Category: today i learned (til)

The Towers of Hanoi

A set of colorful, cascading disks stacked on a peg. What could easily double as a child’s toy also serves as an ancient mathematical puzzle, the Towers of Hanoi. Often used to teach recursive problem solving strategies, the puzzle poses a simple challenge—to move the stack of disks from the leftmost peg to the rightmost peg one disk at a time with one restriction: a disk cannot be placed on top of a smaller disk.

Take a moment to familiarize yourself with the puzzle by playing around with this online version. Setting the number of disks to 3 is a great place to start.

It may be surprising that, no matter how many disks there are, this problem is always solvable with just three pegs. Even more surprising, the optimal solution for any number of disks (the solution that requires the fewest number of moves) directly mirrors the rhythm of counting in binary.

Before diving into this optimal solution (in a later article), this article focuses on understanding what counting in binary looks like and explores the nature of different number systems.

Base-10

The number system we most commonly use involves counting in base-10, a natural choice given the number of fingers we have on our hands. Consider the number 104 for example. Let’s index the digits from right to left, beginning with zero:

• the value at index 0 is 4,
• the value at index 1 is 0,
• and the value at index 2 is 1.

Because we are working in base-10, there are 10 possible values for each digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) and each index represents a consecutively larger power of 10 corresponding to its index. The number 104 can be expressed as the sum of powers of 10 as follows:

• 10^0 * 4 (or 4 ones)
• 10^1 * 0  (or 0 tens)
• 10^2 * 1 (or 1 hundred).

Base-2

Let’s now consider how this same value would be written in a different base: base-2, or binary. The binary system has only 2 possible values for each digit (0 or 1) and is most useful in the field of computer science as it is easy to consider an electrical component as having one of two possible states (on or off). In the binary representation of a number, each index represents a consecutively larger power of 2 corresponding to its index.

After some calculation, we can express 104 as the sum of powers of 2 as follows:

• 2^0 * 0 (or 0 ones)
• 2^1 * 0 (or 0 twos)
• 2^2 * 0 (or 0 fours)
• 2^3 * 1 (or 1 eight)
• 2^4 * 0 (or 0 sixteens)
• 2^5 * 1 (or 1 thirty-two)
• 2^6 * 1 (or 1 sixty-four)

Thus, the binary representation of 104 is 1101000.

Converting Between Bases

To round out this introduction to different counting systems, let’s actually go through the process of converting a value from one base to another.

Consider the base-10 value 2643. Although base-10 is standard, it is good practice to break apart the digits and understand how this value is written. From right to left, we have:

• 10^0 * 3 (or 3 ones)
• 10^1 * 4 (or 4 tens)
• 10^2 * 6 (or 6 hundreds)
• 10^3 * 2 (or 2 thousands)

Now we will determine how to express 2643 in base-8 by recursively answering the same question:

• What is the largest power of 8 less than or equal to 2643?
  • The answer is 8^3 = 512, and we can fit five 512s into 2643 with 83 left over. 
• What is the largest power of 8 less than or equal to 83?
  • The answer is 8^2 = 64, and we can fit one 64 into 83 with 19 left over. 
• What is the largest power of 8 less than or equal to 9?
  • The answer is 8^1 = 9, and we can fit two 8s into 19 with 3 left over. 
• What is the largest power of 8 less than or equal to 1?
  • The answer is 8^0 = 1, and we can fit three 1s into 3 with 0 left over. 

Putting it all together, from right to left, we have:

• 8^0 * 3 (or 3 ones)
• 8^1 * 2 (or 2 eights)
• 8^2 * 1 (or 1 sixty-four)
• 8^3 * 5 (or 5 five-hundred twelves)

Thus, the base-8 representation of 2643 is 5123.

The Value 10

One interesting tidbit about working across different number systems is how different values are represented by 10. In any arbitrary base-n system, the value 10 can be read as:

• n^0 * 0 (or 0 ones)
• n^1 * 1 (or 1 n)

Thus, in any base-n system, the value of 10 is exactly n. To get a bit existential, every number system is, to itself, base-10. 

