, t with nflow(L) = nflow(R) = 0, nflow(s) = excessive(t) for any split, thus max-flow <= min-cut.

Given a max-flow, remove an edge and reducing flow value from all down-stream flowing edge repetitively. Eventually total flow value of removed edge must = nflow(s) and it must be a cut (otherwise the original flow can be arugmented and not maximized).

Better Proof: The (net) outflow of a set of vertice equal the sum of net flow of each vertice (Just write the forumla) and is thus equal to zero due to conservation law. So nflow(A, s) + nflow(A, V \ A \ s) = 0 the former is = - nflow(s).

Still in development

超星电子书扒书指南（PDG转PDF）

Responsive CSS Design Without Breakpoint

\(l^2\)上的线性泛函若在一族无穷子基上每个向量都有\(f(v) \ge 1\), 则l不是有界的。考虑经典的\(\sum_n \frac{1}{n^2}\)

Hypothes.is annotation will be lost in this process of editing metadata, so as he says to make sure annotation are kept.

Charge Integration is Well-define

$$ \begin{array}{r} \text{ By Splitting }A_{i},B_{j},\text{ we have } \ A_{i} \cap B_{j}\text{ is not measure zero } \rightarrow \alpha_i = \beta_j \end{array} $$

By showing \( \mu \) is not affected by the selection of \(p, q\)

Use the limit structure of \(\mathbb{Q}, \mathbb{R}\) , wecan see that additive property leads to positive linar form

Note \(C - C = F^r \), apply linearity to see the form is indeed real.

Column/Row Decomposition for two family of vector in lattice

$$ (x + y)^+ = x^+ + y^+ $$ Link

Meet distribution

Obviously imaginary part is indeed real (its conguation equal to itself)

join and meet operation are compatible with lattice order

If any one of the following exists, the mid one exist. The equality follows from the fact that the two net are equivalent in cauchy sense.

The de morgan law apply to minus, join, meet as well

A record of data.

echo is basically identity function. ~> (echo 3) 3 ~> (echo 3) | describe int

In other word, the ... is also a glob. ~> let glob = ("..." | glob $in) ~> $glob ╭───┬─────╮ │ 0 │ C:\ │ ╰───┴─────╯ ~>

untrack file in git

git update-index --skip-worktree <files>

Dependently nested normal distribution is still normal distribution. See Here

作者主观揣测地认为这些政治人物的决策主要由政治与经济私利驱动的；但同时他不以同样的滤镜审视学生领袖的“民主愿景”。

这很不现实

The section address Bellman-Ford Algorithm.

Problem

In a directed graph, determine whether negative loop exist; if not, find shortest path from s to any node. (In other word, if negative loop exist, shortest path may not be found)

The containing block of absolute element must be nonstatic, which is the use of position:relative

So perfer rem for font-size and unitless number for else

The same argument can be used to justify the use of KL divergence

It's yoneda lemma!

Hamel basis

Log-Sum-Exp is calculating method to avoid underflow

Javascript in console to import and export all cookie

Python Data Science Bootstrap

Python pip & venv: Best Practices for beginner

Virtual envrionment

Safe ways to do things in bash

Python Installation Best Practice for Beginner

Data Science Python Project Structure

A list of P2P file sharing tools

Mathematics

Functional Analysis

Optimization by Vector Space Methods<br /> Lectures and exercises on functional Analysis<br /> Convex Functional Analysis<br /> Functional Analysis for Probability and Stochastic Processes<br /> Abstract Calculus A Categorical Approach <br /> Banach-Hilbert Spaces, Vector Measures and Group Representations

Differential Geometry

Clifford algebra, geometric algebra, and applications<br /> Mathematical Structures From Linear Algebra over Rings to Geometry with Sheaves<br /> Diffeology<br /> Global Calculus<br /> Manifolds, Tensor Analysis, and Applications<br /> Manifolds, Sheaves, and Cohomology

Algebra

Basic algebra groups, rings and fields<br /> Further Algebra and Application<br /> Abstract Algebra - Paul Garrett.

Linear Algebra

Algebra An Approach via Module Theory<br /> Linear Algebra via Exterior Products<br /> Rings, Modules, and Linear Algebra<br /> Modules and Homological Algebra<br /> Module theory an approach to linear algebra<br /> 代数学方法I

Measure, Probability and Statistics

A Basic Course in Probability Theory<br /> Probability Theory An Analytic View<br /> Probability and Stochastics<br /> Measure-Theoretic Probability<br /> Measure-Theoretic Calculus in Abstract Spaces<br /> Plane Answers to Complex Questions<br /> Mathematical Statistics<br /> Time Series Theory and Methods<br /> The Coordinate-Free Approach to Linear Models<br /> Multivariate Statistics A Vector Space Approach<br /> hypo

