Test used in the video
=====four freebies of constructive arithmetic=====
Ref:
https://www.amazon.com/Constructivism-Mathematics-Studies-Logic-Foundations/dp/0444702660
Nikolaj-K
/ scalargrad.py
Last active
October 23, 2023 21:31
A simple implementation of reverse accumulation (back-propagation)
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| """ | |
| Impelmentation of reverse accumulation (backpropagation), discussed in | |
| https://youtu.be/BcCk8I6YAqw | |
| Most of this script is exposition code. The reverse accumulation code still runs if you delete everything except the following 5 classes | |
| * ValAndDVal, ExprBaseRevAcc, VarExprRevAcc, PlusExprRevAcc, MultExprRevAcc | |
| validated using the following 2 functions: | |
| * p, run_VarExprRevAcc_gradient_decent_demo |
Nikolaj-K
/ bandit_strategies.py
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October 10, 2023 15:59
A small pytorch routine approaching the n-armed bandit problem
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| """ | |
| Casino strategies and some pytorch. The code is explained in the video | |
| https://youtu.be/VUVVVi9CgbI | |
| I think you can install pytorch via `pip` or `pip3` through | |
| `pip3 install torch torchvision` | |
| Some mathy reading material: | |
| * http://yuanz.web.illinois.edu/teaching/IE498fa19/ |
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| """ | |
| Code discussed in the video: | |
| https://youtu.be/0A3mAUGFUow | |
| * Motivation: | |
| - Relation between Legendre symbol and quadratic equations on ZxZ | |
| + See https://en.wikipedia.org/wiki/Legendre_symbol#Table_of_values | |
| * For any fixed number, validate |
Nikolaj-K
/ copious_secret_santa.py
Last active
August 19, 2023 18:01
Copious Secret Santa / Voting assignment
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| """ | |
| Script used in the video | |
| https://youtu.be/2b9fOpX0zKY | |
| Formal structure: balanced simple digraph | |
| (Important special properties out-degrees equals the in-degrees, no self-loops, no parallel arrows) | |
| 1. Proof task: Count them, given any assginment of out-degrees. | |
| How does it compare to just random disgraphs with that those out-degrees? | |
| 1. Coding task: Generate one given the out-degrees, fast. (I have a bad, probabilistic solution) |
Nikolaj-K
/ make_voting_assignment.py
Last active
October 28, 2023 10:40
Create a HV-MT voting assignment based on a list of capacities
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| """ | |
| Scirpt discussed in video here: | |
| https://youtu.be/2b9fOpX0zKY?si=hjztP-RAwIgq_Yed | |
| HV-MTL Voting assignment based on users with different voting capactities per day. | |
| More formally: Generation of a balanced simple digraph* (and corresponding plot) | |
| based on a vertex set and their number of outgoing edges, | |
| with a high number of opposing edges (reciprocated votes percentage is a config). |
Nikolaj-K
/ constructive_arithmetic_freebies.md
Last active
September 23, 2023 12:14
Four freebies of constructive arithmetic
Nikolaj-K
/ absorbing_markov_chains.py
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October 1, 2023 12:06
Absorption probabilities in finite Markov chains
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| """ | |
| Code used in the video | |
| https://youtu.be/BiViLT6FCC4 | |
| """ | |
| import random | |
| import numpy as np | |
| class LinAlgLib: # Linear algebra'ish functions |
Nikolaj-K
/ regularity_vs_induction.md
Last active
November 8, 2022 01:24
Regularity versus Induction
Text used in this video:
==== Recall the regularity statement ====
==== Logical definitions and theorems ==== === Definitions ===
Nikolaj-K
/ regularity_nonstandard.md
Last active
September 7, 2022 13:51
Regularity and non-standard models of arithmetic #PaCE1
Text used in the video
==== Regularity statement ====
https://en.wikipedia.org/wiki/Axiom_of_regularity
(Classically)
Text used in the video
==== ==== ==== ==== ==== ==== ==== ==== ==== ==== ==== ==== ==== ====
Theorem:
More concretely:
If equality is governed by set-extensionality, then for any predicate