References

1. https://www.khanacademy.org/computing/computer-science/algorithms/towers-of-hanoi/a/towers-of-hanoi
2. https://www.mathsisfun.com/games/towerofhanoi.html
3. https://www.youtube.com/watch?v=2SUvWfNJSsM

Recently, our project team ran an activity booth at a science-themed block party. The booth was a fun way to teach partygoers about the science behind genetics, phenotypes, and Punnett squares. Our team created an interactive activity that presented partygoers with three genetics-based puzzles at varying levels of difficulty. Because it was close to Halloween, we incorporated the use of candy into these puzzles, which served as an incentive for puzzle-solvers to challenge their scientific skills and learn something new.

The easiest puzzle involved crossing two parents with an identical genotype in a single-trait Punnett square. In this example, taffy was used to represent the dominant allele and hard candy was used to represent the recessive. Two piles of candy were provided to participants, who used the sweets to complete the missing square in the puzzle. Afterwards, we asked a question on the phenotypes of the resulting organisms to ensure conceptual understanding on the part of the participant. The puzzle is included below:

The second puzzle involved the evaluation of a sex-linked trait. In this case, unaffected X-chromosomes were represented by dark colored hard candy while affected X-chromosomes were represented by light colored candy. Taffy was used to represent the Y-chromosome. Participants were now asked to fill in two separate squares using the corresponding candy chromosomes. Two questions regarding the outcome of such a genetic cross were then posed. This puzzle helped to teach participants about why some diseases and conditions are more prevalent in one sex. The puzzle is included here:

Lastly, the third puzzle challenged participants with a dihybrid cross, which involved analyzing two distinct traits using one Punnett square. This example analyzed the traits ‘color’ and ‘shape’. It took on a similar format as previous puzzles, but its complex nature resulted in participants needing more assistance when solving it. This reflects the idea that we were successful in varying the difficulty of the problems. Here is the final puzzle:

Overall, this serves as a fun activity that helps partygoers to engage with some of the scientific concepts behind genetics. When we used them, these puzzles sparked conversations and inspired scientific interest in participants. This is a great activity to try if you’re doing a science-themed event, and it’s fun for kids and adults!

“I am become death, the destroyer of worlds.” The fear of the atomic bomb was felt not only by the citizens who feared enduring its wrath but also by the inventor himself, Robert J. Oppenheimer. With its debut in his 1965 interview, the quote reflects not only the fear of the wrong force holding the atomic bomb but also of the idea that the atomic bomb could set off a sudden atmospheric chain reaction, causing the earth itself to incinerate. This fear is also portrayed in the recent film “Oppenheimer,” which is based on the life story of Robert J. Oppenheimer before, during, and after the Manhattan Project. In the movie, there is an especially memorable scene in which the portrayal of theoretical physicist Edward Teller claims that there is a 3 in one million chance that the world could be incinerated via the ignition of the nitrogen in the atmosphere and oceans. After this tense moment and the initial hesitation of continuing with the Trinity test, the probability is never mentioned again. So was Teller right? Do we still face the slight probability of atmospheric incineration? Thankfully, after further calculation, it’s been determined that this method of mass extinction is not a matter of slim probability; it’s an impossibility.

Post Trinity test, a declassified 1946 Manhattan Report dives into detail proving the impossibility of a thermonuclear reaction caused by an atomic bomb of the size they were dealing with. The report analyzes atmospheric nitrogen as the subject of ignition due to the instability of its nuclei, the reactions of which yield much more energy in the form of gamma rays. On the basis that there is an ignition point of the atmosphere (10 MeV temperature), the high reactivity would need to surpass that point such that “…the thermonuclear reaction may be propagated to all parts of the atmosphere” (Konopinski et al, 1946), setting off a chain reaction. Despite the energy release via nitrogen reactions, the earth’s atmosphere is transparent to the radiation emitted by them: it cannot absorb or reemit these radiation frequencies. The energy instead escapes into other systems, causing the temperature to restabilize and fail to propagate further reactions. However, the best models of the time first considered the energy produced via the nitrogen reaction to go towards the establishment of the temperature required for atmospheric ignition. Using these more conservative models for the sake of establishing a broader safety net, the Stephan-Boltzmann law – which claims that the hotter an object is the faster it cools – affirms the impossibility of such atmospheric detonation. The size of the bomb they were dealing with would only have about 1% of the energy it released be absorbed as heat by the atmosphere. The rest would dissipate as light, kinetic energy, or escape into space (Konopinski et al, 1946). This ultimately renders a nuclear chain reaction impossible; exponentially more fission material is needed to reach atmospheric ignition. For the technology at the time, there just simply was not enough bomb to generate the required energy.

