When learning about hydrocarbon homologous series, I understood the difference between various types of chemical compounds. Different numbers of atoms and bonds would all result in distinct chemical properties. This is especially evident in the homologous hydrocarbon series, as all of the chemical compounds are made of merely carbon and hydrogens.
During one experiment in class, the teacher demonstrated the evaporation process of pentane. When the liquid of pentane is dripped on the table, it is visible that the liquid disappears within a matter of seconds. Whereas a drop of water would last much longer, it was fascinating to see how the hydrocarbon liquid disappeared so rapidly.
This raises several questions about the process of evaporation: Why do hydrocarbon compounds evaporate so quickly? What would change if the number of carbon and hydrogen atoms is different? Does the evaporating speed change when a different bond is formed between the carbon? With these questions in mind, I decided to investigate the following research topic:
The correlation between the enthalpy of vaporization and different hydrocarbon homologous series under respect to boiling point
The enthalpy of vaporization is defined as the enthalpy change in the conversion of one mole of liquid to gas at a constant temperature. The unit of enthalpy of vaporization is kJ/mol, which is the amount of heat per mole when the chemical compound turns into gas molecules.
It is important to note that during the process of vaporization, the chemical compound’s temperature would remain constant.2 When the chemical compound is transforming from liquid to gas, the internal heat energy is being used to break the ions instead of moving freely. Since there is less heat energy, the temperature stays constant. However, this implies that a measurement of the temperature of the chemical compound during its evaporation would be invalid – the temperature would not change. Therefore, in order to obtain the energy released by the chemical reaction, the measurement of the surroundings must be recorded.
In this experiment, the enthalpy of vaporization would be recorded at the respective boiling point of each chemical compound. At the boiling point, a chemical compound is able to evaporate with a sufficient supply of heat energy.
Evaporation is an endothermic process, where energy is absorbed by the chemical from the surrounding. Thus, the energy absorbed by the chemical compound’s evaporation process is:
Here, the mass of the chemical compound is divided by its molar mass to obtain the mole’s number of the compound, it is then multiplied by the enthalpy of vaporization to calculate the energy required per mole.
Then, the energy released by the surrounding water is
Here, the variables are temperature change is calculated by Tf-Ti, where Tibeing the initial temperature which is set to be the boiling point of the specific chemical compound. The mass of water and water’s specific heat capacity is also used to calculate the value.
Since Hsysten= -Hsurroundings
Thus, (Tf-Ti) mwater0.0042kJgC= –mreactantMolar massHvap
By rearranging the equation, we can the formula for enthalpy of vaporization
Hvap= -(Tf-Ti) mwater0.0042kJgCMolar massmreactant
From this equation, greater enthalpy of vaporization results from greater temperature change and smaller molar mass. There are two factors that can contribute to this with regards to the research topic, which is the number of sigma-bonds and pi-bonds.
With more sigma-bonds and pi-bonds, more energy will be released to break the bonds for evaporation. Hence, this will result in an increase of temperature change and thus higher enthalpy of vaporization.
Compared to sigma bonds, more pi-bonds allow the chemical compounds to have stronger electrostatic attraction and intermolecular force with fewer atoms. This suggests that with the same number of carbon atoms, the chemical compounds with more pi-bonds will have a stronger intermolecular force and hence stronger enthalpy of vaporization.
Under room temperature, if the number of carbons and hydrogens of a chemical compound in the hydrocarbon homologous series increase, the enthalpy of vaporization would also increase because more bonds in a chemical bond make the bond more solid and thus harder to break.
Independent Variable: Chemical solutions with substances that have different numbers of covalent bonds, including sigma-bonding and pi-bonding.
Due to the nature of the experiment, the chemical compound can only be used in its liquid form. As such, only 6 organic compounds are chosen for the experiment. The chemical compounds are alkane, alkene and alkyne compounds with 5 and 6 carbons. The chemical compounds are specifically pentane, hexane, 1-pentene, 10hexene, 1pentyne, and 1-hexyne.
|Type of C-C bond||Single Bond||Single Bond||Double Bond||Double Bond||Triple Bond||Triple Bond|
|Boiling Point (C)||36.2+-0.2||68.9+-0.3||31.0+-8.0||64.0+-2.0||40.0+0.7||71.3+-0.9|
|Molar Mass (g/mol)||72.17 g/mol||86.2 g/mol||70.15 g/mol||84.18 g/mol||68.13 g/mol||82.16 g/mol|
Dependent Variable: Enthalpy of vaporization calculated with the obtained values of final temperature, using the formula in the introduction section.
Firstly, all chemical compounds are stored at room temperature. The chemical compounds in this experiment are all liquids with different boiling points. To make sure that the chemical compounds have the same particle movement absorbing heat energy from the water, they need to be stored under the same temperature, which is preferably room temperature.
Second, the air pressure of the room needs to stay constant. A change of air pressure will affect the rate of temperature change and hence inaccurate results. Therefore, to ensure that the chemical compounds undergo a reaction in the same conditions, the air pressure needs to remain constant.
Third, the concentration of the chemical compounds is the same. This will ensure that the same amount of molecule is in the given volume of the chemical compound.
Last, the same volume is used for all the chemical compounds. This allows all the chemical compounds to take place with the same starting amount, which will create a more accurate result.
1 Calorimeter 2 Gas pipes
1 Thermometer 2 beakers
6 * 200 ml of water 1 beaker seal
100 ml for each pentane(C5H12), hexane(C6H14), 1-pentene(C5H10), 1-hexene(C6H12), 1-pentyne(C5H8) and 1-hexyne(C6H10)
First, a beaker with 100 ml of the chemical compound was prepared. Then a cap was placed on the beaker with a hole that was connected to a gas pipe. The sealed beaker with the gas pipe was put in a calorimeter filled with 200 ml of water. The water inside the calorimeter was heated and then cooled off to the boiling point of the specific chemical compound. The calorimeter would be made of styrofoam, which has an effective heat-retaining ability. The beaker would be fully submerged by the water except for the gas pipe that is above the surface of the water. Then a lid will enclose a calorimeter with two holes, respectively, for the gas pipe and the thermometer. Then a steam collector is attached to the beaker with enough space for the products of the chemical compound to evaporate into. The second gas pipe will be attached to a beaker using a support brace, where the condensed steam will be collected.
During the experiment, the chemical compound will evaporate at room temperature. The evaporated gas molecules will go through the gas pipe and arrive at the steam collector. With the steam collector, the vaporized gas molecules will be condensed into water, which then runs down the other gas pipe to the attached beaker. During the process, heat energy is constantly released from the chemical compound to the surrounding water around it. A thermometer will then be used to measure the temperature of the beaker at different moments. The temperature data will be recorded at the start of the experiment, and again when the condescended chemical compound has reached half of the original amount which is 100ml.
The same experiment will be continued to test the other chemical compounds, each one with three trials. The data of the initial temperature and the resultant temperature when the dilute solution reaches 100 ml will be recorded.
Safety goggles and gloves as the chemical solutions that should be handled with caution. Direct contact with the chemical solution should be avoided. Fire extinguishers were prepared as the materials used are combustible.
There are none.
After the experiment, the chemicals need to be disposed of carefully in the organic waste disposal. This prevents the chemicals from causing any harm to the environment.
Since the calorimeter was closed during the experiment, I wasn’t able to observe what happened inside the closed system. As such, I can only observe the extent of evaporation of the chemical compound by looking at the liquid accumulated at the second baker.
The length of the experiment lasted for 2 minutes on average. It is observed that with more atoms and bonds in the chemical compound, more time is needed for the evaporation process to complete.
The final temperature was recorded after the solution from the evaporated chemical compound reached 100 ml in the second beaker. This was done for three trials for each chemical compound tested.
The uncertainty of the calculated average, UV, was found by the following equation:
The values Xmax, Xminare respectively the maximum and minimum of values from the trials.
The maximum and minimum final temperatures recorded for hexane are 28.75 C and 29.37 C. Thus Uhexane=(29.37-28.75)2=±0.31C.
Table 1: The final temperature recorded when 100 ml of the solution is collected in the second beaker for 3 trials
|Initial Temperature (Boiling Point)||Final Temperature (when 100 ml of the solution is collected in the second beaker)||Uncertainty()|
|Trial 1||Trial 2||Trial 3|
From the introduction section, the formula of vaporization is:
Hvap=(Tf-Ti) 200g0.0042kJgCMolar mass100g
The values Tf, Ti, Molar mass are each the initial temperature(boiling point), the final temperature recorded and the molar mass of the specific chemical compound.
Sample Calculation (Hexane):
The initial temperature of Hexane is 68.90 C, the recorded final temperature of the first trial is 28.75 C, and its molar mass is 86.20 g/mol.
Thus, Hvap=(29.75 C-68.90 C)200g0.0042kJgC86.20 g/mol100g= -28.63 kJ/mol.
After these calculations, the following table is produced:
Table 2: The enthalpy of vaporization is calculated for each value of final temperature from table 1
|Enthalpy of Vaporization (kJ / mol)||Uncertainty()|
|Trial 1||Trial 2||Trial 3|
The average enthalpy of vaporization of 3 trials, AV, was found using the equation:
The values X1, X2, X3 are each the vaporization enthalpy calculated by the three trials.
