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.
AntiFungal
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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal 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 AntiFungal page.
Chlorophyll Repurposing
Enzymatic Degradation of Chlorophyll
SDSPAGE Confirmation of HCAR and PPH Purification (Replicates 1, 2, 3, 5)
SDSPAGE Confirmation of HCAR and PPH Purification Replicate 1
SDSPAGE Confirmation of HCAR and PPH Purification Replicate 2
SDSPAGE Confirmation of HCAR and PPH Purification Replicate 3
SDSPAGE 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 TrisHCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X100.
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 NickelNTA 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 TrisHCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X100. 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 NickelNTA 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 TrisHCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X100. 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 NickelNTA 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 TrisHCl, pH 8.0, 150 mM NaCl, and 0.1% Triton X100. 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 nonparametric 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 multidimensional. 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 nclass 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 highdimensional 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
 Jain, A. K., Mao, J., & Mohiuddin, K. M. (1996). Artificial neural networks: A tutorial. Computer. 29(3): 3144. dio: 10.1109/2.485891
 Williams, R. J. & Zipser, D. (1995). Gradientbased 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. 443486). 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 oneversusone 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 nonlinear 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 biasvariance 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 nonparametric 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
Problemsolving 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 
Assemblies
Individual Components
Drawings
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 MultiObjective Problems Second Edition. Boston (MA): Springer.
SPEA2
MultiObjective Optimization Problems
For multiobjective 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 tradeoff for different objectives exist in the set of solutions.
MultiObjective Evolutionary Algorithms

Goals for a MOEA
 "Preserve nondominated 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 multiobjective 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 multiobjective 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:
 Input: \( N', g, f_k(X)\), where \(N'\) members evolved, \(g\) generations, \(f_k(X)\) is functions to solve
 Initialize Population \(P'\)
 Create empty archive \(E'\)
 for current_generation = 1 until current_generation = \(g\)
 Compute fitness of each individual in \(P'\) + \(E'\)
 Copy all nondominated individual in \(P'\) + \(E'\) into \(E'\)
 if \(E'\) > max_size \(\rightarrow\) remove worst from \(E'\)
 else fill \(E'\) with best dominated solutions
 get parents \(M'\) from \(E'\) based on best solutions
 get \(P'\) from \(M'\) after applying mutation and crossover
 Return \(E'\)
References
Coello, C. A. C., Lamont, G. B., & Veldhuizen, D. A. V. (2007). Evolutionary Algorithms for Solving MultiObjective Problems Second Edition. Boston (MA): Springer.
Langmuir Isotherm
C_{o} 
Original chlorophyll concentration (mg/kg_oil) 
M  Mass of oil being processed (g) 
q_{ads}  Content of chlorophyll adsorbed onto the clay (mg/kg_clay) 
M_{clay}  Mass of clay being used (g) 
Ce  Chlorophyll concentration in the oil post processing (mg/kg_oil) 
K_{L}(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  Watertooil 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 