All science, however, is subject to change over time. This was the core argument of a contradictory article written almost 30 years after the initial Trinity tests and the publication of the 1946 report. The article reopens the previously debunked fallacy, arguing it’s not very possible that “…those who were instrumental in developing fusion devices (1948 to 1958) ever seriously considered the ultimate potential or the unexpected results of fusion explosions that were a 1,000 times as powerful as the fission device of 1945″ (Dudley, 1975). The current scope of today’s technology is beyond what would have been fathomed 80 years ago, including the ability to alter the rate of radioactive decay and half-lives, rendering the energy yield of fusion devices difficult to predict. This argument, however, is weak and extremely flawed as it is based on the idea of Murphy’s Law – that anything can go amiss – and maintains almost no mathematical basis. This short-sighted view and misconception was concisely rebuked less than a year later in a much more scientifically sound article. As in the 1946 report, the article looks into the unstable “…collision between two nuclei of N14 because N14 is a nucleus of relatively high energy content” (Bethe, 1976). The energy produced in the reaction that Bethe looks into (eq 1 below) surpasses the Coulomb barrier required for the reaction to occur with little difficulty and is the same process looked at by Konopinski et al.

N14 + N14 = Mg24 + He4 + 17.7 MeV eq 1

Unsurprisingly, Bethe comes up with similar results to those of Konopinski et al, finding that the energy produced by the reaction is only a minute fraction go the energy lost via physical processes such as the rapid dispersion of the energy in the form of radiation (which, as stated before, our atmosphere is transparent to), heating of the atomic nuclei, etc. The main principle is that “The air cannot be heated as hot as the weapon” (Bethe, 1976). For the atmosphere to ignite, the atomic bombs of modern scale would have to be of an entirely different design such that they could reach the required temperature for ignition; these temperatures are so high that it’s nearly impossible to create a bomb that possesses such qualities.

The profound fear associated with the atomic bomb, articulated by Robert J. Oppenheimer’s chilling words, has left an indelible mark on history. This fear extended beyond the devastation it could unleash upon humanity to include the apprehension that it might trigger an unthinkable catastrophe—igniting the Earth’s atmosphere. The portrayal of this fear, as depicted in the recent film “Oppenheimer,” highlighted a pivotal moment when theoretical physicist Edward Teller suggested a slim probability of atmospheric incineration. However, this fear was ultimately disproved via rigorous scientific analysis and understanding. Including the contradiction of these calculations in the film would take away the tension from the generally uninformed audience. While technological advancements have been made since the early days of nuclear weapons development, the fundamental principles of physics governing these devices and the behavior of our atmosphere remain unchanged. We live to see another day without nuclear damnation.

Sources:

Bethe, H. A. “Ultimate catastrophe?” Bulletin of the Atomic Scientists, vol. 32, no. 6, 1976, pp. 36–37, https://doi.org/10.1080/00963402.1976.11455623.

Dudley, H. C. “The Ultimate Catastrophe.” Bulletin of the Atomic Scientists, vol. 31, no. 9, 1975, pp. 21–24, https://doi.org/10.1080/00963402.1975.11458293.

Teller, Edward, et al. 1946, Ignition of the Atmosphere With Nuclear Bombs.

Being a Georgia Tech student sure does come with its ups and downs. There are times during the semester when your life is great, you meet up with friends, finish your work early, and even sleep before 10 pm. On the opposite side, there are weeks where you have tests back-to-back along with a weekly lab report and group presentation all due on the same day. There are so many different types of stress that Georgia Tech students are experiencing at the same time. Whether it is stress within a relationship, academic stress, or even stress about missing a day at the gym, all these stress factors build up and end up decreasing your mental health and leading to depression.

Though there are many things that can lead to an outlet of stress. A reliever of stress that some Georgia Tech students do is clean. Cleaning, often seen as a sign of a tedious and mundane task, has proven to be a powerful tool in reducing stress and anxiety. Cleaning gives a sense of peace in the calm. When the world around you seems to be in chaos, cleaning gives you a sense of control where you have power over certain objects in your life, and cleaning and getting rid of them makes you calmer and more controlled in your life. Even a simple task like clearing your desk or doing the dishes in the sink gives you that sense of control and thus reduces your level of stress. 