Sample Calculation (Hexane):
The calculated value of Hexane’s enthalpy of vaporization are -28.63 kJ/mol, -28.85 kJ/mol and -29.07 kJ/mol, thusAHexane=[(- 28.63kJ/mol)+(- 28.85kJ/mol)+(-29.07 kJ/mol))3= -28.85kJ/mol.
After the average enthalpy of vaporization for each chemical compound and their uncertainty are calculated, the following table is produced:
Table 3: The average enthalpy of vaporization (kJ/mol) is calculated for values of enthalpy of vaporization from the three trials from table 2
|Average Enthalpy of Vaporization (kJ / mol)||Uncertainty()|
The data in Table 2 were then used to make the following graph:
Graph 1: Enthalpy of vaporization (kJ/mol) Vs. the series of Chemical Compound
Graph 1 was created based on the data derived from Table 2. It presents the visualized relationship between the enthalpy of vaporization and the chemical compound. The trend line was created with the help of Google Spreadsheets, it shows the linearized correlation between the two variables.
Graph 2: Enthalpy of vaporization (kJ/mol) maximum, average and minimum trend lines
In Graph 2, the two lines drawn are each the maximum line and minimum line of the linearized graph. The red line represents the maximum line while the yellow line represents the minimum line.
The derived trend line from the data has the same trend line suggested by the hypothesis. The trend lines demonstrate the negative linear between the two variables. Thus, the derived trend line matches the original hypothesis. It can be concluded that the data from the experiment supports the original hypothesis because they have the same relationship between variables.
From the data analysis, it is evident there is an increase in vaporization’s enthalpy when there are more covalent bonds in the chemical compounds.
The most significant factor that changes the enthalpy of vaporization is the number of pi-bonds in the chemical compounds. It can be seen from the graph, that chemical compounds with triple carbon bonds have a higher enthalpy of vaporization than that of chemical compounds with double or single carbon bonds.
The second factor affecting the amount of energy released during vaporization is the number of carbon atoms given the same carbon covalent bond. With more carbon atoms, there will be more carbon bonding (single, double or triple) with carbons and also hydrogen. This will result in a stronger intermolecular force as more bonding makes each molecule have a higher electrostatic attraction force.
Some of the heat energy absorbed by the water will be lost to the container of the water. Although the system should be ideally isolated, some heat energy will be transferred to the container and hence lost from the water. Such a phenomenon will make the temperature measured at the end inaccurate as it doesn’t precisely represent the amount of heat released by the evaporation process of the chemical compound.
Some of the evaporated gas molecules of the chemical compound will not be collected by the steam collector and go into the air. This will make the process of filling the second beaker, hence slowing the overall process.
The measurement of the beakers and thermometer in the experiment might be slightly inaccurate as there is no measurement that could be 100% ensured. The amount of liquid in the beaker (condensed) inaccuracy will lead to inaccurate results and hence issue with a final conclusion.
Enthalpy of Vaporization. (2021, November 13). Wikipedia.
Phase Changes. (n.d.). Lumen learning.
By James Hong
The development of computer science has brought many benefits to human society. This also applies to the handling of the covid-19 pandemic nowadays, that it can effectively spread awareness, allows the society to function normally and provide scientific communication across the globe.
First, computer science can be used to inform and raise awareness of the public. As more and more people have access to the internet, awareness about the pandemic could be spread rapidly through social media and news. It allows people to be informed about the covid-19 and its prevention promptly and hence lets more people avoid risks of infection. For example, online news platforms are able to inform people about the serious situation of the pandemic and methods to prevent infection. The efficiency of spreading awareness is crucial to the eradication of the virus since the virus can only be stopped with the contribution of everyone in society. Therefore, computer science is able to control the spread of the virus by providing the fastest way to spread information to the population.
Second, computer science allows the functioning of normal activities. Due to the contagious nature of the virus, many companies and institutions are restricted from the mass gathering of people. Through the presence of online platforms, the exchange of ideas and communication are able to operate online. For example, online services are used in school to allow teachers to teach the student and keep up with classes, such as Google Meet. This new form of discussion can only be done with the help of computer science, as it can provide audio and video of each person in real-time. Thus, software developed by computer science can maintain the level of communication within companies and institutions without any physical gathering.
Third, computer science is able to provide information to governments and it also provides a place where countries can share their experience dealing with the virus. The information on the internet can be shared among countries, which could be then used to collect data that are helpful for the control of the virus. For example, it allows a country to track the passengers on a flight where an infector was abroad. Furthermore, it also allows the countries to share the progress of research, such as effective measures to counteract the pandemic. This helps the control of the virus by exchanging experiences between countries and increases the speed to develop a vaccination against the virus. Hence, computer science allows a country to gain information about the spread of the pandemic as well as experiences from other countries.
In conclusion, computer science is able to provide significant help to the control of pandemics, because it allows for the spread of awareness among the public, functioning of societal institutions and it allows for the exchange of research works and experiences. If there hasn’t been computer science the pandemic would certainly have a larger impact on the globe and it would claim much more death than what it has now.]]>
Aim to analyze the body action on the sports, improving personal training, tactic and strategy selection when facing different style players during competition.
Apply on all kinds of fencing, including Epee, Foil and Saber. Due to the different rules in each type, the first step will focus on Epee, then applying the algorithms to Foil and Saber should be simple.
Use python working with JSON and load it into the database. https://www.sqlshack.com/working-with-json-data-in-python/
Use normalized database structure to capture and save the player action data, and demonstrated to some tables for reporting and warning triggering
Data dictionary will follow.
The output will be video with or without suggestion caption, comparison report, a benchmark report.
Could this be https://cmu-perceptual-computing-lab.github.io/openpose/web/html/doc/classes.html , need confirmation after a detailed review. https://docs.opencv.org/3.4.15/ is for object motion tracking using OpenCV
TBD after review specs, expect to be included in version 2 Design questionary.
TBD, not able to find in OpenPose for now, some other documents refers to OpenC. i.e. https://www.pyimagesearch.com/2015/09/14/ball-tracking-with-opencv/ has sample OpenCV on how to track a ball, https://www.analyticsvidhya.com/blog/2020/03/ball-tracking-cricket-computer-vision/
It should be possible to mark the videos using both OpenPose and OpenCV methods. However, this can be done by machine learning the footage twice or combining the positions at the database level by using timestamp as a relational key.
The measurement: Speed? Distance? Position? Reaction kind? Reaction Speed?
The goal is to identify different actions and then determine which action or reaction is the response that can have the best chance to score.
The goal is to identify and categorize the ‘fighting style’ by learning tempo and tactic habits.
A neural network is a computing system that is loosely based on the biological neural network of the human brain. It is widely used in the development of artificial intelligence and it allows computers to find patterns with massive amounts of data.
The artificial neural network is able to formulate a complex system of algorithms, by analyzing and “learning” the mass of raw data/input. The math models are used to filter, organize, determine the importance of each data element, and then identify the relationship and the best math model policy for further analysis and prediction purposes. The mathematical models are playing the most important roles when formulating patterns between the input and output values.
For this extended essay, I will be focusing on one mathematical model used for regression data filtering of the neural network, which is called “backpropagation”. Backpropagation is the mechanism where the predicted result from the neural network is compared with the theoretical result and there subsequently adjusts the system until accurate results are yielded. The essay will focus on the explanation and discussion of how to classify and weigh information using this mathematical model. Mathematical knowledge including algebra, vector and calculus will be utilized for modelling purposes. In particular, knowledge about linear regression and derivatives will be applied to backpropagation.
Visual representation of the nodes and different layers in an artificial neural network
The above picture is an illustration of the structure of the artificial neural network. It consists of three parts: the input layer, the hidden layer, and the output layer. The input layer is where the neural network takes in bits of information that will be analyzed. The hidden layer is where that information is analyzed through a complex interconnecting network that filters, or classifies and weighs, the input information. The output layer then presents the outcome from the hidden layer that will produce an output that is expected from the input.
Backpropagation, short for back propagation for errors, refers to the algorithm for computing the gradient of the loss function with respect to the weights. It is the process that allows the algorithm to make adjustments to data filtering and thus make the output data more accurate.
In this investigation, each step of the backpropagation algorithm will be analyzed. The steps are loss function, calculating derivative for gradient descent and performing optimization for gradient descent. Finally, the mathematical model for specific variables in the neural network algorithm will also be deduced.
