# Golden Gate Assembly

Golden gate assembly is a cloning method capable of assembling multiple DNA inserts with compatible overhangs into a vector with the use of a single restriction enzyme (ex. BsaI), in a single reaction. The restriction enzyme has a cut site separate from the recognition sequence, allowing a person to design his own overhangs that are complementary to the part that needs to be ligated together.

After adding ligase, the different parts ligate together in the desired order based on the overhangs that were designed. Using golden gate allows you to efficiently ligate multiple parts together in one reaction.

# Anti-Fungal

## Raw Data Tables

Table 1A. Mycelial growth of Sclerotinia sclerotiorum in dark or light conditions. Growth was tracked for six days after culturing and measurements were taken once a day in eight different (controlled) directions. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm from the plate. This data corresponds to Figure 1A in the Anti-Fungal page.

Table 1B. Mycelial growth of Pestalotiopsis microspora in dark or light conditions. Growth was tracked for six days after culturing and measurements were taken once a day in eight different (controlled) directions. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm from the plate. This data corresponds to Figure 1B in the Anti-Fungal page.

Table 2A. Mycelial growth of Sclerotinia sclerotiorum with pheophorbide a in dark conditions. Eight treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 1, 2.5, 5, 10, 15, 20, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Treatment discs were placed 2.5 cm from the epicentre of the fungal culture on a potato dextrose agar plate. Growth was tracked for four days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. This data corresponds to Figure 2A in the Anti-Fungal page.

Table 2B. Mycelial growth of Sclerotinia sclerotiorum with pheophorbide a in light conditions. Eight treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 1, 2.5, 5, 10, 15, 20, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Treatment discs were placed 2.5 cm from the epicentre of the fungal culture. Growth was tracked for four days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm from the plate. This data corresponds to Figure 2B in the Anti-Fungal page.

Table 3A. Mycelial growth of Pestalotiopsis microspora with pheophorbide a in dark conditions. Eight treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 1, 2.5, 5, 10, 15, 20, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Treatment discs were placed 2.5 cm from the epicentre of the fungal culture. Growth was tracked for six days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. This data corresponds to Figure 3A in the Anti-Fungal page.

Table 3B. Mycelial growth of Pestalotiopsis microspora with pheophorbide a in light conditions. Eight treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 1, 2.5, 5, 10, 15, 20, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Treatment discs were placed 2.5 cm from the epicentre of the fungal culture. Growth was tracked for six days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm from the plate. This data corresponds to Figure 3B in the Anti-Fungal page.

Table 4A. Mycelial growth of Sclerotinia sclerotiorum in different light conditions. Growth was tracked for six days after culturing and measurements were taken once a day. Each point is the average of eight measurements in different (controlled) directions. Each point is the average of eight measurements in different (controlled) directions. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm or 2 cm from the plate. This data corresponds to Figure 4A in the Anti-Fungal page.

Table 4B. Mycelial growth of Pestalotiopsis microspora in different light conditions. Growth was tracked for six days after culturing and measurements were taken once a day. Each point is the average of eight measurements in different (controlled) directions. Each point is the average of eight measurements in different (controlled) directions. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm or 2 cm from the plate. This data corresponds to Figure 4B in the Anti-Fungal page.

Table 5A. Mycelial growth of Sclerotinia sclerotiorum with pheophorbide a in close light conditions. Five treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 5, 15, 25, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Two treatment discs for each concentration were placed 1.5 cm from the epicentre of the fungal culture. Growth was tracked for six days after culturing. Measurements were taken once a day (with an additional measurement at day 2.5) from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 2 cm from the plate. This data corresponds to Figure 5A in the Anti-Fungal page.

Table 5B. Mycelial growth of Pestalotiopsis microspora with pheophorbide a in close light conditions. Five treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 5, 15, 25, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Two treatment discs for each concentration were placed 1.5 cm from the epicentre of the fungal culture. Growth was tracked for six days after culturing. Measurements were taken once a day (with an additional measurement at day 2.5) from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 2 cm from the plate. This data corresponds to Figure 5B in the Anti-Fungal page.