Cleaning also helps reduce sensory overload and improve focus. In the fast-paced world that we live in where our senses are constantly bombarded with stimuli, it can lead to high stress and anxiety levels. By cleaning, you remove unnecessary clutter and create an environment that is free from distraction. This can improve focus and reduce sensory overload. As cleaning can be a form of mindfulness, it allows you to focus on the present moment and forget about worries and anxieties. You can block out distractions and engage in a form of active meditation, which can help improve mental clarity and reduce stress. This mindfulness can have a lasting impact, as it helps to cultivate a positive mindset and promote feelings of calm and peace.

Another reason that cleaning is important is that it can release of endorphins in the brain. Endorphins are neurotransmitters that are produced by the central nervous system, and they are responsible for reducing pain and increasing feelings of pleasure and happiness. When you engage in physical activity like cleaning, your brain releases endorphins in response. This release of endorphins can create a sense of euphoria and elation, commonly referred to as a “runner’s high.” The same phenomenon occurs during cleaning, as it requires physical movement and exertion. The satisfaction of completing a task, combined with the endorphin release, can create a sense of accomplishment and happiness. Endorphins are not only good for your mood, but they can also provide physical benefits. They can act as natural painkillers and boost the immune system, which can help reduce the risk of illness and improve overall health. The release of endorphins during cleaning can also help to reduce stress and anxiety, leading to a more relaxed and calm state of mind. In conclusion, cleaning can be a powerful tool to reduce stress and anxiety levels. Cleaning provides a sense of accomplishment, reduces sensory overload, and improves mental health and mindfulness. 

 

Sources: 

Brain mind clear – free vector graphic on Pixabay. (n.d.). Retrieved May 4, 2023, from https://pixabay.com/vectors/brain-mind-clear-help-support-7283928/

How to release endorphins and what they are. How to Release Endorphins and What They Are. (n.d.). Retrieved May 4, 2023, from https://www.betterup.com/blog/how-to-release-endorphins

The mental health benefits of a clean home. Newport Healthcare. (2023, January 26). Retrieved May 4, 2023, from https://www.newporthealthcare.com/resources/press/clean-home-benefits/ 

Have you heard the story about some scientists trying to turn purple petunias more purple, and instead the petunias threw a tantrum and turned white?

The theory I heard was that because the method to insert new genes into an organism usually involves using a modified virus, when the plant was “infected” with the extra purple, it’s “immune system” treated the gene like an attack and as a result just it shut down all together – and thus, white flowers.

IT TURNS OUT THOUGH, it’s a bit more complex than even that – and eventually, this little failed experiment led to the discovery of a major gene editing tool.

So back in the 90’s, the scientist who tried to purple-fy the petunias (Richard Jorgensen) actually added the gene through transfection instead of transduction – essentially meaning they got the gene into the cell by non-viral means.

HOWEVER, despite not actually being exposed to a virus, those petunias did respond like they were being attacked. This is because inserting foreign genetic material is exactly how viruses work, and in response, most organisms’ from plants to worms to humans, have developed protections against it.

And this is especially true for RNA, since that’s what most viruses are made of – and what most cells need to defend against.

A quick overview of RNA, for the unfamiliar. It’s a nucleic acid like DNA (“ribonucleic acid”), and it’s essentially DNA’s little brother. If DNA holds the blueprints for all the different proteins and things a cell needs to make, RNA is the way those instructions are translated and then messaged to the rest of the cell – AKA mRNA. This comes into play with viruses, because they function essentially like spam mail – they attack cells and add their own RNA instructions, which tricks and hijacks the host cell into making whatever the virus wants (usually more of itself). So cells have a defense to combat this.

For one, mRNA on the job only has one strand (instead of 2 like DNA), so that it’s instructions can be read easily. However, nucleic acids come in pairs, so if another strand of RNA happens to come along that has the right matching pair, the two strands can get stuck together like legos – blocking the instructions and stopping the expression of that gene/protein. This is what researchers figured happened with the petunias, and several similar experiments with worms. However, another surprise occurred when researchers Andrew Fire and Craig Mello tried to do a control experiment where they inserted cells with a strand of mRNA that was supposed to have no effect – they still saw gene silencing! 

Looking deeper into it, they found that the cause was actually double strands of RNA that accidentally formed before injection. Apparently these pre-paired RNA strands were even better at stopping gene expression than a single strand – which raised more questions as to why.

