Research notes
你生之前悠悠千載已逝，
未來還會有千年沉寂的期待
2025
2024
2023
2022
- Multivariate Fubini's Theorem
- Application of Fubini's Theorem
- Beta Distribution
- Integrating sin(x)/x from zero to infinity
- Lebesgue Integration of Complex Value Function
- Khintchine Inequality
- Independence
- Advanced Joint Convexity
- k-Center
- Set Cover
- Clarkson Type Inequalities
- Holder's Inequality
- Heavy-Tailed Distribution
- van Emde Boas Tree
- Report Noisy Max and Exponential Mechanism
- Approximate Densest Subgraph
- Sparse Vector
- Dijkstra's Algorithm With d-Ary Heap
- Total Variance Distance
- Borel Set
2021
- Range Min Query
- Random Variable
- Total Variation Distance and Product Measure
- Coupling Lemma
- Sum of Independent Laplacian Random Variables
- The Number of Binary Trees
- Nonmeasurable Sets
- The Weak and Strong Laws of Large Numbers For Rademacher
- Expectation with Hoeffding
- KLL Sketch
- Cauchy-Riemann Equations
- Power Series--Radius of Convergence
- Complex Mapping
- Data-Processing Inequality
- Fano’s Inequality
- Q-Digest
- Basic Entropy Inequalities
- Amplificatoin by Sampling
- Fubini's Theorem
- Jensen's Inequality
- Lebesgue Integral, Revisited.
- Logarithm Inequalities
- Poisson Tail Bound
- Maximum of Sub-Gaussian Random Variables
- Least Square Estimation Error Bound
- Dual Norm
- Azuma-Hoeffding Inequality
- AMS Sketch For Inner Product Estimation
- L0 Sampling
- AMS Sketch
- The Volume of Hamming Ball
- Sparse Recovery
- Norm of Random Variables
- Fast Fourier Transform In Finite Field
- The Poisson Approximation
- Pairwise Independent Bits
- Fingerprints for Testing Multi Set Equality
- Weighed Random Sampling
- The Number Of Empty Bins.
- k Minimum Values for Set Cardinality
- Beyond Chebyshev's Inequality
- Morris Counter
- Fast Fourier Transform
- Fourier Transformation
2020
- Gamma Function
- Hermitian Inner Products
- Complex Numbers
- Stirling's Approximation
- Inverting Functions
- Prime Number Density
- Releasing Histogram Privately
- SmallDB
- Propose-Test-Release
- PAC Learning From Countable Hypothesis Family
- Advanced Composition
- PAC Learning Basic
- Gaussian Distribution
- Gaussian Mechanism
- Laplace Distribution and Mechanism
- Randomized Response
- Gundam and DP
- Norm
- Bit Guessing Game
- Littlewood–Offord Problem
- Peeling
- Stochastic Multi-Armed Bandits
- Lebesgue Measure Construction
- Median-of-Mean
- Entropy and Message Transmission
- Entropy and Compression
- Entropy
- Integer Shortest Path
- Splay Tree
- Total Law of Variance
- Cycle-Core Connection Game
- Linear Transformation
- Catalan Number
- k-Core Decomposition
- Quake Heap
- Ball in Bins
- Sampling With Or Without Replacement
- LSH
- Working Set BST
- Hessian
- Norm with PSD Matrix
- Gradient Descent
- Characterizations of Beta-Smoothness
- Counting Triangle
- Primal-Dual Algorithm
- The Remainder Term in Taylor Series
- Eigenvalues, Eigenvectors and SVD
- Ellipsoid method
- Determinant, Cross Product and Cramer's-Rule
- Simplex
- Dual Program, Weak Duality, Complementary Slackness, Strong Duality
- Sparse Recovery with Count-Sketch
- Priority Sampling
- Newton's Method
- Online Frequent Directions
2019
- Polyhydra and Polytopes
- Unique Factorization
- Approximate Membership Problem
- AM-GM Inequality
- Frequency Estimators
- Polynomials
- Minimax Theorem
- Balanced Binary Search Tree
- Divided by Three
- Less Communication
- Primality Test
- Chinese Reminder Theorem and Euler's Totient Function
- Matrix Norm
- Kraft Inequality
- The Number of Distinct Elements
- Jaccard Similarity
- Multiplicative Weight Updates
- Monotone Class
- Partial Derivatives
- Lebesgue's Theorem
- Fundamental Theorem of Calculus
- Radon Nikodym Theorem
- Integral
- Exchanging Summation Order
- Function Convergence
- Compact Set
- Convergence Tests
- Reading Notes-Some basic theorems for real numbers
- The Hahn Decomposition
- Strong Duality
- Farkas' Lemma
2018
- Complex Integral
- Separation Plane Theorem
- RSA
- Fermat's Little Theorem
- Euclidean Algorithm
- Bellman Ford
- Fully Binary Tree
- Max Cut
- Facility Location Problem
- Confidence Interval of Berstein Inequality
- Interval Estimate
- Vertex Cover
- Heavy Hitter
- Consistent Hashing
- Birthday Paradox
- Projection of A Random Unit Vector on Its First Dimension
- Unbiased Estimator of Sampling Variance
- Empty Bins
- Connectivity Parameters
- Graph Sparsification
- Karger Algorithm I
- Random Points on Shpere
- Pairwise Independent Hashing
- Sampling Probability
- Fabonacci Number
- Bennett's Inequality
- SVD Computation
- FORA [1]