In order to gain a comprehensive understanding of the back propagation, it is necessary to know how the neural network operates in its most fundamental building blocks. The neural network is made of a massive number of nodes, which is responsible for processing bits of information and producing an output that will be used afterwards. The breakdown of the calculation of every single node is shown as the following:
Visual Representation of the Feedforward Algorithm
In this diagram, iwi stands for “initial weight”, bi stands for “bias” and fwi stands for “final weight”. Weight can be interpreted as the assigned value to each bit of information. Greater weight means that the bit of information is being multiplied to a greater extent, and hence shows that it is being more valued in the entire neural network system. On the other hand, a bias is the value-added after the first weight is being multiplied. A bias also serves to increase or decrease the weight of a specific bit of information. The value produced after the multiplication of the initial weight and addition of the bias is represented as x, which is due to the fact that it will be used as the x-value for the activation function. Hence, the equation of one line of calculation at this point could then be presented as:
The two graphs in the diagram are called the activation functions. The activation function takes in an input that has been weighed by both the weights and the bias, and then produces a corresponding y-value according to the graph. Just as most activation graphs suggest, an x-value is being valued differently by the activation function depending on where the x-value is at. For example, in a type of activation function called ReLU(Rectified Linear Unit), the output of a value becomes zero if this value is negative, and the output is the same as the value if this value is positive. Activation functions are crucial components of the neural network that determine how much input should be weighed. The activation function of a node defines the output of that node given input or a set of input.
There are many activation functions that could be used in neural work, and each one has its own strengths and shortcomings. In this particular case shown in the diagram, an activation function called Softplus is being used. The equation for the Softplus function is written as the following:
Visual Representation of the Softplus Activation Function
Next, the output front he activation function is then multiplied by a factor of fwi, which stands for “final weight”. The output from the activation function is weighed again to supplement the change from the activation function.
Finally, the sum of all of the output is calculated and is then assigned with a final value, called bf which stands for “final bias”. At this point, the calculation of the output is accomplished and could then produce a final output. The predicted value is the final value that the neural network algorithm is solving for. It is calculated as the sum of multiple lines of calculation and then added by a final bias. Hence the equation of one single line of calculation is:
The predicted value can be modelled by the following formula:
Predictedi=yi fwi+yi+1 fwi+1+……………+yn fwn+b3
Next, different input values can be processed by the node and create a line that models the relationship between the input and output, this line cannot be modelled by a mathematical formula as its values are derived by adding multiple lines from the feedforward process together. Hence, this line is being called a squiggle.
As shown in the next picture, the orange and blue lines each represent the line of calculation in the diagram, and the green curve represents the output after the two lines are added together. This example shows how a non-linear or quadratic line could be produced by adding various lines together to better fit the prediction of the final output.
Visual Representation of how the green curve represents the output after the two lines are added together
To clarify this idea, we can use an example to explain the idea behind the predicted value:
For the purpose of simplification, this demonstration will only use two lines of calculation from the feedforward diagram.
Visual Representation of the demonstration of the predicted value calculation
Let the first line of calculation be a blue squiggle and the second line of calculation be an orange squiggle. Then the calculation of each line would be:
Orange Squiggle=softplus(input iw2+b2)fw2=y2fw2
Since each line represents one layer of the calculation, then when they are added together, the predicted value of the entire node is calculated.
Predictedi=blue squiggle orange squiggle + bf
Therefore, the green curve represents the output after the two lines are added together.
The bias b3 adjusts the squiggle to fit the data points
Notice that the predicted data is still one unit off from the observed data, we can then use the final bias, bf to make the final adjustment to the data so the green line would fit the observed data.
As the prediction of data is being made, it shows how a non-linear or quadratic line could be produced by adding various lines together to better fit the prediction of the final output.
However, it is important to note that the variables in this set of lines of calculation have already been optimized. For all of the programs, the prediction value is calculated to be nowhere close to the observed data, and it only improves its precision after numerous trials of optimization, which is a part that will be discussed later.
The loss function is the function that measures the difference between the predicted output of the algorithm and the expected output. In other words, it can effectively determine the error (known as the loss) between the algorithm and the given target value. As such, the loss function is being used to gauge the error of the prediction produced by the backpropagation. Then, this error will be used as an indicator for further optimization and evaluation of the mathematical model.
The loss function is the pivotal component of the backpropagation, as all of the following calculations will significantly be based on the values produced from the loss function. In fact, the main objective of the backpropagation algorithm is to minimize the value of the loss function, which would make the prediction from the neural network as close to the target value as possible.
There are many different types of the loss functions, where each type is used in a different context. In this investigation, I will use the most common and acclaimed type of loss function, known as “sum of squared residual” or SSR in abbreviation.
In SSR, the residue between the observed value and the predicted value for each input is calculated and subsequently squared, followed by adding all these numbers together. Then the formula for “sum of squared residual” is shown below:
Sum of Squared Residue=i=1n(Observedi-Predictedi)
From this function, we can then draw a quadratic formula since the equation is the sum of a number of squared numbers.
Image of how residues are calculated (Left)
Graph of sum squared residue in relation to the slope (Right)
In order to use the loss function, the observed value and predicted value are needed to compute its result. Given that the observed value can be obtained from the dataset used to train the model, only the predicted value from the input data needs to be deduced. The formula of the predicted value has already been discussed in the previous section.
After the values of the loss function are collected and made into a graph, we can then see a quadratic trend. This function shows the amount of error that yields when a different value of the parameter is used in the calculation. To put this in perspective, for each x-value, a higher value in SSR indicates a larger gap between the predicted value and observed value and therefore is considered more inaccurate. Hence, the prediction is most accurate when the y-value (SSR value) is at its lowest, and the corresponding x-value is therefore the optimal value for the parameter.
However, since the produced trend is derived from the loss function, it cannot be modelled by a quadratic function. One way to find the optimal value is through plugging in numbers into the input and comparing the calculated output to the observed output and finding which value yields the smallest difference between the two. However, this method will not be efficient and accurate at the same time, since increasing the accuracy will require more numbers tests which would then extend the calculating time indefinitely.
Nevertheless, a more efficient way to obtain the optimal value of the parameter is through gradient descent.
Gradient descent is an optimization algorithm used for minimizing the loss function. It is more efficient and accurate since gradient descent only does a few calculations far from the optimal solution and increases the number of calculations closer to the optimal value. This method helps to greatly reduce the number of calculations and increase the precision of the data. The reason is that gradient descent is able to quickly locate the range where the optimal value exists with fewer steps, and closely pinpoint the optimal value within that range by decreasing the scale of its steps.
This image shows how gradient descent calculates the optimal value of the quadratic graph
The next two sections will respectively discuss the two main aspects of gradient descent, which are calculating the derivative and performing optimization.
Calculating the Derivative for Gradient Descent
In the calculation of the gradient descent, the calculation would mostly be based on the mathematical rule of the chain rule, which states that;
The chain rule is used to find the derivative of a composite function. The function of the feedforward process involves multiple calculations made to the initial input. Since the chain rule can only be used if the two variables are linked directly, finding the derivative of the loss function to the specific variable requires using the chain rule multiple times. Hence, the following formula is produced from the formula for a single line of calculation:
d SSRd weight/bias=d SSRd Predictedd Predictedd yid yid xid xid weight/bias
Additionally, It is important to note that the purpose of the gradient descents is ultimately to decrease the value of the SSR (sum of squared residue), where a smaller SSR implies that the prediction value is closer to the observed value, and hence improve the accuracy of the neural network algorithm in predicting the output with a given input.
Visual Representation of the derivatives of the quadratic function
In the following part, each derivative presented in the previous question will be solved one by one and combined to produce the full equation for the derivative of SSR to a specific variable.
Calculating the Gradient Descent of the loss function to the predicted value:d SSRd Predicted=dd Predictedi=1n(Observedi-Predictedi)2
Using the chain rule:
d SSRd Predicted=i=1n(-2)(Observedi-Predictedi)
Calculating the Gradient Descent of the predicted value to the y-value (output from Activation Function):
d Predictedd yi=dd yiyi fwi+yi+1 fwi+1+…………..+yn fwn+b3
d Predictedd yi=fwi+0+….+0+0=fwi
Calculating the Gradient Descent of the y-value to the x-value (Output of Activation Function to its input):
d yid xi=dd xilog(1+exi)
In order to solve this derivative, we need to use the following two formulas:
d yid xi=dd xilog(1+exi)=11+exiexi=exi1+exi
Calculating the Gradient Descent of x-value to the weight or the bias
d xid iwi=dd iwiInputiiwi+bi=Inputi
d xid bi=dd biInputi iwi+bi=1
Performing the Optimization for Gradient Descent
Optimization is the process where the gradient descent of the neural network is used to gradually increase the accuracy of the parameters. First, the value of the gradient descent is used in the function to produce an output, then that output is optimized repetitively by evaluating the loss function of the new variable.
This is the place where the “learning” takes place, where the program gradually optimizes its value by gradually adding or subtracting from the specific parameter. It plays a crucial role in the function of the program
The learning rate can be set by the designer of the program, it is set as a percentage, such as 0.1. The smaller the learning rate is, the longer it is going to take for the gradient descent to reach the optimal value. The new value of the parameter is then calculated by subtracting the step size from the old value. The formulas for step size and new value are shown us the following:
step size=derivative learning rate
new value=old value-step size
With these two formulas, the step size would be greater when the SSR is higher and it would be less when the SSR is lower. This matches the gradient objective of changing the parameter greatly when it is far from the optimal value and decreases the scale of change as the value is getting closer to the optimal value. The effects of optimization can be seen from the following graph, which shows the step size getting increasingly smaller and closer to the optimal value of the graph.