Table 6A. Mycelial growth of Sclerotinia sclerotiorum with pheophorbide a in dark conditions. Five treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 5, 15, 25, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Two treatment discs for each concentration were placed 1.5 cm from the epicentre of the fungal culture. Growth was tracked for four days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. This data corresponds to Figure 6A in the Anti-Fungal page.

Table 6B. Mycelial growth of Sclerotinia sclerotiorum with pheophorbide a in light conditions. Five treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 5, 15, 25, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Two treatment discs for each concentration were placed 1.5 cm from the epicentre of the fungal culture. Growth was tracked for four days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm from the plate. This data corresponds to Figure 6B, 9A, 9B, 9C, and 9D in the Anti-Fungal page.

Table 7A. Mycelial growth of Pestalotiopsis microspora with pheophorbide a in dark conditions. Five treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 5, 15, 25, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Two treatment discs for each concentration were placed 1.5 cm from the epicentre of the fungal culture. Growth was tracked for four days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. This data corresponds to Figure 7A in the Anti-Fungal page.

Table 7B. Mycelial growth of Pestalotiopsis microspora with pheophorbide a in light conditions. Five treatments were applied as treatment discs impregnated with pheophorbide a, solubilized in 25% acetone (0, 5, 15, 25, 35 mg/mL). The 0 mg/mL treatment was 25% acetone. Two treatment discs for each concentration were placed 1.5 cm from the epicentre of the fungal culture. Growth was tracked for six days after culturing. Measurements were taken once a day from the epicentre of the original culture to the edge of the mycelial growth toward the disc. Growth is maxed at 4.2 cm due to the potato dextrose agar plate capacity. Light conditions were done using 1400 lumen white LED light at a distance of 25 cm from the plate. This data corresponds to Figure 7B in the Anti-Fungal page.

# Chlorophyll Repurposing

## SDS-PAGE Confirmation of HCAR and PPH Purification (Replicates 1, 2, 3, 5)

SDS-PAGE Confirmation of HCAR and PPH Purification Replicate 1

SDS-PAGE Confirmation of HCAR and PPH Purification Replicate 2

SDS-PAGE Confirmation of HCAR and PPH Purification Replicate 3

SDS-PAGE Confirmation of HCAR and PPH Purification Replicate 5

## Thin Layer Chromatography and Pheophytinase (PPH) Characterization

Figure A1. Thin Layer Chromatography Analysis of Chlorophyll derivatives.Samples were eluted using 100% hexane solvent and flexible cellulose plates. Lanes (read left to right) contain pheophorbide a, pheophytin, chlorophyll a and b.

Figure A2.Thin Layer Chromatography Analysis of Chlorophyll derivatives.Samples were eluted using 100% acetone solvent and flexible cellulose plates. Lanes (read left to right) contain pheophorbide a, pheophytin, chlorophyll a and b.

Figure A3. Thin Layer Chromatography Analysis of Pheophytinase Reactions. Samples were eluted using a methanol:hexane (70:30) solvent system on a silica plate. Lanes (read left to right) contain pheophytin, pheophytinase + reaction buffer, pheophytin + pheophorbide a, elution 3 day reaction, elution 3 60 minute reaction, elution 3 10 minute reaction, pheophorbide a without reaction buffer. . Reaction buffer: 25 mM Tris-HCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X-100.

Figure A4.Thin Layer Chromatography Analysis of Pheophytinase Reactions. (Replicate #1) Samples were eluted using a methanol:hexane (70:30) solvent system on a silica plate. Lanes (read left to right) contain 24 hour reactions using Nickel-NTA purified PPH elution fraction 3, 2, 1, whole cell lysate (containing recombinant PPH) fraction 2, 1, pheophytin + reaction buffer solution, pheophytin + pheophorbide a + reaction buffer. Reaction buffer: 25 mM Tris-HCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X-100. This is one of three replicates. The left figure is the raw image taken using an LG G6 Camera whereas the right is the same image with modified brightness:contrast ratio using the imaging software FIJI.

