This is the last week of the TEqb summer bridge program. On Thursday we must make presentations, our group on fractals. I'm in charge of finding a sweet hands on activity for everyone to do, so people don't fall asleep during the group's presentation. In class, this week we are doing complexity, emerging properties, and fractals. Seeing as we are learning about fractals in class, I think it would be impossible not to do any reteaching during the presentation.

On to complexity.  We learned about fractals and how they can be used to explore chaos.  Simply put, fractals are geometric structures that are self-similar.  Fractals have their own dimensions.  Say a fractal is scaled by 1/n. That gives us n copies.  Assuming they are self-similar, the dimension satisfies n^d if scaled by 1/n.  For example, a Sierpinkski Triangle is scaled by 1/2, which yields 4 copies. Therefore, n=2, and n^d=4, which means the dimension is 2.  This can lead to fun fractional dimensions, as in the example of the Koch curve, which has a dimension of about 1.26186.  In the 1980s, a certain man named Barnesly came up with a Collage Theorem which said that any image can be approximated by a fractal.  Microsoft Encarta used fractals to reduce the amount of memory it needed to be stored on a disk to where it could fit on a single cd.  Moving on, it should be stated that the most important thing to know about chaos is that it is not random.  Apparently, Period 3 implies chaos. I don't really quite get that, so feel free to explain it to me.  Chaos has sensitive dependence on initial conditions, a totally disconnected fractal microstructure, and topological transitivity or "wandering orbits." 

So this has been a pretty neat program, getting to know some cool people has been fun. And I guess I'll wrap up this journal. It's been good.

This week we discussed many  interesting molecular biological topics.  First we discussed the concept of genetic drift.  Genetic drift is the term used to describe how alleles randomly vary from statistical expectations and eventually become fixed at zero or one hundred percent, evidently in contradiction of the Hardy-Weinburg Law.  Genetic drift was primarily the work of Sewall Wright in the 1930s.

We then moved on the Neutral Theory, an influential theory that was introduced by Motoo Kimura in the late 1960s. The theory primarily states that neutral mutations of non-coding segments of DNA are widespread.  Non-conserved parts of protein molecules, third positions of synonymous codons, introns, spacers between genes, and pseudogenes(genes which have lost their ability to code proteins or have ceased being expressed in the gene) can all evolve neutrally. Most mutations that are not neutral are negative, but since these mutations do not lead to a better creature, they can't become prevalent alleles in the population.  For the few that are positive, I suppose the opposite is true.

Coalescence is a recent idea in biology. It says that any sample of organisms can be traced back to a common ancestor in the past.  The more variance in the number of offspring each creature had in previous generations, the sooner back in time coalescence occurred. Coalescence occurs sooner in smaller populations.  For example, populations which are known to have had a bottleneck in their past population must have coalesced out of the time of the bottleneck.  Most human genes coalesced out of the time that humans started migrating out of Africa about fifty-thousand years ago.  Coalescence occurs sooner back in male lineages than in female lineages, since males can typically have more children, especially in the hierarchical government systems of past societies. Mitochondrial DNA is only passed matrilineally, and Y-chromosomes are only passed patrilineally. Therefore, the y-chromosome and mtDNA can both be traced back to a mitochondrial Eve and a y-chromosome Adam. Pretty sweet, yeah?

 

This is the fourth to last journal entry that I will be writing logging the events concerning a small group of biology and math students grouped together in a college classroom for five weeks of the summer. A group that could have very well entered into...THE TWILIGHT ZONE!

