vault backup: 2023-05-23 17:05:48

Affected files:
.obsidian/graph.json
.obsidian/workspace-mobile.json
.obsidian/workspace.json
STEM/AI/Literature.md
STEM/AI/Neural Networks/MLP.md
STEM/AI/Properties.md
STEM/Quantum/Orbitals.md
STEM/Quantum/Schrödinger.md
STEM/Quantum/Wave Function.md
STEM/Signal Proc/Convolution.md
STEM/Signal Proc/Image/Image Processing.md
STEM/img/hydrogen-electron-density.png
STEM/img/hydrogen-wave-function.png
STEM/img/orbitals-radius.png
STEM/img/radial-equations.png
STEM/img/radius-electron-density-wf.png
STEM/img/wave-function-nodes.png
STEM/img/wave-function-polar-segment.png
STEM/img/wave-function-polar.png

AI/Literature.md

@@ -1,7 +1,7 @@
 #lit
 [https://web.stanford.edu/~jurafsky/slp3/A.pdf](https://web.stanford.edu/~jurafsky/slp3/A.pdf)
 [Towards Data Science: 3 Things You Need To Know Before You Train-Test Split](https://towardsdatascience.com/3-things-you-need-to-know-before-you-train-test-split-869dfabb7e50)
-[https://machinelearningmastery.com/train-final-machine-learning-model/](https://machinelearningmastery.com/train-final-machine-learning-model/)
-[https://medium.com/@canerkilinc/hands-on-tensorflow-2-0-multi-label-classifications-with-mlp-88fc97d6a7e6](https://medium.com/@canerkilinc/hands-on-tensorflow-2-0-multi-label-classifications-with-mlp-88fc97d6a7e6)
-[https://stackoverflow.com/questions/61557536/how-tensorflow-keras-go-from-one-hot-encoded-outputs-to-class-predictions-for](https://stackoverflow.com/questions/61557536/how-tensorflow-keras-go-from-one-hot-encoded-outputs-to-class-predictions-for)
-[https://stackoverflow.com/questions/35226198/is-this-one-hot-encoding-in-tensorflow-fast-or-flawed-for-any-reason/35227732#35227732](https://stackoverflow.com/questions/35226198/is-this-one-hot-encoding-in-tensorflow-fast-or-flawed-for-any-reason/35227732#35227732)
+[train-final-machine-learning-model](https://machinelearningmastery.com/train-final-machine-learning-model/)
+[hands-on-tensorflow-2-0-multi-label-classifications-with-mlp](https://medium.com/@canerkilinc/hands-on-tensorflow-2-0-multi-label-classifications-with-mlp-88fc97d6a7e6)
+[stackoverflow - how-tensorflow-keras-go-from-one-hot-encoded-outputs-to-class-predictions-for](https://stackoverflow.com/questions/61557536/how-tensorflow-keras-go-from-one-hot-encoded-outputs-to-class-predictions-for)
+[stackoverflow - is-this-one-hot-encoding-in-tensorflow-fast-or-flawed-for-any-reason](https://stackoverflow.com/questions/35226198/is-this-one-hot-encoding-in-tensorflow-fast-or-flawed-for-any-reason/35227732#35227732)

AI/Neural Networks/MLP.md

@@ -19,4 +19,4 @@ A finite feed-forward MLP with 1 hidden layer can in theory approximate any math
 ![[tlu.png]]
 - $o_1$ to $o_4$ must all be one to overcome -3.5 bias and force output to 1
 ![[mlp-non-linear-decision.png]]
-- Can generate a non-linear decision boundary
+- Can generate a non-linear [[Decision Boundary|decision boundary]]

AI/Properties.md

@@ -36,13 +36,13 @@ Explanation-based learning uses both
 ## Level of Explanation
 -   Classical has emphasis on building symbolic representations
 	-   Models cognition as sequential processing of symbolic representations
--   Neural nets emphasis on parallel distributed processing models
+-   [[Properties+Capabilities|Neural nets]] emphasis on parallel distributed processing models
 	-   Models assume information processing takes place through interactions of large numbers of neurons
 
 ## Processing style
 -   Classical processing is sequential
 	-   Von Neumann Machine
--   Neural nets use parallelism everywhere
+-   [[Properties+Capabilities|Neural nets]] use parallelism everywhere
 	-   Source of flexibility
 	-   Robust
 
@@ -50,7 +50,7 @@ Explanation-based learning uses both
 -   Classical emphasises language of thought
 	-   Symbolic representation has quasi-linguistic structure
 	-   New symbols created from compositionality
--   Neural nets have problem describing nature and structure of representation
+-   [[Properties+Capabilities|Neural nets]] have problem describing nature and structure of representation
 
 Symbolic AI is the formal manipulation of a language of algorithms and data representations in a top-down fashion
 

