From this comes marvelous adaptations of which this is the procedure .

Transistor-Level Inverter

• Inverter layout dimensions were modified for a 180nm process.
• Source and drain lengths were minimized to 0.27um to reduce parasitics.

NAND Gate

• NAND gate layout dimensions were modified for a 180nm process.
• Source and drain lengths were minimized to 0.27um to reduce parasitics.

Photosynthesis: The Basis of Life

• Autotrophs sustain themselves without consuming organic molecules from other organisms.
• Photoautotrophs use light energy to produce organic molecules.
• Photosynthesis converts light energy into chemical energy and produces oxygen.
• Heterotrophs consume plants, animals, or decompose organic material.

Photosynthesis Occurs in Chloroplasts

• Chloroplasts are the sites of photosynthesis in plants.
• Chlorophyll, a pigment in chloroplasts, converts solar energy to chemical energy.
• Mesophyll is the green tissue in the interior of leaves.
• CO2 enters and O2 exits the leaf through stomata.
• Veins deliver water absorbed by roots.
• Stroma is the thick fluid enclosed by two chloroplast membranes.
• Thylakoids are interconnected membranous sacs suspended in the stroma.
• Thylakoids enclose the thylakoid space.
• Grana are stacks of thylakoids.

Scientific Inquiry: Chloroplasts in Photosynthesis

• Theodor Engelmann illuminated alga with light passed through a prism in the 1800s.
• Aerobic bacteria congregated around alga segments exposed to red-orange and blue-violet light.
• Engelmann concluded that bacteria gathered where the most oxygen was released by photosynthesis.

Two Stages of Photosynthesis

• Photosynthesis, like respiration, is a redox process.
• In photosynthesis CO2 becomes is reduced to sugar (endergonic).
• Water molecules are oxidized, they lose electrons (exergonic).

The Two Stages of Photosynthesis

• The two stages of photosynthesis are light reactions and the Calvin cycle.

The Light Reactions

• Light reactions occur in the thylakoid membranes.
• Water is split, providing electrons and H+, releasing O2 as a by-product.
• Light energy is absorbed by chlorophyll, driving electron and H+ transfer from water to NADP+, forming NADPH.
• ATP is generated through chemiosmosis via photophosphorylation.

The Calvin Cycle

• The Calvin cycle occurs in the stroma.
• CO2 is incorporated into organic compounds in carbon fixation.
• Following carbon fixation, carbon compounds are reduced to sugars.
• The Calvin cycle requires NADPH and ATP from the light reactions to produce sugar.

The Light Reactions: Solar Energy to Chemical Energy

• Visible light drives the light reactions.
• Electromagnetic spectrum includes all electromagnetic wavelengths.
• Visible light includes the wavelengths that drive photosynthesis.
• Photons are discrete packets of energy that light behaves as.
• Pigments, or light receptors, absorb some wavelengths and reflect other wavelengths.
• Chlorophyll absorbs blue-violet and red-orange light and reflects green light.

Photosystems Capture Solar Energy

• A photosystem consists of an antenna complex and a reaction-center complex.
• The Antenna complex contains pigment molecules that absorb light and pass it on to the reaction center.
• The reaction-center complex contains a molecule that receives electrons from the antenna complex and passes them to an electron transport chain.

Photosystems Cooperate in Light Reactions

• Photosystem II (PS II) functions first
• Photosystem I (PS I).
• The reaction center of PS II is P680, absorbing light at 680 nm.
• The reaction center of PS I is P700, absorbing light at 700 nm.

ATP and NADPH Generation in Light Reactions

• A photon strikes a pigment molecule in PS II, boosting an electron to a higher energy level
• Excited electrons are captured by the primary electron acceptor in PS II.
• An enzyme extracts electrons from water and supplies them to P680+, replacing the electrons, which splits water into hydrogen ions and oxygen, forming O2.
• Photoexcited electrons pass PSII to PSI via an electron transport chain.
• The exergonic "fall" of electrons provides energy for ATP synthesis by chemiosmosis.
• Light energy excites an electron of P700 in photosystem I, then it is captured by photosystem I's primary electron acceptor.
• Photoexcited electrons are passed to an electron transport chain from PS I to NADP+, which is reduced to NADPH.

Chemiosmosis Powers ATP Synthesis in the Light Reactions

• Chemiosmosis produces ATP using the energy of H+ gradients across membranes to phosphorylate ADP.
• The electron transport chain pumps H+ across the thylakoid membrane, generating a gradient.
• ATP synthase uses the energy of the gradient to make ATP.