And here’s where viral defense come in. Double strands of RNA (dsRNA) don’t really occur normally in cells, but they ARE common in certain viruses. So what these researchers discovered (and won a Nobel Prize for), was that plant and animal cells have a naturally occurring enzyme call Dicer that (as you might guess) finds and dices these dsRNA into little parts; and then it goes even further and takes those un-paired parts and uses them to hunt down and deactivate their partners – effectively erasing whatever virus, protein, or gene that was encoded in the targeted RNA. This is called the RNA interference pathway, or RNAi.

Now it was known at this point that, at least in mammals, introducing long strands of dsRNA for potential gene therapies/medicines wasn’t really possible, since they often triggered a larger immune response. However, learning about this silencing method inside cells allowed scientists to determine that very small strands of dsRNA could be used to reduce and effectively erase a gene or protein. And these small interfering RNA (siRNA) have become key to creating groundbreaking new gene therapies, like treatments for debilitating genetic diseases, HIV, and potentially even cancer. 

Quite a lot, to come from a seemingly failed flower experiment!

 

https://en.wikipedia.org/wiki/Virus#cite_note-Collier9699-73

https://www.independent.co.uk/news/science/how-an-experiment-to-change-the-colour-of-a-petunia-led-to-a-breakthrough-in-the-treatment-of-cancer-and-aids-5547175.html

https://www.genengnews.com/insights/plucking-rnai-from-the-gene-silencing-nettle/

https://faseb.onlinelibrary.wiley.com/doi/10.1096/fj.06-6014rev

Since ancient times the causes of severe infectious diseases in humans have been puzzling to people. Specifically, the recurrence of outbreaks, the severity of outcomes after infection ranging from permanent sequelae to premature death as well as the large impact in numbers in human populations have created the need to search for ways to learn about and prevent them. By continuous observations and through trial and error, civilizations were able to identify and distinguish the common features of certain infectious diseases and so to differentiate one from each other. Once fairly identified, people have been searching for effective and disease-specific ways to prevent them. It is in this search for prevention how vaccines appeared as tools against the nasty outcomes of infection. In this essay I will attempt a brief review of concepts related to how the immune system and vaccines work, and some key events in vaccine development.

Infectious diseases with severe outcomes in humans are several and new diseases  continuously appearing. Yet, using the particular causes or the origins of infectious diseases, they can broadly be classified into four groups: bacterial, viral, parasitic and fungi. Among these causes, there are not yet vaccines against any parasite or fungus causing severe disease in humans. Among all those diseases caused by bacteria or viruses only a few of them have a vaccine to prevent humans from their burden. Even less, the available vaccines are only against a few strains, serotypes or serogroups of a given bacterium or virus. Therefore, the number of pathogens (bacteria and viruses) that could cause severe infectious diseases in humans is several times larger than the number of vaccines we have against them. 

In general, bacterial and viral diseases are often grouped as pathogens causing diseases      

Humans have been exposed to environments full of dangerous pathogens. These continuous exposure to pathogens caused outbreaks and diseases. The threat of infection requires response from human bodies and so the human body often reacts and fights the attacks of pathogens using an innate nonspecific immunity level, which is part of the immunity system. This is often called “primary response” which occurs following the first exposure to a foreign agent. If the response is quick and effective, the infection will be contained or eliminated. Sometimes, however, the response fails so infection would cause a disease.  This could happen when the human body’s immunity is low and/or when the pathogen has a virulence to overcome the response, rapidly multiplying itself inside the human body and causing great damage to cells and tissues.     

When humans were or are able to survive and recover from certain infectious diseases, their bodies generate some specific level of immunity to reinfections. It is because the human bodies have an immune system which is essential for our survival and where some specific memory about previous infections is stored and keeps the defense abreast.  Specifically, that specific memory set in the immune system works as a first line of defense when potential reinfections with the same pathogens happen. Sometimes, such memory could wane in time and so make humans again susceptible to infection and disease; other times, exposure to the same pathogen would boost a decaying specific immunity and keep the protection against the attack of that pathogen high. Another important reason for humans becoming susceptible again is when the specific pathogen mutates and evolves, becoming unidentifiable and so making useless the previous specific memory of protection in our immune system.   