Last Friday, we went to the Oak Ridge National Laboratory. Attending were all of us, minus Katie, and the distinguished individuals Dr. Boland, Dr. Joplin, and Dr. Miller. Lev Yurievich was not in attendance.  Our dear friend Andrew had a little bit of trouble getting into the laboratory as he had accidentally left his identification in his dorm. Once we got into the facility, we went to the visitor's center and got radiation pamphlets and name badges. We proceded to the graphite reactor, which was the first one in existance, created at the time of the Manhattan Project. We then went to the environmental science area where we learned about inbreeding mice to make sure that all of their genes are as close to the same as possible.  A visit to the Oak Ridge cafeteria followed. After that, an Ed Uberbacher informed us of the various options available in computational biology. We learned that computer programming skills are a very important part of it. Their own supercomputer took 3 days to model the behavior of a million atoms in a certain situation. After his talk, we visited the huge computer that has some 10,000 processors. Apparently, it uses the same amount of electricity as a small city.  They said that it required constant repairs, and that it was able to bypass any dead parts.  I don't really understand how it all works together, but it was pretty impressive. After that, we went to a place where they did experiments with aquatic life.  After that, we headed home.

As an expansion on the Natural Tunnel experience, I will begin this blog entry with a brief description of our lesson on plant identification. Plant families can be found by many different attributes including inflorescense, leaf compoundness, flower petals, and smell. We saw such glorious plants as vetch, clover, chicary, black-eyed susans, Queen Anne's lace, and a very peculiar pine sap flower. This was a parasitic flower which had no chlorophyll. It was pretty sweet.

This week we have been talking about such things as the spread of a disease. The calculation of the spread of a disease involves the rates of change of the suscesptibles and the infecteds, and those who can't contract or spread the disease. This is called SIR, and is great when using a closed population without quarantine.

At this point we are discussing a lot of molecular biology. Some properties of genomes include being long messages, aperiodic, error resistant, and self replicating.  DNA replication involves DNA polymerase, which matches nucleic acids to a single strand of DNA which has split from a double helix during the process of replication. Genes are expressed by first being transcribed to RNA which is then translated to Proteins.

After going over these things we discussed a Polymer Chain Reaction (PCR).  This is a process used to amplify a piece of DNA. First, a double-helix of DNA is heated so that the strands seperate, being around 95 degrees C. After the strands cool off, the primers bond to each of the strands. Polymerase puts nucleic acids together so you end up with a lot of the same segment of DNA. Dr. Yampolsky performed a BZ reaction for us, which was an oscillatory reaction that varied between two colors. Our guest speaker, M. Woodruff, spoke about the effects of morphine on apoptosis, which is programmed cell death.

We also have been playing around with the GeneBank and comparing various pieces of DNA and proteins. We went over some phylogeny, involving the fantastical creatures of planet X, the schmooms. An exciting week in the summer bridge program.

On Wednesday, we discussed such things as intrinsic rates of change, differential equations, and equillibria. To this day, I am still incapable of grasping these concepts entirely. Since populations have a particular carrying capacity, they can't increase indefinitely like in an exponential function. By making a logistic function that decreasing the rate of growth as the carrying capacity is neared, the curve is more realistic looking.

After somewhat recovering from this attack of confusement, we plunged straight into an ambush of competition models.  By making a phase portrait, one can imagine the future behavior of the populations of two competing species, and the location of a stable equilibrium. If one population is the y-axis and another population is the x-axis, 2 lines can be drawn, on each side of which a population increases and on the opposite side decreases. The lines for each population cross its own axis at its carrying capacity, and the other population's axis at the rate of growth divided by the alpha (the meaning of which is uncertain to me) of the other population. This can also be used to describe predator-prey populations. In these phase portraits, the populations move in a cyclical or focused manner.  Prey populations peak closely prior to the peak of the predator population. Such names as Lotka and Volterra were mentioned.

I have had enough mathematical confusion. On to a description of the grandoise weekend escapades to the splendid greenery and geological amusements of Natural Tunnel State Park in Virginia. While on the subject, I saw a sign that said Virginia state parks have been voted the best in the nation. What do you think?  Anyways, we walked around quite a bit and learned about different families of plants to give us some basic skills at identifying plants. We also went for a dip in the Clinch River and looked at various fish, mussels, and a very friendly and gentlemanly little turtle named Chester Lee Turtleton.  We stayed up ridiculously late both nights, and I am now ridiculously tired.

