Mill Pond Research’s Post

Some useful mathematical formulas....

EVEN mode: BATMATH curve with Mathematica ;-) See for example this link : you tube https://lnkd.in/eeM7EXrP (I have slight corrections)

Last week we covered various techniques for calculating derivatives and broke down some parts of gradient descent. Today, we continue this theme and calculate derivates using symbolic math. This breakdown will allow you to come up with derivatives for the sum of squares function. Using this we can actually create a pretty robust method for finding local minima in Linear Regression (More on that tomorrow). What I like most about this method is that it is extremely easy to do and can be done in under 7 lines of code if we remove whitespace. Note that we are not actually using numerical values here. All values are symbolic. A few key takeaways for this breakdown: ➡️Uses symbolic math to set up linear regression equations ➡️Defines variables for slope (m) and y-intercept (b) ➡️Calculates the sum of squared errors function ➡️Finds partial derivatives of the error function ➡️Prepares for finding the best-fit line, but doesn't actually solve for it ➡️Translates math concepts into code for further analysis P.S. Have you seen my YouTube channel? I break down complicated math and stats into fun videos. I already have one on the 'Birthday Paradox' and the next video will be about the 'Monty Hall' problem. It comes out in a little under 2 weeks. Link in the comments below.

CppNorth, The Canadian C++ Conference 2024 • July 21-24, 2024 • Toronto Preview: Ben Deane: "Message Handling with Boolean Algebra" Please Like, Follow, & Share: CppNorth, The Canadian C++ Conference https://lnkd.in/gvM2Y98q Message reception and dispatch is something common to many codebases. And deep down, we know that Boolean algebra underlies everything we do. But we seldom give it a second thought, or if we do, we probably dismiss it as trivial; something we learned in college and quickly outgrew. This talk shows the unreasonable effectiveness of going back to basics and really understanding and unlocking the power of Boolean algebra in the design of a message handling library. We'll talk about separating message layout and semantics, how to match against messages for dispatch, and particularly how to compose and simplify constraints at compile time, in order to do the least at runtime. We'll also introduce Boolean implication and see a non-obvious application which is key to a generic approach. Finally we'll see how message matchers can be generically transformed using compile-time information, allowing complete flexibility of expression and maximum runtime performance. Registration is open: store.cppnorth.ca (select 'Early Bird') Make your room reservations now: https://lnkd.in/g-2dePpQ

"This post serves as a tutorial on EnKF. It will introduces the basic mathematics of EnKF, provide step-by-step code, and showcase the practical implementation using a toy case." Don't miss Wencong Yang's accessible guide to data assimilation with the ensemble Kalman filter.

➡️In Class print("Hello, World!") Result: "Hello, World!" 🥱 ➡️Homework : def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) print(factorial(5)) # Output: 120 Reality: "Wait, why is my recursion depth exceeded?! 🤯" ➡️Exam import numpy as np def forward_propagation(X, weights, biases): z = np.dot(weights, X) + biases a = 1 / (1 + np.exp(-z)) # Sigmoid activation return a X = np.array([[1], [0]]) weights = np.random.rand(1, 2) biases = np.random.rand(1, 1) print(forward_propagation(X, weights, biases)) Exam Stress: "What is this math? Where did np.exp come from? Why is this running on paper and not a computer?! 😭"

I am happy to say that.(108/180) This week I have completed the entire topic of Opps from these lectures I learned the topics below 1 various types of class. 2 object 3 static vs dynamic memory allocation. 4 constructor create 5 copy constructor 6 Destructor. 7 Static data member. 8 Encapsulation . 9 Abstracction. 10 Inheritance. 11 multiple inheritance. 12 multilevel inheritance. 13 Hierarchical inheritance. 14 hybride inheritance. 15 multipath inheritance. 16 poly morphism 17 vurtual function 18 Exeption Handeling. 19 filehandling

"Maths is the mother of all Science". 😡 People think Maths is not important for web3 or any dapp. This is complete lie, if you want to deep dive into like zero knowledge proofs and want to do some revolutionary kind of things like Elon Musk and Sam Altman, they must have to make their fundamentals strong in Maths, because "maths is the mother of all Science". So, for you, if anyone want to make their linear algebra great, here's the surprise for you: This github is Awesome for "Linear Algebra", link: https://lnkd.in/eK-ad4Mx and yeah Graphic notes on Gilbert Strang's "Linear Algebra for Everyone". There is chinese and japanese version also. With Quality graphic notes. I think this is the best notes for Linear algebra, go for it.

Today I am simply working through some basic oversights, lost in the shuffle when doing fancy simulations: I just patched up "-d" to accept no input or "std::cin" as input (as "-h" promises); but for now the std::cin mode only accepts one graph typed into the command line. One can combine it with input files listed in sequence, and one can specify "std::cin" more than once. I intend today to rewrite this early code all over again with my improved knowledge of C++ and of streams; I'd like to be able to enter graphs ad nauseum on the fly; I also intend to use established technique to write a formula parser and criterion consisting of a formulaic equality or inequality, i.e. that twice the radius is at most the diameter done graph by graph (rather than just noting the extreme min or max of a run). Earlier I found C++ already has infinity built in, so that is up and running as the result of say girth measure applied to a tree or to a forest (I've also added forest and tree as separate correct concepts).

introduction to the tidyverse package in R and its features, including basic operations such as creating vectors, matrices, and lists, and performing basic arithmetic operations such as addition, subtraction,