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Author: camargomau

MAC/6th Semester/Procesos Estocásticos.md

@@ -101,7 +101,7 @@ In a Markov chain, the [[First-Passage Time|first-passage time]] from a state $i
 
 Similarly, the [[Recurrence Time|recurrence time]] of a state $i$ is the amount of steps it takes to _return_ to $i$ _for the first time_.
 
-We can calculate the [[Average First-Passage Time|average first-passage time]] from a given state $i$ to another state $j$. 
+We can calculate the [[S Études/S1 MAC/S1.6/S1.63.K Estocásticos/Incompleto/Average First-Passage Time|average first-passage time]] from a given state $i$ to another state $j$. 
 
 ## Absorption Probability
 

Mathematics/Exhaustive Enumeration Method for MDPs.md

@@ -26,7 +26,7 @@ The exhaustive enumeration method consists of the following steps.
 **Calculating the [[Expected Value|expected]] _long term_ cost for every policy $r$:**
 
 $$
-\mathbb{E}[C_{r}] = \sum_{i=0}^{m} C_{ik} \pi_{i}
+\mathbb{E}[C_{r}] = \sum_{i=0}^{m} C_{ik}\ \pi_{i}
 $$
 
 …where $C_{ik}$ denotes the cost incurred for making the decision $k$ (defined _according to the policy_) in the state $i$, while $\pi_{i}$ denotes the [[Steady State Probability|steady state probability]] of the state $i$ _given the policy_. 

Mathematics/First-Passage Time.md

@@ -15,4 +15,4 @@ In the context of a [[Markov Chain|Markov chain]], the **first-passage time** is
 
 Compare to the [[Recurrence Time|recurrence time]], which is the minimum amount of steps needed to _return_ to a given state (for the first time, too).
 
-We can obtain the [[Average First-Passage Time|average first-passage time]] for a given state when starting at another given state.
+We can obtain the [[C Scio/Mathematics/Average First-Passage Time|average first-passage time]] for a given state when starting at another given state.

Mathematics/Integral Transform.md

@@ -2,7 +2,7 @@
 date: 2024-02-01
 type: 🧠
 tags:
-  - MAC/6D
+  - MAC/6/ED2
 ---
 
 **Topics:** [[Integral Transform]]

Mathematics/Laplace Transform.md

@@ -0,0 +1,24 @@
+---
+date: 2024-02-01
+type: 🧠
+tags:
+  - MAC/6/ED2
+---
+
+**Topics:** [[Integral Transform]]
+
+---
+
+_**(definition)**_
+
+The **Laplace transform** is an [[Integral Transform|integral transform]] defined as:
+
+$$
+\mathcal{L}\{f(t)\} := \int_{0}^{\infty} e^{-st} f(t) \ dt = F(s)
+$$
+
+We can easily obtain the [[Laplace Transform of Simple Functions|Laplace transform various simple functions]]. We can prove [[Fundamental Theorems of the Laplace Transform|several fundamental theorems for Laplace transforms]]. 
+
+We can easily obtain the Laplace transform of a [[Piecewise Function|piecewise function]] by first [[Expressing a Piecewise Function with Shifted Unit Step Functions|rewriting the piecewise function in terms of shifted unit step functions]], then applying one of the previously mentioned fundamental theorems (see the corresponding note).
+
+We can assure the [[Laplace Transform Conditions of Existence|existence of a Laplace transform through the consequences of various theorems]].

Mathematics/MDP as a Linear Programming Problem.md

@@ -35,7 +35,7 @@ $$
 D_{ik} = \mathbb{P}(k \mid i)
 $$
 
-Id est, the probability of making the decision $k$ given that the state is in the [[State Set|state set]] $i$. 
+Id est, the probability of making the decision $k$ given that the system is in the [[State Set|state]] $i$. 
 
 Under this reinterpretation, we'll be actually using other variables in the [[Objective Function|objective function]]: $Y_{ik}$. These represent the [[Unconditional Transition Probability|unconditional]] [[Steady State Probability|steady state probability]] of being in the state $i$ _and_ taking the decision $k$, satisfying:
 

Mathematics/Policy Improvement Method for MDPs.md

@@ -58,4 +58,4 @@ $$
 
 The third and last step is to **determine whether we've obtained the optimal policy** or not, continuing with another iteration if it is not the case.
 
-If $r_{n+1} = r$, then we have the optimal policy. If not, then we shall make another iteration ($n \leftarrow n+1$ and back to step 1). 
+If $r_{n+1} = r_{n}$, then we have the optimal policy. If not, then we shall make another iteration ($n \leftarrow n+1$ and back to step 1). 