The Calvin Cycle: Making Sugar

• Calvin cycle occurs in the stroma.
• Carbon enters the cycle as CO2 and leaves as sugar.
• The Calvin cycle uses ATP and NADPH to reduce carbon dioxide to sugar.

Three Phases of the Calvin Cycle

• Carbon fixation: CO2 is incorporated into organic molecules in the chloroplast.
• Reduction: ATP and NADPH are used to reduce 3-PGA to G3P.
• Release of one molecule of G3P: For every three molecules of CO2 that enter the cycle, one molecule of G3P is produced.
• Regeneration of RuBP: The remaining G3P is used to regenerate RuBP, which enables the cycle to continue.

Other Methods of Carbon Fixation

C3 Plants

• In C3 plants, the first product of carbon fixation is a three-carbon compound, 3-PGA.
• On hot, dry days, C3 plants close their stomata to conserve water.
• When CO2 decreases and O2 increases in the leaf, photorespiration occurs.

C4 Plants

• C4 plants preface the Calvin cycle with an alternative mode of carbon fixation that forms a four-carbon compound as its first product.
• The four-carbon compound acts as a CO2 shuttle and moves CO2 from the mesophyll cells to the bundle sheath cells. It proceeds with the Calvin cycle even if the stomata are closed and CO2 concentration in the leaf is low

CAM Plants

• CAM plants conserve water by opening their stomata and admitting CO2 only at night.
• CO2 is fixed into a four-carbon compound.
• The four-carbon compound banks CO2 at night and releases it to the Calvin cycle during the day.

Photosynthesis Reduces Global Warming

• Greenhouse effect: Solar radiation warms the Earth's surface, and radiating heat is absorbed by gases which reflect some of the heat back to Earth. It keeps Earth warm enough to support life.
• Global warming involves increasing concentrations of greenhouse gases, including CO2.
• Photosynthesis moderates global warming by removing CO2 from the atmosphere and storing it in plant biomass.

Areas Between Curves

• Let $A$ is the area of the region bounded by the curves $y = f(x)$, $y = g(x)$ and the lines $x = a$ and $x = b$, where $f$ and $g$ are continuous and $f(x) \geq g(x)$ for all $x$ in $[a, b]$, then: $$ A = \int_a^b [f(x) - g(x)] dx $$

How to find Area between Curves

• Trace the curves
• Find the intersection points of the curves
• Find the superior function $f(x)$ and the inferior finction $g(x)$
• Integrate the difference between those functions over the defined interval.

Matrix, Geometry & Mathematica: The Cross Product

Motivation

• A way of multiplying two vectors in $\mathbb{R}^{3}$ to get another vector in $\mathbb{R}^{3}$
• Works ONLY in $\mathbb{R}^{3}$

Definition

• For $\mathbf{v} = \begin{bmatrix} v_{1} \ v_{2} \ v_{3} \end{bmatrix}$ and $\mathbf{w} = \begin{bmatrix} w_{1} \ w_{2} \ w_{3} \end{bmatrix}$, then the cross product is

$\mathbf{v} \times \mathbf{w} = \begin{bmatrix} v_{2}w_{3} - v_{3}w_{2} \ v_{3}w_{1} - v_{1}w_{3} \ v_{1}w_{2} - v_{2}w_{1} \end{bmatrix}$

Mnemonic for the definition

$\mathbf{v} \times \mathbf{w} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \ v_{1} & v_{2} & v_{3} \ w_{1} & w_{2} & w_{3} \end{vmatrix} = \begin{vmatrix} v_{2} & v_{3} \ w_{2} & w_{3} \end{vmatrix}\mathbf{i} - \begin{vmatrix} v_{1} & v_{3} \ w_{1} & w_{3} \end{vmatrix}\mathbf{j} + \begin{vmatrix} v_{1} & v_{2} \ w_{1} & w_{2} \end{vmatrix}\mathbf{k}$

Important properties

• $\mathbf{v} \times \mathbf{w} = -\mathbf{w} \times \mathbf{v}$
• $\mathbf{v} \times \mathbf{v} = \mathbf{0}$
• $\mathbf{v} \times \mathbf{w}$ is orthogonal to both $\mathbf{v}$ and $\mathbf{w}$.
• $\left | \mathbf{v} \times \mathbf{w} \right | = \left | \mathbf{v} \right |\left | \mathbf{w} \right | \sin \theta$, where $\theta$ is the angle between $\mathbf{v}$ and $\mathbf{w}$.
• $\left | \mathbf{v} \times \mathbf{w} \right | $ is the area of the parallelogram with sides $\mathbf{v}$ and $\mathbf{w}$.