The two steps above are repeated until it has met their limits. There are often two cases of limits, the first case is that the gradient descent stops when the step size is very close to 0, which the gradient descent would only have negligible on the optimization of the parameter. The second case is that the gradient descent stops when a certain number of calculations is reached, this number of repetitions could be set by the designer of the program. The limits are usually set in a way that can prevent the program from running indefinitely, which is meaningless as the value is increasingly closer to a set number.
Modelling each Variable (iwi, bi, fwi, bf)
With enough information about the backpropagation, we can now deduce the mathematical model for each type variable that will be used in this model. The variables are respectively iwi, bi, fwi, bf. The following section will be demonstrating the calculations that lead to the final mathematical models.
In addition, it is important to know how to initialize the variable. To minimize the uncertainty of the initial function, we only need to initialize the value of fwi. The value of other variables can then be initialized as 1 or 0 depending on if it’s an addition or a multiplication.
Through the calculation of the gradient descent and optimization for each of the variables, the variables will gradually become closer and closer to the desired values for the specific neural network.
For iwi , the derivative is:
In order to solve for the derivative for the value of Iwi, the derivative of the loss function to the Iwi is calculated. The derivative can then be extended to an equation consisting of multiple derivatives. It can then be solved by solving each individual derivative.
d SSRd iwi=d SSRd Predictedd Predictedd yid yid xid xid iwi
The last term of the derivative for iwi would be:
d xid iwi=dd iwiInputiiwi+bi=Inputi
Hence, the derivative of SSR ro iwi is:
d SSRd iwi=i=1n(-2)(Observedi-Predictedi) fwiexi1+exiInputi
For bi , the derivative is:
For bi , the mathematical model is largely identical to that of iwi, except for the driviative of:
d xid bi, where it equals to 1.
Then the equation is:
d SSRd bi=d SSRd Predictedd Predictedd yid yid xid xid bi
d xid bi=dd biInputiiwi+bi=1
d SSRd bi=i=1n(-2)(Observedi-Predictedi) fwiexi1+exi
For fwi , the derivative is:
d SSRd fwi=d SSRd Predictedd Predictedd yi
When calculating fwi , notice how this variable is multiplied to yi , this indicates that the last term of the equation isd Predictedd yi :
d SSRd fwi=i=1n(-2)(Observedi-Predictedi) yi
For bf , the derivative is:
d SSRd fbi=d SSRd Predicted
When calculating bf
d SSRd fbi=i=1n(-2)(Observedi-Predictedi)
This essay explores the mathematical model of artificial neural work. The important steps of the process include calculating the loss function, gradient descent, and optimization of the parameter. Next, the mathematical model for the backpropagation algorithm for all types of variables in the backpropagation model is deduced.
The neural network is centred around the application of mathematics, throughout the process of backpropagation, many mathematical methods and knowledge are being utilized. These include knowledge in algebra, calculus, statistics, and mathematical analysis. In particular, the gradient descent algorithm and functions such as activation functions and loss functions are crucial in the design of the neural network algorithm. The loss function helps to identify the amount of gap between the predicted output and the target put. The activation functions are able to convert data into the modified data that would be favourable for the neural network. Most importantly, the gradient descent algorithm allows the program to use the loss function as an indicator to optimize the parameters of the neural network algorithm, and hence produce a better prediction of the output.
With a thorough understanding of the algorithm, we can demystify the nature of neural networks. The algorithm is often regarded as a highly sophisticated system of programs, but when it is being analyzed in its most fundamental units, it can be completely modelled by mathematical equations.
Mesquitam, Déborah. “Python AI: HOw to Build a Neural Network & Make Predictions” Real Python, https://realpython.com/python-ai-neural-network/#computing-the-prediction-error. Accessed 23 September 2021.
Dasaradh, S.K. “A Gentle Introduction To math Behind Neural Networks” Towards Data Science, https://towardsdatascience.com/introduction-to-math-behind-neural-networks-e8b60dbbdeba. Accessed 23 September 2021.
Loy, James. “How to build your own Neural Network from scratch in Python” Towards Data Science, https://towardsdatascience.com/how-to-build-your-own-neural-network-from-scratch-in-python-68998a08e4f6. Accessed 23 September 2021.
Brilliant. “Backpropagation” Brilliant, https://brilliant.org/wiki/backpropagation/. Accessed 23 September 2021.
Wikipedia. “Backpropagation” Wikipedia, https://towardsdatascience.com/how-to-build-your-own-neural-network-from-scratch-in-python-68998a08e4f6. Accessed 23 September 2021.
Starmer, Josh. “Gradient descent, Step-by-Step” YouTube, uploaded by StatQuest with Josh Starmer, 5 Feb 2019, https://www.youtube.com/watch?v=sDv4f4s2SB8&t=1s
Starmer, Josh. “Neural Networks Pt.2: Backpropagation Main Ideas” YouTube, uploaded by StatQuest with Josh Starmer, 31 August 2020, https://www.youtube.com/watch?v=CqOfi41LfDw
Starmer, Josh. “Backpropagation Details Pt. 1: Optimizing 3 parameters simultaneously” YouTube, uploaded by StatQuest with Josh Starmer, 19 Oct 2020, https://www.youtube.com/watch?v=IN2XmBhILt4
Starmer, Josh. “Backpropagation Details Pt/ 2: Going bonkers with The Chain Rule” YouTube, uploaded by StatQuest with Josh Starmer, 2 Nov 2020, https://www.youtube.com/watch?v=GKZoOHXGcLo
The purpose of this experiment is to determine the relationship between the mass attached to a spring and the period of the spring’s oscillation. To conduct the investigation, I designed and implemented an experiment, and processed my findings through analysis.
The motion of spring has always been mysterious and irregular to me. Hence, when I first saw the formula that models the motion of spring, I decided to discover more about it on the internet. However, while I found plenty of written documentation, I could hardly find any visual demonstration that proves the spring’s oscillation is modelled by the physics formulas. Dissatisfied with my findings, I decided to experiment and find out the answer to the following research question:
How does the mass attached to a spring affect the period of the spring’s oscillation?
In mechanical physics, the term period is defined as the time for an oscillating object to make one complete cycle of oscillation.1 In a simple harmonic motion, an object’s period remains the same throughout all of its oscillations.
One of the most well-known examples of the simple harmonic motion is the spring-mass system, which was invented by English physicist John Michell in 1783.1 The motion of springs after they are compressed or extended obeys the laws of simple harmonic motion. Once force is exerted upon, the springs would display common features of simple harmonic motion including constant period and displacement proportional to its force.2 As a result of its features of the uniform period, springs are widely used in precision instruments such as mechanical watches and integrated circuits.3
This behaviour of the spring is due to the force applied to it. The force in a spring-mass system is directly converted into acceleration, which also contains a gravitational force that varies with the mass. Hence, the attached mass of the spring is one of the factors that affect the period of oscillation.3
1 “ Simple Harmonic Motion in spring-mass system review”, (n.d.)
2 “Motion of a mass on a spring”, (n.d.)
3 “Torsion Spring”, 2020
As one of the most important theories for simple harmonic motion, the relationship between the masses attached to a spring and the period of its oscillation can be modelled by the formula:
(T = period(s), m = mass(kg), k = spring constant(N/m) )1 T = 2π√km This formula clearly shows the theoretical relationship between the mass of the spring and its oscillation period. The formula can be interpreted that a more massive object would oscillate with a longer period.2 This formula suggests an inverse relationship between the two variables, which can be represented by the equation: T ~. The reason behind this formula 1m is that massive weights would generate greater inertia. Thus the oscillation takes more time for its acceleration to change.
It is important to note that different springs have different spring constants, and therefore would result in different periods of their oscillation. The value of the spring constant of a spring is directly related to the period of the spring’s oscillation. A spring with a higher spring constant has a smaller period. The greater value of the spring constant indicates that the spring can exert a stronger restoring force upon its attached mass, and thus reduce the time to complete one cycle of motion.3
Predicted Quantitative Relationship:
Since the spring that I used had a spring constant of 60N/m, thus the theoretical equation would be:
T = 2π T .81 √m60 ⇒ =2π
√60× √m ⇒ T = 0 √m
The overall trend of the predicted quantitative relationship is a square root function. It suggests the period will increase as the mass of the weight increases. The coefficient of the equation was predicted to be less than 0.81 by some extent depending on the mass attached. Whereas the y-intercept was predicted to be near zero.
My experiment will generate relevant data produced by six different weights attached to a spring tested under the same environment. This theoretical equation will be introduced and elaborated in the analysis section.
The mass of the weight attached to a spring.
The period for 10 oscillations of the spring, after the weight has been applied a certain force downward.
I placed the retort stand on a desk with its pole perpendicular to the ground. A measuring tape was taped around its pole from the ring clamp to the bottom of the stand. To begin with, I set up my phone stand on the floor and mount my phone onto it, to film my experiment process in slow-motion. I attached one end of the spring to the ring clamp using the hook at the end of the spring. The spring and the ring clamp were held together with the help of solder wires. The experiment was conducted in a windless and indoor environment at room temperature (presumably 21-celsius degrees), and there were no other external factors such as wind that might affect the validity of the experiment.