Figure A5. Thin Layer Chromatography Analysis of Pheophytinase Reactions (Replicate #2).Samples were eluted using a methanol:hexane (70:30) solvent system on a silica plate. Lanes (read left to right) contain 24 hour reactions using Nickel-NTA purified PPH elution fraction 3, 2, 1, whole cell lysate (containing recombinant PPH) fraction 2, 1, pheophytin + reaction buffer solution, pheophytin + pheophorbide a + reaction buffer. Reaction buffer: 25 mM Tris-HCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X-100. This is one of three replicates. The left figure is the raw image taken using an LG G6 Camera whereas the right is the same image with modified brightness:contrast ratio using the imaging software FIJI.

Figure A6. Thin Layer Chromatography Analysis of Pheophytinase Reactions (Replicate #3).Samples were eluted using a methanol:hexane (70:30) solvent system on a silica plate. Lanes (read left to right) contain 24 hour reactions using Nickel-NTA purified PPH elution fraction 3, 2, 1, whole cell lysate (containing recombinant PPH) fraction 2, 1, pheophytin + pheophorbide + reaction buffer solution, pheophorbide a without reaction buffer. Reaction buffer: 25 mM Tris-HCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X-100. This is one of three replicates. The left figure is the raw image taken using an LG G6 Camera whereas the right is the same image with modified brightness:contrast ratio using the imaging software FIJI.

# Artificial Neural Network (ANN)

## Machine Learning/ Deep Learning

Artificial neural networks (ANNs) are non-parametric machine learning computational structures that can be utilized as function approximators (Jain et al., 1996).They consist of a graph of nodes that form an input layer, hidden layers, and an output layer. The nodes of the input layer receive input data, which is typically multi-dimensional. The other nodes in an ANN compute weighted sums of their input values, usually (but not always) from nodes in preceding layers. As the majority of these nodes comprise the hidden layers of the neural network, the hidden layers are responsible for intelligently prosecuting the computational function of the ANN. Finally, the output layer contains a number of output nodes corresponding to the problem assigned to the neural network. For example, an ANN created for a regression problem should have 1 output node, while an ANN created for an n-class classification problem should have n nodes to create a probability distribution for selecting classes.

Figure TODO: The general layout of a neural network consists of an input layer, one or more hidden layers, and an output layer

The output of any given node in a neural network is given as: $$f(\sum_{i=0}^{m}(w_{i}x_{i})+b)=Y$$ where $$f$$ is a normalizing activation function such as softmax, $$m$$ is the total number of inputs from previous nodes to the node, $$x_{i}$$ are the individual inputs from the previous nodes, $$w_{i}$$ are the individual weights assigned to each node edge connection, $$b$$ is a constant modifier value known as a bias, and $$Y$$ is the output of the node.

Figure TODO:Node function for a node with two input values

With the specific weights and biases for each node in a neural network each being a variable, the cost/error function of a neural network is an extremely high-dimensional function.

ANNs learn how to solve problems through the supervised learning technique of backpropagation (Williams and Zipser, 1995). Backpropagation uses gradient descent to incrementally adjust the parameters of the ANN through multiple epochs of training with labeled training data so that the model approaches local minimums in error. The general formula of backpropagation can be described as $$\Theta ^{t+1}=\Theta ^{t}-\alpha \frac{\mathrm{dE(X,\Theta ^{t}))} }{\mathrm{d} \Theta }$$ where $$\alpha$$ defines the learning rate, $$\Theta ^{t}$$ defines the weight and bias parameters of the ANN at an iteration $$t$$ in the training, and the error function $$E(X,\Theta ^{t})$$ defines the error between predicted and label target values for the model.

When creating the training data for neural networks, typically some labelled data is omitted from the training data. This data is known as testing data, and it is not seen by ANNs when training. In order to determine neural networks’ abilities to generalize to new data, the performance of neural networks on the testing data is evaluated. Significantly lower accuracy on testing data relative to training data performance indicates memorization, instead of learning. Therefore, in order to achieve high levels of general accuracy, ANNs require large volumes of labelled data; ANNs are unsuitable to be applied to problems where there is insufficient labelled data. With proper data and learning optimizations, ANN architectures can be utilized as powerful modelling tools.