Logic Category Type

THE OPEN LOGIC TEXT<br /> Categorical Logic and Type Theory

Algebraic Topology

Fundamentals of Algebraic Topology<br /> Algebraic Topology - A Structural Introduction<br /> Homology, Cohomology, and Sheaf<br /> Combinatorial Algebraic Topology<br /> Algebraic Foundations for Applied Topology and Data Analysis<br /> Topology A Categorical Approach<br /> hypo

Combinatorics and Discrete

Introduction to the Theory of Species of Structures<br /> Discrete Calculus Methods for Counting<br /> Combinatorics the rota way

Biology

Genetics and Genomics in Medicine<br /> Genetics Analysis of Genes and Genomes githack<br /> hypo

Test

Dummy Githack Dummy Rawcdn

Programming

Programming Languages

What I Wish I Knew When Learning Haskell<br /> JavaScript the Definitive Guide<br /> Beginning C++23.pdf<br /> Programming Rust<br /> The Well-Grounded Rubyist<br /> Mathematica programming an advanced introduction<br /> Advanced R<br /> TypeScript Basics<br /> SQL Query Design Patterns and Best Practices<br /> SQL必知必会<br /> hypo

Web

CSS in Depth<br /> Vue.js 3 Design Patterns and Best Practices<br /> React in Depth <br /> Modern Full-Stack Development Using TypeScript, React, Node.js, Webpack, and Docker <br /> Fullstack Web Components<br /> Fullstack Vue 3<br /> Fullstack Rust<br /> Frameworkless Front-End Development<br />

Penetration

Black Hat Ruby<br /> Understanding Network Hacks<br /> Metasploit The Penetration Tester‘s Guide<br /> RubyFu

Certificate

CCNA

Cisco CCNA Simplified

Electrician

低压电工上岗速成

CS

PLType

Type Theory and Functional Programming.pdf<br /> The Hitchhiker's Guide to Logic.pdf<br /> Foundations for Programming Languages.pdf<br /> Formal syntax and semantics of programming languages<br /> Formal Reasoning About Programs<br /> Computation and reasoning A type theory for computer science

Language, Parse and Compile

Language Server Protocol & Implementation <br /> Crafting Interpreters<br /> Introduction to Compilers and and Language Design<br /> Techniques for Searching, Parsing, and Matching.pdf

LLM, ML, Data

Probability and Statistics for Machine Learning<br /> Machine Learning A Probabilistic Perspective<br /> Large Language Models A Deep Dive<br /> Foundations of Machine Learning<br /> Data Science for Mathematicians <br /> Transformers for Machine Learning

纺锤体极

Better local require() paths for Node.js

Use url/cdn import for javascript module. <br /> Use 'unpkg.com/...?module' to replace bare module specifier with absolute path.

note that xxx.yyy is required to assign property to exported value

super will remember the object literal it was defined on, so rebinding object won't change the output, but rebinding prototype of object itself or class' prototype can work. Note that when rebinding prototype, it's best to also rebind the class(constructor) function so that static methods are also rebound.

Q1. Previous Brainbow tools work quite well in various applications. Why did the author bother to improve it further?

Q2. What issues do Brainbow 3.x address? And how did the authors achieve that? (Hint: 6 sentences won’t be able to cover all the improvements that 3.x made. Please describe only two aspects).

Q3. What is the purpose of making Flpbow? Can you give an example of using it in combination with Brainbow?

It's worth mentioning that javascript a.p = (b.p = c) will set a.p = c, i.e. the return value in b.p setter is meaningless

The file Content

preserve_interword_spaces 1

mypdfocr中文识别空格问题

Make PDF file searchable OCRmyPDF

test

\(\epsilon\) here is not necessary. The statement is more precise

Positive/Negative stands for whether support the alternative hypothesis, in which case always exist.

githack is a proxy tool for changing content-type header and is useful with via.hypothes.is for pdf

Hypo Link

Hypo Link

Two alternative css position:absolute bottom: 0; transform: translateY(100%); css /* remove top, bottom simple position:absolute would suffice*/

Both are not necessary: absolute without specified value will cause element to appear at its normal flow positon without affecting other.

best practice: use aria-label on the button

Percentage for fixed element refer the viewport

flex-basis initial value is auto, note short-hand empty set it 0%

For functions whose range is uniform space, the function then thus be defined as uniform space: $$ (f_1 \times f_2) (X) \subseteq U $$ Where \(U\) is entourage. We can apply Moore-Osgood Theorem to such function \( f(x, y) \) if \(f_x \rightrightarrows f\)

External <link><br /> Internal head > style<br /> inline <tag style="...">

It's actually possible. see Link

User-agent, User, author

Together, each \(x \in \theta_0\) and each \(y \in \theta_1\) intersect, making the map surjective.

In term of congruence, it means \(I_i \vee I_j = R\), which make decomposition map for algebra with permutable congruence surjective

Mathematical Structures From Linear Algebra over Rings to Geometry with Sheaves

几乎消除