This is a picture of the experiment setup. The weight was being attached to the spring, which was
hanged from the ring clamp of the retort stand. The measuring tape was used to control the amount of force applied for each experiment.
Next, I started the process of my experiment. I first placed the specific weight onto the hook at the other end of the spring and used solder wires to secure them together. To make sure that the circumstances for each experiment were consistent, the same spring was used for all of the experiments. First, I started the slow-motion recording on my phone. Then, I pulled down the weight with my hand. To confirm that the force applied to the weights was consistent, all weights were being pulled down by precisely 3 centimetres. The measuring tape was used for the measurement of the distance that the weights were being pulled down. Then, I released the weight and I stopped the camera until it had oscillated more than 10 times. I repeated this process for a total of 6 different experimenting weights, and each one with 3 trials.
Referencing the interaction between the spring and the weight, the weight was being pulled down from 24cm(top) to 27cm(bottom), which was a displacement of 3 cm.
After all the trials filmed on my phone. I uploaded the recorded videos to the computer. By using video editing software Adobe Premiere Pro 2020, I determined the period of the oscillations with a time scale in milliseconds. The period was measured from the moment that the object lost contact with my hand to the moment that it completes its tenth oscillation. For the measurement to remain constant, the process of identifying starting and ending moments was carefully executed. However, measuring errors might still exist, which will be explained in the evaluation section.
The two picture shows the start(left) and the end(right) of 10 oscillations of 0.5kg weight, its period were calculated by 10.37s-4.63s=5.74s
Safety, Ethical and Environmental issues:
If the weights are not secured with the spring’s hook, the weight would lose contact with the hook. This might hurt people in the surroundings as the weight was being ejected from the spring.
There are none.
There are none.
After I released the weights from pulling down, the weights oscillated up and down with varied displacement and periods depending on their mass. The displacement of the weights decreased overtime during the oscillations at a steady rate. However, the periods of oscillation seemed to remain constant throughout the course of motion.
The movement of the spring-mass system varied greatly with the measure of its attached weight. It was observed that as the mass of the weights increased, the oscillation would have larger displacement and a longer period. In addition, the spring would be stretched to a greater extent due to a greater mass. The different extent of extension of spring will be addressed in the evaluation section.
Ideally, there was zero horizontal force applied on the mass, and thus the mass should not move horizontally. However, the horizontal displacement still occurred to a limited extent. The masses moved horizontally throughout the oscillatory motion, and such motion became more obvious as the number of oscillations increased. The horizontal force of the weights can be described as centripetal force. This phenomenon was more evident in heavier weights, which have greater horizontal centrifugal force. The concern of horizontal force’s impact on the experiment will be discussed in detail in the evaluation section.
The period of 10 oscillations of spring was recorded at a set of attached weights. The measurement uncertainties of the mass and time were presumed to be 1% to its measurement, which is the hundredth place. The following quantitative table was produced from the data collected:
Table 1: Recorded period for 10 oscillations of the spring depending on 6 masses attached
|Period for 10 Oscillations of the Spring(±0.0001)|
|Trial 1||Trial 2||Trial 3|
The average period of 10 oscillations, A10, was found using the equation: A X ) 10 = ( 1 + X 2 + X 3 ÷ 3
The values X 1, X 2, X 3 are each the period recorded by the three trials. The average period of one oscillation would then be calculated by: A 0 1 = A 10 ÷ 1
Sample Calculation (0.05kg mass):
With a weight of 0.05kg attached, the period for 10 oscillations were 1.87s, 2.00s and 1.91s, thus A 1.87 .00 .91) .926 .93s. The average period for 1 period was 10 = ( + 2 + 1 ÷ 3 = 1 ≈ 1 then calculated as A .93 10 .19s
1 = 1 ÷ ≈ 0
The uncertainty of the calculated average, U , was found by the following equation: 10 U X ) 10 = ( max − X min ÷ 2
The values X max, X min are respectively the maximum and minimum period of 10 oscillations recorded. The uncertainty for one oscillation would be calculated by: U 0 1 = U 10 ÷ 1
Sample Calculation(0.05kg mass):
With a weight of 0.05kg attached, the maximum and minimum period of the 10 oscillations recorded were respectively 1.91s and 1.87s. Thus U 10 = (1.91 − 1.87) ÷ 2 = ±0.02s. The uncertainty of the period of one oscillation is then U .02 0 0.002s. 1 = 0 ÷ 1 = ±
After these calculations, the following table is produced:
Table 2: recorded period for 10 oscillations of the spring depending on 6 weights attached, including the averages and their uncertainty
|Mass(kg)(±0.0001)||Average period for 10
|Uncertainty for 1 oscillation||Average period for 1 oscillation||Uncertainty for 1 oscillation|
The data in Table 2 were then used to make the following graph:
Graph 1: Average Period for one oscillation(s) Vs. Mass attached to the spring(kg) This graph was created based on the data derived from Table 2. It presents the visualized relationship between the period of spring’s oscillations and the weight attached to the mass. The vertical bars that run through the points in the graph are error bars that show the range of uncertainty for each data point.
The trend line was created with the help of Logger Pro, it shows the visualized relationship between the two variables. The relationship is modelled as a square root function which states P = 0.802(± 0.017)√M .
As Graph 2 shows a square root relationship, an attempt was made to linearize the equation, in order to verify the experimental relationship with the theoretical equation. The square root of mass was used to create such a graph and it succeeded in doing so. Sample Calculation:
The square root of 0.05kg is calculated as: √M = √0.05kg ≈ 0.22√kg
Table 3: The average period of one oscillation(s) versus the square root of mass attached to the spring( √M )
|Mass (kg) (.15)||Square root of Mass ( √M )(√kg )(.15)||Average Period for one Oscillation of the Spring||Uncertainty(±)|
The data from Table 4 were then used to produce the following graph, which shows the linear relationship between the square root of the mass attached to the spring and the resultant period oscillation.
Graph 2: The linearized graph of with the maximum and minimum trend lines
In Graph 2, the two lines drawn are each the maximum line and minimum line of the linearized graph. The green line represents the maximum line while the red line represents the minimum line.
The gradient of the maximum line is 0.825, while the gradient of the minimum line is 0.657. This indicates that the range of the slope of the best fit line would be from 0.657 to
0.825. The y-intercepts of the two lines are respectively 0.007 and 0.054. Thus the y-intercept of the best fit line would be between 0.007 and 0.054.
Given that this graph shows the relationship between the mass attached to a spring and the period of oscillation is linear. Thus, it suggests the equation P = a√M + b (P = period(s), M = mass(kg) ) would be used to model this relationship, where a is the coefficient or the slope of the best fit line, and b is the y-intercept of the best fit line.
In order to deduce the best fit line, the line would be expected to be the average of the maximum line and minimum line. This gives us the equation X = (X max + X min) ÷ 2, where X is the value of a or b, while Xmax and Xmin are the variable’s maximum value and the variable’s minimum value. The two values would then be derived from the maximum and minimum lines.
Using the equation X = (X max + X min) ÷ 2 , the value of a would be
(0.825 + 0.657) ÷ 2 = 0.741 , and the value of b would equal to (0.007 + 0.054) ÷ 2 = 0.031 . In addition to the values of a and b, the uncertainty of the two values is calculated by the equation: uncertainty = (maximum value − minimum value) ÷ 2 . With this equation, we would get the uncertainty of the slope as (0.825 − 0.657) ÷ 2 = 0.084 , and the uncertainty of the y-intercept as (0.054 − 0.007) ÷ 2 = 0.024 . Therefore, the uncertainty for the slope and y-intercept of the best fit line are each ±0.084 and ±0.024.
Therefore the formula for the line of best fit would be:
P = 0.741(±0.084) √M + 0.031(±0.024)
Given the spring constant of the spring used in the experiment is 60N/m, the theoretical equation of this experiment was found in the introduction section as T = 0.810√M. On the other hand, the experimental equation is derived to be P = 0.741(±0.084) √M + 0.031(±0.024). The two equations will be compared to determine if the derived equation supports the theoretical equation.
First, both the derived equation from the data and the theoretical equation have the same trend. The two equations both demonstrate the square root relationship between the two variables. This can interfere with the fact that the variable M is under a square root, and the curved trend line of the derived equation observed from Graph 1. Thus, the two equations have the same trend.
Second, the coefficient of each equation also matches with each other. The range of the value for the coefficient of the derived equation is 0.741. The coefficient of the theoretical equation has a value of 0.810, which is included in the range of 0.741 ± 0.084. As such, the coefficients of the two equations are corresponding.
In addition, the values for the y-intercept should be taken into consideration. The y-intercept derived from Graph 2 is found as 0.031m ± 0.024. Given the value for the y-intercept of the theoretical equation is 0, which is not included in the range of 0.031m ± 0.024m. However, since the range of the y-intercept of the derived equation is from 0.007 to 0.055, it is very close to the y-intercept of the theoretical equation which is 0. Therefore, the y-intercept of the derived equation matches the y-intercept of the theoretical equation as well. Lastly, after comparing and analyzing the two equations, it can be concluded that the data from the experiment supports the theoretical equation because both equations have the same relationship between variables and both their coefficient and y-intercept are within the uncertainty range of the derived equation.