## References

1. Jain, A. K., Mao, J., & Mohiuddin, K. M. (1996). Artificial neural networks: A tutorial. Computer. 29(3): 31-44. dio: 10.1109/2.485891
2. Williams, R. J. & Zipser, D. (1995). Gradient-based learning algorithms for recurrent networks and their computational complexity. In Y. Chauvin & D. E. Rumelhart (Eds.), Developments in connectionist theory. Backpropagation: Theory, architectures, and applications (pp. 443-486). New Jersey, NJ: Lawrence Erlbaum Associates, Inc.

# Support Vector Classification

## Theory

Support Vector Classification (SVC) provides a classification approach which finds a hyperplane that divides two classes of vectors within a space. The goal is to find the maximum margin between the labelled data and generate parameters for a hyperplane that would divide this margin. The optimization problem of generating a separating hyperplane between two classes holding $$n$$ data points can be summarized: $$\max_{\beta_0, \beta_1, \beta_2, \beta_3, \epsilon_i, \ldots, \epsilon_n} \mathcal{M}$$ subject to, $$\beta_0^2 + \beta_1^2 + \beta_2^2 + \beta_3^2 =1$$ $$y_i(\beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \beta_3 x_{i3} \geq \mathcal{M}(1-\epsilon_i)$$ $$\sum\limits_{i=0}^{n} \epsilon_i \leq \mathcal{C}, \>\>\>\>\> \epsilon \geq 0, \>\>\>\>\> y_i \in \{1, -1\}.$$ Where $$\mathcal{M}$$ is the size of the margin, $$\beta_i$$ are the parameters defining the hyperplane, $$y_i$$ is the label of each vector which can only be 1 or -1. $$\epsilon_i$$ is the error for each vector which is constrained by $$\mathcal{C}$$, the cost parameter (James et al. 2017).
Since we have four phase classes to be separated, we applied the one-versus-one approach, where divisions were constructed for each pair of classes, meaning this optimization was solved 6 times - $${4}\choose{2}$$ is the number of distinct pairs between $$4$$ elements.) Since the data is not linearly separable, a non-linear radial basis function (RBF) was used as a kernel: $$K(v_0, v_i) = e^{- \; \gamma \; v_0 \; \dot \; v_i}$$ Where $$v_0$$ is the vector to be labelled, and the kernel is applied on each training vector $$v_i$$ for this test observation. $$\gamma$$ is a parameter subject to choice.
The second parameter $$\mathcal{C}$$ specifies the amount of errors allowed within the separating hyperplane, allowing the adjustment of the model’s bias-variance trade off. This trade off is an important consideration in the approximation of any function. Approximations that are more flexible have greater variance (tend to follow the data closely) and have low bias. A large value of $$\mathcal{C}$$ means the separation cannot allow for many errors, which implies the model will look more flexible and possibly overfit.

# K -Nearest Neighbours

## Theory

The aim of a general classification model is to provide the likelihood a new unlabelled vector lies within a class. The $$\mathcal{K}$$-Nearest Neighbours method is a non-parametric approach which looks at the $$\mathcal{K}$$ nearest (in terms of distance) vectors within the space and assigns a label based on those closest neighbours. The probability given a vector from described above will be labeled with phase can be calculated with KNN by: $$Pr( \> Y = y \> | \> X = v) = \frac{1}{\mathcal{K}} \sum_{i \in \mathcal{N}}^{} I(\> y_i = y \>)$$ Where $$i$$ indexes through the $$\mathcal{K}$$ nearest vectors in $$\mathcal{N}$$ and I is the identity function which outputs a 1 if the label of the neighbour is equal to and 0 otherwise (James et al. 2017).

# Educational Package

This education package was designed as a training package for the new members of the iGEM 2019 team and was taught by the returning members. This package includes a list of learning outcomes, lecture slides, laboratory manuals, assignments and worksheets, and bioinformatics guides for wet lab. For dry lab the package includes lecture slides, and assignments and worksheets. The full package can be downloaded here.