Among all types of pathogens, the new or foreign ones of great concern are those that cause severe disease and often overwhelm the immune system by making their response slow and ineffective. Often are those that cause a heavy disease burden in the human population with plenty of sequelae or death. One way to prepare the immune system to such rapid and virulent attacks and to build a defense against them is with vaccines.  Although there are different types of vaccines even against the same pathogen, in general all of them work like sparring for box or combat fighters; namely, as a sparring does, a vaccine safely and effectively stimulates the immune system, trains its rapid response and prepares it to fight. Effective vaccines are often able to mimic some or all specific characteristics – also known as antigens– of the pathogen. To keep the training of the immune system safe, these antigens in the vaccine are often weakened or killed versions of the real pathogen. In average, during the first two weeks after vaccination, the vaccine is able to prime the immune system to respond fast and with force, should an infection with the particular pathogen in full strength happen in the future. Some refer to this process as programming of the immune system and to the rapid and specific response as “secondary response” or “vaccine-induced response.” An effective secondary response is often faster and with force in the production of pathogen-specific antibodies and in creating more cellular memory in the immune system for future attacks. Yet, vaccine’s protection also could wane with time or the specific pathogen could mutate and evolve. Similar to natural immunity that could also wane, vaccine immunity could also wane or become useless against new versions of the pathogen making human bodies susceptible again to infection.

From the first vaccine developed in 1796 to the latest Covid19 vaccine, they are considered one of the greatest achievements of modern medicine. Throughout the last three centuries, several developments ranging from the advances in laboratory techniques, the discoveries in germ theory, the introduction of attenuated toxins, the cultivation of viruses, the evolution of cell culture to the introduction of recombinant DNA and the whole genome sequencing techniques have allowed the development of different vaccines and enjoy the progress and benefits we see today from them. In general, diseases that have caused the highest burden in morbidity and mortality in societies have received more attention and resources from those interested in developing vaccines. 

Although vaccines have been an effective tool against infectious diseases, the development of each vaccine for a specific pathogen has often been a slow and research intensive process. Still, there were several attempts against some pathogens that did not end up with a safe and effective vaccine.  Vaccine development follows a rigorous scientific process focused primarily on safety and then on its effectiveness. All these processes should have a sound foundation on basic biology research, scientific discovery of vaccine candidates as viable proof of concept. This is the point when the application of the investigation of a new vaccine should be submitted. After approval, a three-phase clinical studies and trial begins.  

Roughly summarized, Phase I is focused on vaccine safety conducting trials in small groups of both animals and humans; phase II is focused on vaccine effectiveness trials in an increased number of humans. Phase III is one of the most important ones. In this phase, thousands of individuals are recruited and the sample distribution should be representative of the population where the vaccine will be targeted. Individuals are then randomly assigned to often two groups  – this is referred to as random control trials or RCT.  RCTs often have a control group not exposed to the vaccine (control) and a trial group that will be exposed to the vaccine (trial group). Except for the exposure to the candidate vaccine, it is expected that both groups have very similar demographics and clinical characteristics to avoid confounding factors. Then, both groups are followed and clinical and lab data collected. By comparing the rates of disease cases in the exposed group with those of the control group is how the vaccine safety and effectiveness are determined. If successfully safe and effective, the vaccine data is then submitted for analysis by independent institutions and then the vaccine is licensed and recommended.     

In the recent past, the research and development of new vaccines used to take about 15 to 20 years. However, thanks to more than three decades of advances in DNA sequencing and the stable production of proteins in human cells exposed to messenger RNA (mRNA), the research and development time has been reduced substantially and made possible the development of Covid19 vaccines in less than a year. Had the Covid19 pandemic occurred 30 years ago, we would have been in worse shape to control or prevent their consequences.  

Overall, human’s immune systems could rely on more effective and safe vaccines to prime their response against pathogens’ attacks. Yet, the burden of infectious diseases could only be partially reduced by vaccines. As mentioned above, among all those diseases caused by bacteria or viruses only a few of them have a vaccine to prevent humans from their burden and for those with a vaccine, the protection is often partial and may wane in time.   

 

*Note: All the ideas developed in this essay were based on the references listed below.  