Systematic Errors (Affecting the accuracy of results):
During the experiments, it was likely that the spring has been stretched out by weights. As a result, the spring’s spring constant might be reduced over time due to the extension. The inconsistency of the spring constant would then lead to the inaccuracy of the spring’s oscillation period over time. This error can be avoided in the future by using new springs that have the same spring constant for each experiment. As such, the spring constant would remain the same throughout the experiments.
During this experiment, the heavier mass has a bigger volume and accelerates to higher speeds than the smaller mass, air resistance could be another factor impacting the accuracy of the results. I did not estimate the air resistance because the masses’ travel distance is relatively short in this experiment, which even the heaviest 0.5kg mass did not accelerate to a considerable speed. As an improvement, I could implement this experiment in a vacuum environment to eliminate the effect of air resistance.
Another minor factor that might affect the experiment is the temperature where the experiments were performed. Spring tends to be stiffer at lower temperatures and more extended at higher temperatures.4 Such fluctuation in the spring’s stiffness would result in the uncertainty of the spring’s constant, and thus affects the period of the spring. This can be prevented by experimenting at a constant temperature to eliminate the impacts of the temperature.
The time that the oscillation starts and ends are determined completely by eyesight, which could potentially be inaccurate and inconsistent. This error can be prevented in the future by using different methods of measuring the time. One way that this could be done is through the use of electronic devices. For example, an Arduino with an ultrasound detector module can be programmed to measure its distance from the oscillating object at a rapid rate. The data recorded by an Arduino are then transmitted into the computer and to be used to determine the crest and trough of the oscillation by the highest and lowest values.
When the weight performs horizontal movements, a portion of the applied force is directed horizontally. This would reduce the vertical component and force, which would then reduce the extension and compression of the spring. As the spring is not stretched to the fullest, it would have less force and hence impacts the period of one oscillation. This random error could be reduced by pulling the weights in a line that is perfectly perpendicular to the ground, using tools such as construction level.
4 Briant T.W,(n.d.)
Overall, the results from the experiment support the theoretical data that was predicted. The experiment proves the hypothesis that with the same force applied if the mass attached to the spring increases, the period of one oscillation of the spring also increases. Additionally, the two variables would demonstrate a square root relationship between them. This can be seen from the fact that both equations have the same exponent of ½ as their exponent of the variable.
However, some discrepancies do exist between the theoretical and experimental data. These differences are attributed to a few systematic and random errors. The systematic error includes the extension of the spring and the potential inconsistency of measurement, while the random error includes the diversion of the force of the spring into a horizontal direction. The improvements that could be made to eliminate these factors were mentioned in the evaluation section.
In conclusion, this experiment was successful. It succeeded in proving the theoretical theory through obtained experimental data. The result of the experiments answered my research question, which as the mass attached to a spring increases, the mass-spring’s oscillation period would also increase. However, there are things that can be improved. For future occasions, I could consider more thoroughly the factors that potentially have an impact on my experiment results, such as the horizontal movement of the spring. It might be more accurate if I prepare six springs with the same constant for six masses, so one spring for every single experiment could be used.
Through the investigation of this experiment, there are more interesting topics raised. I am interested to do further investigations on the following topics:
Motion of a mass on a Spring. (n.d.). The physics Classroom.
Simple Harmonic Motion in spring-mass system review. (n.d.). Khan Academy. https://www.khanacademy.org/science/high-school-physics/simple-harmonic-motion/ simple-harmonic-motion-in-spring-mass-systems/a/simple-harmonic-motion-of-sprin g-mass-systems-ap
Torsion Spring. (2020, October 14). Wikipedia. https://en.wikipedia.org/wiki/Torsion_spring
Allain, Rhett. (2015, January 9). When does the air resistance make a difference? Wired. https://www.wired.com/2015/01/air-resistance-force-make-difference/
Brian T. Werner, Bonnie R. Antoun, George B. Sartor. Thermal Degradation of Extension Springs. Sandia National Laboratories.
Small steps forward, pressure with your tip (don’t do extra actions i.e. parry, catching the blade)
Note: Every OP’s step back is a victory
1. Stand still (at certain point)
– Keep distance (tip to tip)
– Try to hit the hand (straight)
– Wait for OP to attack
2. OP attacks
– Step back (let them fall short just a little so you can repost)
– Repost straight to the elbow
– Attack in prep (straight to elbow)
– Draw attack from OP, and then repost or attack on prep
– Keep hits straight
– Do not raise your arm (as in scared)
– Do not opposition your arm when straight hit (As in Scared being touched!)
– Don’t attack in the foot when you are pressured, and if the one you pressured in hitting your foot, straight hit to the shoulder but don’t chase after their arm/hand.
– Always let your tip stay on TOP
by James Hong
While knowledge is enlightenment acquired from education and practical understanding, experience is an apprehension gained from the knowers themselves. A diary conceals an amalgam of knowledge and episodes in a person’s life. As the writer documents newly learnt information, they refer to their knowledge; while they record memorable events or feelings and incorporate their personal encounters.
By establishing an immediate correspondence between consciousness and events, the writer can accurately transcribe their thoughts and feelings onto paper. The relationship is so intertwined that they influence each other, as the writer finds a way to combine the two in accordance. For instance, by means of one’s affairs and adventures, a piece of writing seems authentic in order to support ideologies and beliefs. In this process, the ideas presented by the diary would be subjective from the writer’s perspective. Hence, a diary provides a primary source of perceiving someone’s frame of thought. It provides an insight into a person’s unique perspective and mental approach that they are exposed to and how they associated themselves with particular knowledge.
As a knower, the acquisition of knowledge comes hand-in-hand with distinct happenings. However, personal experience may come in various forms: verifying a concept or visualizing the ideas. Such interaction between the knower and the knowledge develops a bond between the two, thus incorporating a piece of external information into one’s mind. While learning is necessary, the knowledge would be of no significance to a knower unless they are interrelated with the information; otherwise, the knower would not possess the information as to their own. Every individual has a peculiar way of bridging with knowledge, keeping a diary being one of them. Therefore, the interconnection between knowledge and personal experiences shapes a person’s identity as a knower.]]>
Amazon is an American multinational technology company founded by Jeff Bezos in 1994 and today it is estimated to have a worth of 1.7 trillion dollars. It owns the world’s largest online marketplace that has generated $280 billion of sales revenue in 2019.
Live streaming shopping is an emerging trend of E-commerce that combines livestream and the ability to purchase products directly from the live stream. It stands out from traditional e-commerce platforms as it allows live interaction between the buyers and sellers. The idea of live streaming was first introduced in the Chinese e-commerce market in 2016, which has since revolutionized the country’s e-commerce industry. In 2019, Chinese livestream shopping sales account for 9% of the country’s all $1.8 trillion e-commerce sales revenue, while 30% of China’s population has viewed live shopping streams in 2019.
Amazon launched its livestream shopping platform in February 2019, known as Amazon Live. However, it has little success which it only has an average of viewers on a daily basis. The stark difference of live stream shopping’s popularity and sales revenue between the two has various reasons, but can mostly be attributed to Amazon Live’s lack of promotion and marketing. Amazon has done little in promoting its live stream platform, and its link is not even featured on Amazon’s website. With Amazon’s worldwide dominant role of online e-commerce, coupled with the booming live stream industry due to the Covid-19 lockdown, Amazon Live has a huge potential for its growth. Therefore, I decided to investigate:
Should Amazon promote its live stream platform thereby enhancing the shopping experience to maximize sales growth?
This commentary will evaluate how Amazon’s live stream can increase the sales growth of Amazon through enhancing customers’ shopping experience, how itself as a product can pursue further growth of Amazon’s sales revenue. This commentary will be based on a number of journals and articles from authentic sources, such as Forbes, Entrepreneur and Bloomberg. Amazon’s financial reports and articles from the retailing business publications will be referenced in the commentary as well. Throughout the analysis, marketing techniques and tools including Marketing Mix, Product Perception Map and the Product Perception Map will be used.
Also, the platform allows the sellers to showcase how their products can be used and give the audience a realistic perspective of the products. Through demonstration, sellers can verify to the users about the effectiveness of the products, which usually cannot be obtained from traditional e-commerce platforms. As such, the users would have a better sense of the product and therefore be more inclined to purchase the product.
Unlike the traditional e-commerce platforms, live stream shopping requires the retailer to engage in selling products attentively for many hours. In order to maximize their output from their limited time and energy, they will choose to sell the most popular goods to catch most people’s attention, therefore achieving a higher number of sales.
Therefore, most of the products selected by the retailers would expect to be up-to-date and trending products that are mostly targeted towards the female demographics. In 2011, research published by Harvard Business Review indicates that women contributed to 70% of total consumer spending in the United States. As live stream allows retailers to resolve customers’ concerns through demonstration, it would greatly benefit from targeting the female demographic.
The following product perception map is created to analyze different types of products that are mainly targeted towards female demographics, in terms of their consumption rate and
average cost spent. It is important to note that these products are only some of the major categories of products offered by Amazon, the actual products offered by e-commerce platforms are much more diverse.