The wet lab package is as follows and can be downloaded here.
Lecture Slides
1. Introduction to molecular Biology
2. DNA Parts and Genetic Circuits
3. Bioinformatics
4. Experimental Chassis
5. DNA Manipulation Part 1
6. DNA Manipulation Part 2
7. DNA Manipulation Part 3
8. DNA Manipulation Part 4
9. DNA/RNA/Protein Interactions
10. RNA and Protein Assays
11. Synthetic Biology to Address Real World Issues

Laboratory Manuals and Assignments
Lab 1= Ligations and Transformations
Lab 2= Polymerase Chain Reactions
Lab 3= Minipreps and Digest Confirmations
A laboratory coordinator guide is also provided.

Assignments and Worksheets
Biotechnology Company Presentation
Problem-solving assignment
Restriction mapping exercise
Bioinformatics worksheet
The rubrics and answer keys are also provided.

Bioinformatics Guides
Guides for Benchling, BLAST, Mendeley, NCBI, and OligoAnyalyzer are provided.

The dry lab package is as follows and can be downloaded here.
Lecture slides
1. Introduction to iGEM
2. Dry Lab Crash Course for Wet Lab Members
3. Human Practices
4. Web Development
5. Process Engineering Basics
6. Hardware Programming

Assignments and Tutorials
Past projects analysis
Human Practices assignment
Website demonstration
Modelling approaches
Hardware programming

# Mean Green Machine

## Materials List

Pieces Required for Mean Green Machine
Piece Name Material Thickness Amount
Top Link Steel 3/8 " 2
Top Bushing Lexan 1/4 " 2
Top Lexan 1/4 " 1
Right Lexan 1/4 " 1
Left Lexan 1/4 " 1
Hinge Lexan 1/4 " 4
Back Lexan 1/4 " 1
Front Lexan 1/4 " 1
Door Bottom Bushing PLA 3/4" 2
Door Top Bushing PLA 3/4" 2
Door Lexan 1/4 " 1
Camera Holder Lexan 1/4 " 1
Camera Top Lexan 1/4 " 1
Camera Stop Lexan 1/4 " 1
Camera Side Lexan 1/4 " 2
Camera Lip Lexan 1/4 " 1
Camera Front Lexan 1/4 " 1
Camera Back Lexan 1/4 " 1
Bottom Link Steel 3/8 " 2
Base Acrylic 1 " 1
Back Lexan 1/4 " 1
Bolt Steel 1/4 " 10
Nut Steel 1/4 " 6
Camera - - 1
LED Lights - - 1 Strip
Light Diffuser Translucent Plastic - 1

# Genetic Algorithms

Genetic algorithms are a subset of evolutionary algorithms. (Coello et al, 2007)

## How do they work

Just like evolutionary algorithms, genetic algorithms attempt to replicate life and evolution. Instead of trying to find the optimal solution to a problem mathematically, genetic algorithms create a population of possible solutions, evaluate them (which is often easier than fixing them) and then picking the top performers, then mutating and performing crossover on the remaining solutions to create a new population of possible solutions. genetic algorithms return the set of solutions when either convergence is achieved or an arbitrary number of generations have passed.

A major advantage of using genetic algorithms to solve complex problems is that there is no need to create a complex algorithm. Which is why the book cited in this section has 1790 references, most of which are applications.

## References

Coello, C. A. C., Lamont, G. B., & Veldhuizen, D. A. V. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems Second Edition. Boston (MA): Springer.

# SPEA2

## Multi-Objective Optimization Problems

For multi-objective optimization problems such as optimizing codons for both maximizing expression and minimizing repeats, it is very difficult to assign weights before heavy studying of the specific problem definition and solutions associated to the problem. (Coello et al, 2007) is a great read on multiobjective evolutionary algorithms and all information in this section will refer to this book.

Remember that whilst optimizing for one objective there is usually a unique optimal solution, but multiple objective optimization there is an uncountable set of solutions, as trade-off for different objectives exist in the set of solutions.

## Multi-Objective Evolutionary Algorithms

Goals for a MOEA
• "Preserve non-dominated points in objective space and associated solution points in decision space.
• Continue to make algorithmic progress towards the Pareto Front in objective function space.
• Maintain diversity of points on the Pareto front (phenotype space) and/or Pareto optimal solutions - decision space (genotype space).
• Provide the decision maker "enough" but limited number of Pareto points for selection resulting in decision variable values."