References:

1. “A Brief History of Vaccination.” World Health Organization, World Health Organization, https://www.who.int/news-room/spotlight/history-of-vaccination/a-brief-history-of-vaccination. 
2. Coon, Lisa. “The History of Vaccines and How They’re Developed.” OSF HealthCare Blog, 11 Feb. 2022, https://www.osfhealthcare.org/blog/the-history-of-vaccines-and-how-theyre-developed/. 
3. Diseases.” History of Vaccines RSS, https://historyofvaccines.org/diseases.
4. Dolgin, Elie. “The Tangled History of Mrna Vaccines.” Nature News, Nature Publishing Group, 14 Sept. 2021, https://www.nature.com/articles/d41586-021-02483-w. 
5. Offit, Paul. “Developments by Year.” Children’s Hospital of Philadelphia, The Children’s Hospital of Philadelphia, 20 Nov. 2014, https://www.chop.edu/centers-programs/vaccine-education-center/vaccine-history/developments-by-year. 
6. Saleh A, Qamar S, Tekin A, Singh R, Kashyap R. Vaccine Development Throughout History. Cureus. 2021 Jul 26;13(7):e16635. doi: 10.7759/cureus.16635. PMID: 34462676; PMCID: PMC8386248. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8386248/#:~:text=The%20first%20trials%20to%20develop,the%20United%20States%20in%201945. 
7.  “U.S. Vaccine Safety – Overview, History, and How It Works.” Centers for Disease Control and Prevention, Centers for Disease Control and Prevention, 9 Sept. 2020, https://www.cdc.gov/vaccinesafety/ensuringsafety/history/index.html. 
8. “Vaccine Development, Testing, and Regulation.” History of Vaccines RSS, https://historyofvaccines.org/vaccines-101/how-are-vaccines-made/vaccine-development-testing-and-regulation.

Brachistochrone – A word originating from Greece that means “shortest time.” The brachistochrone problem is a well known problem in the world of physics that involves finding a curve such that, assuming there is no friction, a ball traveling along this curve would reach its destination in the shortest possible time. Initially discovered by Johann Bernoulli, a famous Swiss mathematician, the brachistochrone curve has a variety of interesting properties, such as the fact that it is a cycloid, the path mapped out by a point on a circle as it rolls on a flat surface. Additionally, a subsection of the curve also acts as a tautochrone curve, a curve that causes a ball to reach its destination in the same amount of time regardless of where it begins its journey. However, perhaps the most interesting fact about the brachistochrone is that it was initially solved by Bernoulli using Snell’s law, a law that dictates the path traveled by light when moving between different mediums.

Initially, it may not be readily obvious why Snell’s law would approximate a brachistochrone curve, but with a bit of physical intuition, it makes perfect sense. First, the reason why Snell’s law works must first be understood. Snell’s law states that the ratio of the sines of the angles formed by the refraction of light when passing through a medium is equal to the ratio of the speed within the two media.

With a bit of calculus not shown here (perhaps in a future article), it can be shown that this equation comes as a consequence of minimizing the time taken for light to travel from one point to another between the two media. This is because light naturally always takes the path of shortest time, and this is what connects Snell’s law to the brachistochrone. When a ball is dropped, it is constantly changing velocity due to gravity, so you can envision a ball as traveling through a continuous set of layers of different velocities. If the ball wanted to travel the path of shortest time, it would follow Snell’s law at every point in its path, so the brachistochrone curve should have the property of having the ratio of instantaneous change in the velocity of the ball match the ratio of the angles formed by a vertical line at that point of the curve.

Of course, it’s one thing to be told that Snell’s law maps out the brachistochrone, but it’s not as satisfying as seeing it for yourself, which is why I coded a simulation in Python to try and match up a curve constructed from Snell’s law with a brachistochrone curve.

The top two sliders change the initial conditions of the actual brachistochrone in blue, while the bottom two sliders change the initial angle and the number of layers for the Snell’s law approximation in orange.

For more information on the brachistochrone curve, check out Vsauce or 3Blue1Brown’s videos on the topic below:

• 3Blue1Brown: https://youtu.be/Cld0p3a43fU
• Vsauce: https://youtu.be/skvnj67YGmw

 

This semester I took a course called Locomotion Neuromechanics. Like me, you might think that it would be a course where you would learn more about the movement within one’s body, different things that can affect mobility, etc. However, after attending the first class, I realized it was focused on the student’s own interest in a topic relating to Locomotion Neuromechanics. I found this method interesting because it allows the student to either dive deeper into their own research or explore other topics, related to locomotion, that they wouldn’t be able to in another class.