Quantum/Orbitals.md

@@ -1,14 +1,6 @@
-$$\psi(r,\theta,\phi)=R(r)\cdot Y_{ml}(\theta, \phi)$$
-Wave functions are products of
-Radial Function
-- $R_{n,l}(r)$
-Spherical Harmonic
-- $Y_{ml}(\theta, \phi)$
+[[Wave Function]]
 
-Absolute value of wave function squared gives probability density of finding electron inside differential volume $dV$ centred on $r, \theta, \phi$
-
-$$|\psi(r,\theta,\phi)|^2$$
-# Quantum Numbers
+## Quantum Numbers
 $$n$$
 Principal quantum number
 - 1, 2, 3...
@@ -23,4 +15,31 @@ Orbital Angualar Momentum Number
 $$m$$
 Z-component / Magentic of $l$
 - $-l$ to $+l$
-- ***Orientation*** of orbital
+- ***Orientation*** of orbital
+
+![[wave-function-polar-segment.png]]
+
+## Filling
+
+1.  Aufbau
+	-  Start lowest in energy
+2.  Pauli's Exclusion
+	-  Max two electrons per orbital
+	-  No two electrons can have same n, l, m, s tuple
+3.  Hund's Rule of Maximum Multiplicity
+	-  Orbitals with same energy filled one at a time
+	-  Degenerate
+
+![[orbitals-radius.png]]
+![[wave-function-nodes.png]]
+
+## Radial
+![[radial-equations.png]]
+
+- Z = Atomic number
+- Bohr radius
+	- $a_0=\frac \hbar {\alpha mc}$
+- Normalisation
+	- $\int_0^\infty r^2R_{nl}^*R_{nl}dr=1$
+
+![[radius-electron-density-wf.png]]

Quantum/Schrödinger.md

@@ -1,6 +1,6 @@
 $$-\frac{\hbar^2}{2m}\nabla^2\psi+V\psi=E\psi$$
 - Time Independent
-- $\psi$ is the wave function
+- $\psi$ is the [[Wave Function]]
 
 Quantum counterpart of Newton's second law in classical mechanics
 

Quantum/Wave Function.md

@@ -0,0 +1,21 @@
+$$\psi(r,\theta,\phi)=R(r)\cdot Y_{ml}(\theta, \phi)$$
+Wave functions are products of
+Radial Function
+- $R_{n,l}(r)$
+Spherical Harmonic
+- $Y_{ml}(\theta, \phi)$
+
+Forms [[Orbitals]]
+
+Absolute value of wave function squared gives probability density of finding electron inside differential volume $dV$ centred on $r, \theta, \phi$
+
+$$|\psi(r,\theta,\phi)|^2$$
+![[wave-function-polar.png]]
+
+![[hydrogen-wave-function.png]]
+![[wave-function-polar-segment.png]]
+![[wave-function-nodes.png]]
+
+![[hydrogen-electron-density.png]]
+
+![[radius-electron-density-wf.png]]

Signal Proc/Convolution.md

@@ -6,13 +6,13 @@ $$x(t)=x_1(t)\circledast x_2(t)=\int_{-\infty}^\infty x_1(t-\tau)\cdot x_2(\tau)
 
 # Properties
 1. $x_1(t)\circledast x_2(t)=x_2(t)\circledast x_1(t)$
-	1. Commutativity
+	- Commutativity
 2. $(x_1(t)\circledast x_2(t))\circledast x_3(t)=x_1(t)\circledast (x_2(t)\circledast x_3(t))$
-	1. Associativity
+	- Associativity
 3.  $x_1(t)\circledast [x_2(t)+x_3(t)]=x_1(t)\circledast x_2(t)+ x_1(t)\circledast x_3(t)$
-	1. Distributivity
+	- Distributivity
 4. $Ax_1(t)\circledast Bx_2(t)=AB[x_1(t)\circledast x_2(t)]$
-	1. Associativity with Scalar
+	- Associativity with Scalar
 5. Symmetrical graph about origin
 
 # Applications
@@ -23,4 +23,8 @@ $$x(t)=x_1(t)\circledast x_2(t)=\int_{-\infty}^\infty x_1(t-\tau)\cdot x_2(\tau)
 	- Find system output given input and transfer function
 
 # Polynomial Multiplication
--   Convolving coefficients of two poly gives coefficients of product
+-   Convolving coefficients of two poly gives coefficients of product
+
+# Discrete
+$$G[i,j]=H[u,v]\circledast F[i,j]$$
+$$G[i,j]=\sum^k_{u=-k}\sum^k_{v=-k} H[u,v]F[i-u,j-v]$$

Signal Proc/Image/Image Processing.md

@@ -0,0 +1 @@
+[[Convolution#Discrete]]