This week started along the same lines as the previous week. We trudged through more genetics in the context of conditional probabilities.  We worked on problems that involved calculating the expected number of trials before reaching a particular result. For example, we calculated  the number of children a couple would be expected to have in order to have one child of each one of the types of brown-eyed boy, blue-eyed boy, brown-eyed girl, and blue-eyed girl, given that the father is of a heterozygous brown-eyed genotype, and the mother has blue eyes. This results in eight and one-third children.  We also used blood types in the same conditional probability-type problems.

From there, we moved on the estimating animal abundance.  The concept of estimating population by capture and recapture were discussed.  In order to use such a method, you must first capture N creatures. After releasing them and allowing them to disperse and randomize, you recapture M number of creatures, and find that T of the M are tagged. By multiplying the M and N values and then dividing the resulting number by the value of recaptured tagged creatures, an estimate for the total population can be found. However, these are not necessarily close to the real answer. The same sort of concept is used with line transect population estimation, using instead the number of creatures observed, the observed area, the percentages of observable bears observed, and the total area.

We went over the chi square tests for goodness and overgoodness of fit. By taking the the sum of the observed values minus the expected values squared divided by the expected values, it is possible to know how well some observed data fits. This can also be used to find and overgood fit, which could mean an overeager scientist made up data.

We went over null and alternative hypotheses, and how to label each. The hypotheses should be labled in such a way that the more serious error is the type I error. A type one error is when the null hypothesis is rejected when it is true, and type two error is when it is accepted when actually false.

Dr. Knisely discussed some calculus and modelling of populations, which was rather confusing. We went over intrinsic rates of change and worked on different population models and curves, as well as phase portraits.

This weekend we are going on a grand adventure to the Natural Tunnel park in Virginia. I am told this will include hiking, spelunking, and swimming. But alas, all will be for naught if we run into a bear with a machete.

 

This has been the first week of five that I will be participating in the Talent Expansion in quantitative biology summer bridge program. The point of this is to introduce us students to quantitative biology, being a field using both math and biology, with the hope that we will go into a career in the field. It's sort of a marriage counselor between these two areas of study who just don't feel like they have much in common. But oh! they do. And the smallest tip of a conceptual iceburg has merged with my mind, leaving me kind of confused. Of what I do comprehend, some is fascinating, some is mind-numbingly dull. So I imagine after this program is over I should have some career ideas and interesting tidbits of knowledge. Not to mention five hundred dollars.

All the excitement began the morning of July the tenth. Arriving a small amount of minutes late, I  exherted some effort to get to the room in which the first meeting was to take place. Upon arriving, I discovered a scrumptious array of breakfast items, while the staff responsible for instruction and organization of the program introduced themselves. After meeting this myriad of bright doctors and the other students, the whole group proceded to another room. This room is where most of the instruction and work takes place, and the site of the first lecture.

Dr. Yampolsky began by explaining just what life is, and the ideas of entropy and randomness. Entropy is a measure of randomness, which is increased spontaneously. The decrease of entropy requires energy as well as the increase of entropy in another system. The prediction of many random events is much easier and possible than predicting single random events, which involves statistics.  For the rest of the week, basic genetics and statistics were discussed. The natural number, "e", was shown to have many statistical and biological applications.  Many phenotypical and genotypical problems were discussed. Dr. Seier discussed the proper ways of designing experiments.  An experiment should have replication, randomization, and control over other variables and factors.

On Friday, we went to the Georgia Aquarium in Atlanta.  There were many interesting examples of sea life, some highlights including huge whale sharks, beluga whales, sea otters, and penguins. The venture's enjoyment was somewhat lessened by the massive crowds squeezed into the aquarium building. After several hours, we left to start the long journey back to Johnson City. We arrived at some time around 1 a.m., thoroughly exhausted. Thus, the first week of the program ended.