Mathematics/Unconditional Transition Probability.md

@@ -2,7 +2,7 @@
 date: 2024-04-04
 type: 🧠
 tags:
-  - MAC/N/PE
+  - MAC/6/PE
 ---
 
 **Topics:** [[Markov Chain]] - [[Transition Probabilities in a Markov Chain]]

Notkesto/Course Tag List.md

@@ -55,9 +55,9 @@ Programación Orientada a Objetos had no Scinotoj, so it has no associated tag.
 
 ## 6th Semester
 
-- #MAC/6/ES - Estadística II
-- #MAC/6/OP - Optimización II
+- #MAC/6/E2 - Estadística II
+- #MAC/6/O2 - Optimización II
 - #MAC/6/PE - Procesos Estocásticos
-- #MAC/6/ED - Ecuaciones Diferenciales II
-- #MAC/6/SE - Seminario Sobre Ética y Responsabilidad Social
+- #MAC/6/ED2 - Ecuaciones Diferenciales II
+- #MAC/6/SER - Seminario Sobre Ética y Responsabilidad Social
 - #MAC/6/DW - Desarrollo Web

Photography/A Camera is a Simple Device.md

@@ -0,0 +1,16 @@
+---
+date: 2024-06-24
+type: 🧠
+---
+
+**Topics:** [[Photography]]
+
+---
+
+Think about it: a camera is actually a **very simple device**. It's simply a device that can record light by focusing light on a photosensitive surface.
+
+It consists of three parts:
+
+- The [[Photosensitive Surface|photosensitive surface]], which records the light that incides on it.
+- The [[Camera Lens|lens]], which focuses the light on the photosensitive surface.
+- The [[Camera Body|body]], which puts it all together and is light-sealed so that just the light that wants to be captured gets in.

Photography/Photography Gear is the Medium.md

@@ -0,0 +1,14 @@
+---
+date: 2024-06-22
+type: 🧠
+---
+
+**Topics:** [[Photography]]
+
+---
+
+It can be easy to care more about photography gear than the art itself (see [[Photography is More About Art than Technology]]), but ultimately it's important to realise that **the gear is just the medium**.
+
+The gear is the medium that we use to record our vision. It's what allows us to take that photo, _the true goal_.
+
+Having great gear can be fulfilling and help us create better photos (technically, at least), but one must be cautious as to not let it distract us from what we're actually capturing, the final product. 

Photography/Photography is More About Art than Technology.md

@@ -0,0 +1,16 @@
+---
+date: 2024-06-22
+type: 🧠
+---
+
+**Topics:** [[Photography]]
+
+---
+
+With all the photography gear that's available nowadays, and the way it's pushed by manufacturers, it may be easy to fall into the trap of thinking that technology and gear are all that there is to photography. It may be easy to think that the latest technology is key for a good photo.
+
+It's not.
+
+While good gear certainly helps, **photography is more about art** than technology. Understanding gear can lead to technically good photos, but _great photos_ that touch the viewer need also an understanding of the artistic side of photography.
+
+Remember: [[Photography Gear is the Medium|gear is the medium]]. 

Self/Action Leads to Motivation .md

@@ -0,0 +1,28 @@
+---
+date: 2023-12-10
+type: 🧠
+aliases: ["L'appétit vient en mangeant"]
+---
+
+**Topics:** [[Productivity]] - [[Motivation]]
+
+---
+
+We often fall into the trap of wanting to feel motivated before doing something. We keep waiting for that motivation, procrastinating until it comes.
+
+Sure, motivation can come on it's own and, when it does, it can be very inspiring. However, that won't always happen. Motivation can only surely come once we've taken action. We will feel inspired once we've gotten started and the ball is rolling. 
+
+This is what's behind [[Habits are Built By Getting Used to the Habit First|habit building]].
+
+_**When nothing else inspires us, taking action is the first step. Motivation then comes and keeps us rolling.**_
+
+> [!tip] L'appétit vient en mangeant
+> There's this French phrase that summarises this concept nicely:
+> 
+> > L'appétit vient en mangeant.
+> > 
+> > _(Appetite comes by eating._)
+> 
+> We can't depend on appetite to get things done. Sometimes we have to start doing things to get an appetite.
+
+Do note that this is just a cycle, since [[Motivation Leads to Action]].

Self/Action Leads to Motivation.md

@@ -0,0 +1,10 @@
+---
+date: 2024-06-24
+type: 🧠
+---
+
+**Topics:** [[Self]]
+
+---
+
+When giving feedback, it's important for it to be **constructive** and **actionable**. This means it should have a positive attitude, lean towards improvement for the other person, as well as offer concrete advice as to _what_ can be improved and _how_ it can be improved.