The solution: "a vector of decision variables which satisfies constraints and optimizes a vector function whose elements represent the objective functions. These functions form the mathematical description of performance criteria which are usually in conflict with each other. Hence, the term "optimize" means finding such a solution which would give the values of all the objective functions acceptable to the decision maker."

## Pareto

Vilfredo Pareto made it possible to optimize multi-objective problems.

Pareto Optimality: A solution $$x \in \Omega$$ is Pareto optimal w.r.t. $$\Omega \iff \nexists x' \in \Omega$$ for which $$v$$ = $$F(x')$$ = $$(f_1 (x')$$, ..., $$f_k (x'))$$ dominates a $$u$$ = $$F(x)$$ = $$(f_1 (x)$$, ..., $$f_k (x))$$.

$$x*$$ is Pareto optimal if there is no $$x$$ which would increase one criterion without decreasing another.

Dominance: $$u$$ dominates $$v \iff\ \forall i \in$$ {1, ..., $$k$$}, $$u_i \leq v_i \land \exists i \in$$ {1, ..., $$k$$} : $$u_i < v_i$$.

Pareto Optimal Set: $$P*$$ := {$$x \in \Omega$$|$$\nexists x' \in \Omega$$ $$F(x') \preceq F(x)$$}

Pareto Front: $$PF*$$ := {$$u$$ = $$F(x)$$|$$x \in P*$$}.

This Pareto Front is ubiquitous in determining solutions for multi-objective problems

## Strength Pareto Evolutionary Algorithm 2

SPEA2 is a robust MOEA that is capable of solving a very diverse set of problems. SPEA2 is used as a benchmark against which new MOEAs are compared to, and SPEA2 tends to outperform. Meaning it is a great MOEA to use for new applications.

Procedure:

1. Input: $$N', g, f_k(X)$$, where $$N'$$ members evolved, $$g$$ generations, $$f_k(X)$$ is functions to solve
2. Initialize Population $$P'$$
3. Create empty archive $$E'$$
4. for current_generation = 1 until current_generation = $$g$$
5. Compute fitness of each individual in $$P'$$ + $$E'$$
6. Copy all nondominated individual in $$P'$$ + $$E'$$ into $$E'$$
7. if |$$E'$$| > max_size $$\rightarrow$$ remove worst from $$E'$$
8. else fill $$E'$$ with best dominated solutions
9. get parents $$M'$$ from $$E'$$ based on best solutions
10. get $$P'$$ from $$M'$$ after applying mutation and crossover
11. Return $$E'$$

## References

Coello, C. A. C., Lamont, G. B., & Veldhuizen, D. A. V. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems Second Edition. Boston (MA): Springer.

# Langmuir Isotherm

 Co Original chlorophyll concentration (mg/kg_oil) M Mass of oil being processed (g) qads Content of chlorophyll adsorbed onto the clay (mg/kg_clay) Mclay Mass of clay being used (g) Ce Chlorophyll concentration in the oil post processing (mg/kg_oil) KL(T) Langmuir constant (mg/kg_oil), expressed as a temperature dependent function

# Winsor Classification

The phases were classified based on the following criteria:

Winsor 1:

• Identifiable bulk separation between top and bottom phases
• Top phase is comparatively more translucent than bottom phase
• Opacity in the bottom phase is produced by emulsion structure

Winsor 2:

• Identifiable bulk separation between top and bottom phases
• Bottom phase is comparatively more translucent than top phase
• Opacity in top phase is produced by emulsion structure

Winsor 3:

• Identifiable bulk separation between bottom, middle, and top phases
• Middle phase is comparatively more opaque than top and bottom phases

Winsor 4:

• No identifiable bulk separation

# Emulsion Compositions

Name
Aqueous Volume Fraction Organic Volume Fraction Water-to-oil ratio Surfactant Volume fraction
C6 0.33 0.42 0.786 0.25
C7 0.39 0.41 0.951 0.2
C8 0.42 0.43 0.977 0.15
C9 0.43 0.47 0.915 0.1
C10 0.45 0.5 0.9 0.05