Product Perception Map Analysis:
Product Perception Map of some categories of products sold on Amazon, in terms of the product’s average cost and consumption rate
In this graph, the horizontal axis represents the average cost spent for a specific product, while the vertical axis represents the product’s consumption rate. The products that will be favoured by retailers on live stream platforms are in the upper right segment of the graph. These products have a high consumption rate and low average cost, which the audiences will be more willing to buy for these two reasons.
Furthermore, it is worthwhile to note that such demonstrations would help to reduce the return rate of the products, which the users would know about the products before the purchase. This could potentially save Amazon millions of dollars from delivery costs.
Pricing strategy is one of the most important elements of marketing a product. The better understanding of the buyer’s perspective, the better the seller can arrive at a value-based price that could better suit the market. The live stream provides a personal engagement tool for the sellers to work out the questions and doubts their clients might have. Furthermore, they could explain the value of the product and convince their client that the price is justified. Consequently, the customers would be likely to find the price acceptable and therefore purchase the product. Such direct connection to each potential client gives the seller confidence and options to perform a more flexible pricing strategy during the live show.
Unlike the unresponsive graphics and text that explain the products on the traditional e-commerce platforms, live streaming provides a more engaging experience to the customers with real-time human interaction. With real human voice, looks, body language and humour, much more information about the products can get to the buyers effortlessly as if they are having a conversation. Research by Analytic Partners shows that an online video impression is worth three times more than a digital display impression, in terms of return on investment. This shows how more profitable and persuasive human interaction is to the e-commerce industry than inanimate texts and images.
Not only that the audience can be more engaged, but real human interaction also allows the audience to ask questions directly to the retailers about the product. Explanations can take place instantly while receiving clients’ messages through live chat. A research published on Forbes shows that companies that responded to a client in five minutes compared to thirty minutes saw 100 times more odds of qualifying for a lead. This shows that the faster the customer’s concern is resolved, a sale would be more likely to be made.
In addition, the hands-on tutorials about the products can easily keep an audience’s attention. Customers would be drawn into a live stream out of a learning purpose. For example, customers might be interested in the make-up routine of a good-looking influencer, and end up
Watch the influencer’s live stream in order to learn how they do their make-up. Due to these hands-on tutorials and demonstrations, customers would end up buying products that they had never heard of before they watched the live stream. Therefore, Live streaming allows retailers to bring their products to new customers by advertising based on their targeted group of customers’ interests.
During the Covid-19 pandemic, stores are forced to shut down and people are bound to their houses most of the time. As a result, people who have the habit of shopping and purchasing turned to e-commerce platforms such as Amazon. However, for products such as cosmetic products and clothing, the shopping experience online would be more limited than that of physical stores. The explanation of the products with merely text and graphics is also far less engaging for customers than a salesperson and solid products. Nonetheless, the popularity of Amazon Live would allow salespeople to have direct interaction with their customers in real-time, without any physical contact. This would greatly increase the shopping experience online, especially regarding products such as cosmetic products and clothing, where the retailers can now explain the product and display its effect. As a result, the live stream would greatly help the retailers to sell their products, and hence hugely increase the number of sales.
As people now have more free time to spare due to the lockdown, the time people spent on live streams has greatly increased. Since the start of the pandemic lockdown, live stream viewers across different platforms spent 47% more time watching live streams. This is an opportunity for Amazon Live to increase its scale as live streams become increasingly popular during the lockdown.
Also, live streaming allows the resellers to present their products anywhere they prefer. For example, a business can sell their kitchenware by actually cooking inside a kitchen, which would not happen if the product is to be sold in a physical store. Just like the products review videos on the internet, the ability for sellers to choose their physical location to better present their products better. As a result, it would have a positive impact on the sales of the products in return.
Product Life Cycle Analysis:
The Product life cycle Graph of Amazon’s E-commerce Website This is the product life cycle of Amazon’s online e-commerce platform. The blue line shows Amazon’s sales revenue from 2004 to 2020, whereas the red line shows the projected sales revenue from after 2020 until 2050. Amazon is currently in the growth state as a product,
in order to maximize the net profit of Amazon, it would need to use an extension strategy to boost its number of sales. Live Stream shopping, from the above analysis, is definitely one of the main extension strategies that Amazon can employ.
In conclusion, Amazon should promote Amazon live to increase its users’ shopping experience, and thus generate a higher sales revenue growth. The live stream shopping platform has the advantages of targeting popular products, pricing strategy, highly effective promotion and disregard to location. Amazon live is analyzed to have better customer segmentation and better promotion than the traditional e-commerce platforms. It is able to boost Amazon’s user
experience with human interaction in real-time and demonstration of the product is regardless of location. It provides a new alternative to the e-commerce industry and it would connect the sellers with the buyers in an innovative way. With Amazon’s huge active user base and the booming industry of live streaming, it has the potential of growth that is beyond imagination.
Genovese, Maira. (2020, Nov 23). A Comprehensive Guide to Livestream Shopping. Influencer Marketing Hub.
Hensel Anna. (2020, Nov 9). As Singles Day continues to grow, the U.S. livestream shopping wars heat up. Modern Retail.
Liu, Stephanie. (2020, Sept 7). Amazon Live is a Thing: Here’s How Your Brand Can Benefit. Entrepreneur. https://www.entrepreneur.com/article/355642
Masters, Kiri. (2020, Nov 16). Amazon Live Video Shows Us The Future Of E-Commerce. Forbes.
Amazon. (2020). 2019 Annual Report. Amazon.
Blakeley, Lindsay. (2020, Dec 4). Livestream Shopping Is Here to Stay. Here’s How to Nail the Art of Making Sales Entertaining. Inc.
Canales, K., Sonnemaker, T. (2020. Aug 26). Jeff Bezos is now worth more than $200 billion, making him the richest person in the world by nearly $90 billion. Business Insider. https://www.businessinsider.com/amazon-ceo-jeff-bezos-net-worth-passes-200-billion-20 20-8#:~:text=It’s%20now%20valued%20at%20%241.7,quarter%20on%20COVID%2Dre lated%20initiatives.
Charlton, Alistair. (2018, June 19). Amazon is working on an online TV shopping service for Youtube-loving millennials. Gear Brain.
Greenwald, Michelle. (2020, Dec 10). Live Streaming E-Commerce Is The Rage In China. Is The U.S. Next?. Forbes.
Hallanan, Lauren. (2019, Mar 15). Amazon Live is Alibaba’s Live-Streaming Without The Good Bits. Forbes.
LaSala, Joe. (2018, July 23). Are All Impressions Created Equal?. Analytic Partners. https://analyticpartners.com/news-blog/2018/07/are-all-impressions-created-equal/
Krogue, Ken. (2012, July 12). Why Companies Waste 71% of Internet Leads. Forbes. https://www.forbes.com/sites/kenkrogue/2012/07/12/the-black-hole-that-executives-dont know-about/?sh=4c13cde438e3
O’Shea, Dan. (2019, Feb 13). Amazon launches live-stream shopping. Retail Dive.
Perez, Sarah. (2019, Feb 8). ‘Amazon Live’ is the retailer’s latest effort to take on QVC with live-streamed video. Tech Crunch.
Rueter, Thad. (2020, July 17). Amazon Tries to ‘Live-streaming Commerce”. Retail Leader. https://retailleader.com/amazon-tries-build-live-streaming-commerce
Sabanoglu, Tugba. (2020, Nov 30). Annual net sales of Amazon 2004-2019. Statista. https://www.statista.com/statistics/266282/annual-net-revenue-of-amazoncom/
Silverstein, Micharl J. (2011, July 28). Why Retailers Should Target Female Consumers. Harvard
Business Review. https://hbr.org/2011/07/back-to-school-is-going
Townsend, M., Kharif, O. (2020, Sept 14). Livestreams are The Future of Shopping in America. Blomberg.
Waters, Michael. (2020, Nov 23). As big tech goes all in on live stream shopping, the future may be for small brands. Modern Retail.
Farming practices in Canada have changed dramatically over the last 50 to 60 years. The number of small family farms has significantly declined, and larger intensive factory farms have become the norm for food production in the 21st century.
Farmers, faced with pressures to produce in greater quantities and at lower prices, succumbed to increasingly harsh and industrial techniques that treat animals as machines, rather than living, breathing individuals with natures, instincts, and needs.
Factory Farming is a system of farming in breeding and raising vast numbers of animals in cramped, unnatural conditions, in order to produce a large amount of meat, eggs, or milk as cheaply as possible.
In the past 45 years, there exists an inverse relationship between the number of farms in Canada and the average number of animals on each farm. The number of farms has decreased significantly, while the average number of animals per farm has shot up dramatically.
From 1976 to 2016, the total number of animal farms decreased from 412,404 to 119,699. Meanwhile, the number of animals increased from 117 million to 181 million. This means that more animals live on fewer farms, yet more animals are being slaughtered at ever increasing rates. This is in large part due to selective breeding and use of hormones which significantly reduce the life span of farm animals so that they reach their slaughter age extremely young.