Matlab 1: Introduction to Matlab

• Matlab lets you create several subwindows: Current Folder, Command Window, Workspace, Command History etc

Using Matlab as a Calculator

• Type in the equation on a command line, and press enter to output the answer.

Defining Scalar Variables

• Use the assignment operator (=)
• Variable names are case sensitive

Defining Matrixes

• You can use square brackets to define matrixes ([]).
• Seperate by commas, or spaces for colums
• Seperate by semicolons for rows

Script Files

• Create new 'm' files of executable code

Plotting Simple Graphs

• Use the plot function

2024 Goals

• Data Scientist
• Master linear algebra, calculus, probability, and statistics
• Have expertice in these concepts: supervised learning, unsupervised learning, and deep learning.
• Enter at least 10 Kaggle competitions
• Study at least 20 hours a week
• Complete at least 1 personal project

Chemistry: Inorganic Compounds

Introduction

• The IUPAC (International Union of Pure and Applied Chemistry) develops standards to denominate elements and chemical compounds.

Types of Compounds

• Oxides: Combination of an element with oxygen.
  • Basic oxides: Metal + Oxygen
  • Acid oxides (anhydrides): Nonmetal + Oxygen
• Hydrides: Combination of hydrogen with another element
  • Metallic hydrides: Metal + Hydrogen
  • Nonmetallic hydrides: Nonmetal + Hydrogen (gaseous, acidic)
• Hydracids: Nonmetallic hydrides that have an acidic character in aqueous solutions e.g.
• Hydroxides: Combination of a metal with the hydroxide group (OH-)
• Acids Oxoacids: Combination of an acid oxide with water.
• Binary Salts: Combination of a metal with a nonmetal (different from oxygen or hydrogen)
• Oxisales: Combination of an oxoacid with a hydroxide

Oxidation numbers Definition

• The number reprensents the electrical charge on an atom in a chemical compound.

Common Oxidation Numbers

• The number of oxidation of the oxygen is -2 (except in peroxides, that is -1).
• The number of oxidation of the hydrogen is +1 (except in metallic hydrides, That is -1)
• The number of oxidation of an ion monoatomico is equal to his load.
• The sum of the numbers of oxidation of all the atoms in a neutral compound is zero.

Prefixes

• Mono (1), di (2), tri (3), tetra (4), penta (5), hexa (6), hepta (7), etc.

Naming Compounds with varying Oxidation values

• Single: Use the suffix "-ico".
• Two: use -oso (minor oxidation number) or ico
• For four oxidation states use the 'hypo' y with the suffixes osos, -oso, 'ico' also pre 'per' and suff 'ico"

Algorithmic Game Theory

Definition of Game Theory

• Study of mathematical models of strategic interactions among rational agents; economics, political science, biology, and computer science.

Definition of Normal-Form Games

• The players choose their strategies simultaneously

What Normal-Form games are defined by

• A set of players $N = {1, 2,..., n}$
• A set of strategies for each player $S_i$
• A payoff function for each player $u_i: S_1 \times S_2 \times... \times S_n \rightarrow \mathbb{R}$

What makes Nash Equilibrium special

• No player has an incentive to deviate from their chosen strategy, assuming that the other players do not deviate.

Normal formula for Nash Equilibrium

$u_i(s_i^, s_{-i}^) \geq u_i(s_i, s_{-i}^*)$

Dominated Strategies

• If the payoff of another strategy is strictly higher than the payoff of others,

$(s_i', s_{-i}) > u_i(s_i, s_{-i})$

Calculus

Definition

• From a set D to a set R is a rule that assigns to each element x in D a unique element y in R.
• The set D is called the domain
• y is the value of f(x) if x is assigned. The range of all results would be in set R.
• Independent variable is x
• Dependant variable is y and relates to the independent bariable.
• Dependant varables depends on independent variables. Also, equations may define a fu.

Definition

• The Domain is required to consider x values that may be excluded in results. That said, values like (-1)^0.5 are not valid since that is an even root that can only be positive. Similarly, values such 3/0 are not valid since a zero cannot be on the bottom of a fraction.

Functions

• Even Functions: $f(-x) = f(x)$, is symmetric compared to the y-axis
• Odd Functions: $f(-x) = -f(x)$, is symmetric compared to the origin

Combinations of Functions

• Sum:(f + g)(x) = f(x) + g(x)
• Substracation:(f g)(x) = f(x) g(x), Domain: A intersect B
• Compositions (f0g)(x) - F(g(x))