After the first round of presentations, the class had a broad range of topics that would be focused on like robotics, animal/insect locomotion, neurodegenerative diseases that impact mobility, flying snakes, spinal cord injuries, etc. At first, I had no idea on what topic I would be focusing on. I initially presented on something related to spinal cord injuries, but instead of focusing on humans, I was looking at animals like cats and mice. This changed after I was researching stuff that I would enjoy more. I then focused on the anterior cruciate ligament or commonly known as the ACL. This topic can go any way from what is the ACL, how it works, ACL injuries, etc.

Before I start, you might be wondering what the ACL is. The ACL is a ligament that connects the femur to the tibia. The femur and tibia in layman’s terms are the thigh bone and shinbone, respectively, found in your leg. This ligament is important for knee and joint stability. You might wonder why your knee doesn’t move forward when you walk, jump, play sports, etc. The ACL is in charge of preventing the movement of the knee to go from the front to the back or side to side. It is most commonly known to have ACL injuries while playing sports such as soccer, football, basketball, gymnastics, etc.

Below are some of the interesting research facts that I found on my literature search about the ACL:

• The two most common ACL reconstruction surgeries: bone patellar tendon bone graft and the hamstring graft
• Hamstring strength recovered at a faster rate than quadricep strength (3)
• Anterior knee pain influences the recovery of muscle performance of a patient after ACL reconstruction (3)
• Younger patients had a higher rate of subsequent ACL injury rate, distinctly that young males had higher rate of rupture than females (6)
• Researchers are trying to focus on rehabilitation programs that focus on the different forces that might heal an ACL (6)
• Depending on some factors like the type of graft used, how the graft works post-operatively and the different fixation techniques (6)
• In addition to rehabilitation programs, literature states that they are examining pre and post operative rehabilitation, neuromuscular training, electrostimulation and other protocols that an individual can go through after ACL reconstruction. (5)
• A long term consequence of ACL reconstruction is osteoarthritis which is known to be a disease of the joints. Factors that can influence the outcome consists of sex, age, family history and muscle strength (4)

These were just a couple of interesting literature facts that my research came across focusing on ACL before and after reconstruction surgeries.
I am working on the final project for this class so if anyone is interested in other facts about the ACL or interested to learn more, let me know.

 

References:

1. Cavanaugh JT, Powers M. ACL Rehabilitation Progression: Where Are We Now? Curr Rev Musculoskelet Med. 2017 Sep;10(3):289-296. doi: 10.1007/s12178-017-9426-3. PMID: 28791612; PMCID: PMC5577427.   https://pubmed.ncbi.nlm.nih.gov/28791612/
2. Freeman. “ACL Injuries.” NJ’s Top Orthopedic Spine &; Pain Management Center, 7 Mar. 2023, https://redefinehealthcare.com/acl-injuries/.
3. Kobayashi A, Higuchi H, Terauchi M, Kobayashi F, Kimura M, Takagishi K. Muscle performance after anterior cruciate ligament reconstruction. Int Orthop. 2004 Feb;28(1):48-51. doi: 10.1007/s00264-003-0502-5. Epub 2003 Aug 26. PMID: 12942198; PMCID: PMC3466568. https://doi.org/10.1007/s00264-003-0502-5
4. Lohmander, L. S., Englund, P. M., Dahl, L. L., & Roos, E. M. (2007). The long-term consequence of anterior cruciate ligament and meniscus injuries: osteoarthritis. The American journal of sports medicine, 35(10), 1756–1769. https://doi.org/10.1177/0363546507307396 
5. Perry A, DeFroda S, Leporace G, Metsavaht L, Coxe CR, Bierman AM, Chahla J. ACL Rehabilitation: How Can We Lessen Injury Rates? Operative Techniques in Sports Medicine, 30,1, 2022. ISSN 1060-1872, https://doi.org/10.1016/j.otsm.2022.150892. https://www.sciencedirect.com/science/article/pii/S1060187222000041
6. Webster KE, Feller JA. Exploring the High Reinjury Rate in Younger Patients Undergoing Anterior Cruciate Ligament Reconstruction. Am J Sports Med. 2016 Nov;44(11):2827-2832. doi: 10.1177/0363546516651845. Epub 2016 Jul 7. PMID: 27390346.  https://pubmed.ncbi.nlm.nih.gov/27390346/
7. https://www.shutterstock.com/image-illustration/torn-anterior-cruciate-ligament-176343242