Over this time period, the most significant intensification occurred for chickens and pigs. The most staggering example is pig farming – the number of pig farms decreased from 63,602 to 8,402, while the average numbers of pigs per farm increased over 18 times, from just 91 in 1976 to 1,677 in 2016
Over 834 million land animals were bred and killed last year in Canada, yet their existence and suffering is shrouded in secrecy.
According to the CDC, as of December 2, 2019, 102 people infected with the outbreak strain of E. coli have been reported from 23 states.
Eating or drinking food or water contaminated with certain types of E. coli can cause mild to severe gastrointestinal illness. Some types of E. coli can be life-threatening.
Generally, the symptoms include severe stomach cramps, diarrhea, fever, nausea, and/or vomiting.
In total, 70 laboratory-confirmed cases of Salmonella Enteritis illness were reported in: Newfoundland and Nova Scotia.
Young children, the elderly, pregnant women or people with weakened immune systems are at higher risk for contracting serious illness.
These outbreaks show us that food poisoning exists and could mainly be caused by the dirty environment of factory farming. In order to prevent such things happening, or even decrease the chance of this, we need to change to healthier and cleaner farming such as organic farming.
Organic Agriculture: Organic farming is a farming technique that involves the raising of plants and animals in natural ways. This process involves the use of biological materials, avoiding synthetic substances, and thus minimizing pollution and wastage.
Organic agriculture is defined as the sustainable cultivation of land for food production that nourishes soil life, nurtures animals in their natural environment and feeds them according to their physiology.
Crop rotation: the practice of planting different crops sequentially on the same plot of land to improve soil health, optimize nutrients in the soil, and combat pest and weed pressure.
Organic farms are found in every province in Canada.
In 2019, there were 5677 organic farms in Canada. And Canada’s Organic production is the 5th in the world.
Quebec had the highest percentage of certified organic farms (28.6%) in Canada in 2016, and then Saskatchewan (22.5%), which comes second.
There are some issues that needs to be addressed before implementing this method of farming:
At the moment, corporations have been able to keep the laws favorable to industrial farming practices. A well-organized movement can produce better policies—California voters just passed Proposition 12, which established “minimum space requirements based on square feet for calves raised for veal, breeding pigs, and egg-laying hens.” Reforms like this will improve millions of lives, even if they are small. And while improving laws will increase the prices of animal-based products, that’s not necessarily a bad thing: Those prices will better incorporate the “true costs” of the food, just as products made without worker exploitation are often costlier.
Animal Justice, A. J. (2020, September 18). Canada Slaughtered 834 Million Animals in 2019. Animal Justice. https://animaljustice.ca/blog/canada-slaughtered-834-million-animals-in-2019.
Hill, S., & J. MacRae, R. (1999). Organic Farming in Canada. https://eap.mcgill.ca/publications/eap104a.htm.
Carey, J. (2020, October 8). What Is a CAFO? The Truth About Animal Agriculture. Sentient Media. https://sentientmedia.org/what-is-a-cafo/.
Chait, J. (2019). How Organic Farming Benefits the Environment. The Balance Small Business. https://www.thebalancesmb.com/environmental-benefits-of-organic-farming-2538317.
C.O.G, C. O. G. (2020). Organic Organizations In Canada. cog.ca. https://www.cog.ca/organic-organizations-in-canada/.
D.Ho, M. (2020). What is Erosion? Effects of Soil Erosion and Land Degradation. WWF. https://www.worldwildlife.org/threats/soil-erosion-and-degradation.
Dalhousie, U. (2013). About Organic in Canada. Dalhousie University. https://www.dal.ca/faculty/agriculture/oacc/en-home/about/organic-canada.html#:~:text=Of%20these%20operations%2C%20Saskatchewan%20was,organic%20farms%20increased%20by%2066%25.
Derrick, C. (2020, November 28). Undercover footage from Ontario pig farm shows alleged abuse but new laws may ban future probes. W5. https://www.ctvnews.ca/w5/undercover-footage-from-ontario-pig-farm-shows-alleged-abuse-but-new-laws-may-ban-future-probes-1.5207579
Environmental Working Group, E.W.G (2020). Case Study: Iowa Cities Struggle to Keep Farm Pollution Out of Tap Water. Environmental Working Group. https://www.ewg.org/research/case-study-iowa-cities-struggle-keep-farm-pollution-out-tap-water.
Factory Farm Collective, F. F. (2019, November 14). Does Factory Farming Exist in Canada? Here’s what the data says. Factory Farm Collective. https://factoryfarmcollective.ca/does-factory-farming-exist-in-canada-heres-what-the-data-says/.
Factory Farm Collective, F. F. C. (2020, December 19). Animal Agriculture in Canada. Factory Farm Collective. https://factoryfarmcollective.ca/animal-agriculture-in-canada/.
Government of Canada, S. C. (2021, May 28). The 2021 Census of Agriculture and organic farming in Canada. Government of Canada, Statistics Canada. https://census.gc.ca/resources-ressources/cst-tsc/agriculture/organic-biologique-eng.htm.
Hein, T. (2020, August 31). Agriculture in Canada. The Canadian Encyclopedia. https://www.thecanadianencyclopedia.ca/en/article/agriculture-in-canada#:~:text=Challenges%20and%20Progress%20in%20Canadian,labour%2C%20climate%20change%20and%20health.
Humane Canada, H. C. (2020, March 16). Realities of Farming in Canada. Humane Canada. https://humanecanada.ca/our-work/focus-areas/farm-animals/realities-of-farming-in-canada/.
Institute, R. (2020, December 15). Crop Rotations. Rodale Institute. https://rodaleinstitute.org/why-organic/organic-farming-practices/crop-rotations/.
Kateman, B. (2017, June 19). How to stop cruel factory farming: start with one animal. Vox. https://www.vox.com/the-big-idea/2017/6/19/15827828/factory-farming-switchetarian-beef-chicken.
Lingel, G. (2021, April 13). Factory Farming: What the Industry Doesn’t Want You to Know. Sentient Media. https://sentientmedia.org/factory-farming/.
Lowndes, S. (2013). Organic Agriculture. Organic Agriculture | The Canadian Encyclopedia. https://www.thecanadianencyclopedia.ca/en/article/organic-agriculture.
Media, S. (2021, March 25). Pig Farming Uncovered: The Pork Industry’s Disturbing Truths. Sentient Media. https://sentientmedia.org/pig-farming/.
Miller, S. (2020, July 28). What is Organic Farming – Definition, Features, Benefits & Principles. Conserve Energy Future. https://www.conserve-energy-future.com/organic-farming-benefits.php#:~:text=Organic%20farming%20is%20a%20technique,thereby%20minimizing%20pollution%20and%20wastage.
Peta, P. (2020, December 30). Factory Farming: The Industry Behind Meat and Dairy. PETA. https://www.peta.org/issues/animals-used-for-food/factory-farming/.
Piper, K. (2018, November 15). We could end factory farming this century. Vox. https://www.vox.com/future-perfect/2018/11/15/18088776/end-animal-farming-vegetarian-vegan-meat-alternatives-jacy-reese.
Robinson, N. J. (2018, December 12). Can We End Animal Farming Forever? Current Affairs. https://www.currentaffairs.org/2018/11/can-we-end-animal-farming-forever/.
Statistics Canada, S. C. (2017, December 11). Selected livestock and poultry, historical data. https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3210015501.
Sulaeman, D., & Westhoff, T. (2020, February 7). The Causes and Effects of Soil Erosion, and How to Prevent It. World Resources Institute. https://www.wri.org/insights/causes-and-effects-soil-erosion-and-how-prevent-it.
Temple, J. (2020, April 2). Sorry-organic farming is actually worse for climate change. MIT Technology Review. https://www.technologyreview.com/2019/10/22/132497/sorryorganic-farming-is-actually-worse-for-climate-change/.
One that do many Faint:
One that has a long reach:
(continuously make renewed attacks)
One that attack with preparation on the blade:
One who continuously beats the blade:
This action will tire the sword hand and slow one’s action
Meets at for the First Time:
Patient Fencer (epee):
Who remains on guard well-covered, keeps out distance and evades attempts to make preparations on the blade
Generally have very accurate stop hits at wrist
One who absent the blade:
Who attacks into attack:
Who fences at close quarters:
Perfected time and executed at maximum speed/ acceleration
Rapid recovery after attacks (parried or for second-intention attack):
Who rapidly retreat from lunges:
Left handed Fencer:
They like to parry quarte or bring the blade to the quarte. Because in that line they obtain the top of the blade and therefore can control it.
They like the action of beat, and an attack on the outside or the top of the arm
If the beat in made outside:
Beat on top of the blade:
These are only a few broad tactical ideas, each person must observe each opponent and study their game before the tactics can be done.
Never use more complex movements than necessary to achieve the desired results.
“To hit a worthy opponent with a complex movement is satisfying, and show one’s mastery of techniques; to hit the same opponent by a simple movement is a sign of greatness.”
BEAUMONT, Charles Louis De. Fencing Ancient Art and Modern Sport. Oak Tree Publications; revised edition (Feb. 1 1979)