Math 151 - Fall 2003

References Cited for Lectures

August 20, 2003 lecture: Histograms

An Experimental Study of Search in Global Social Networks
by Peter Sheridan Dodds, Roby Muhamad, Duncan J. Watts
Full paper as a PDF file - Science Aug 8 2003 301: 827-829

Comments: Experiment to determine how many contacts are necessary, using email, to reach a specific target individual about which the location, name and occupation are provided to the initial email sender. Histograms show the length of an email chain necessary to reach the target.

August 20, 2003 lecture: Linear regression and tree graphs

Phylogenetics and the Cohesion of Bacterial Genomes
by Vincent Daubin, Nancy A. Moran, and Howard Ochman
Full paper as a PDF file - Science Aug 8 2003 301: 829-832
see also
Passages Found Through Labyrinth of Bacterial Evolution
by Elizabeth Pennisi
News article as a PDF file - Science Aug 8 2003 301:745-746

Comments: In determining the phylogeny, or evolutionary relationship, between different bacteria, it has been hypothesized that the difficulty in determining these relationships is due to lateral gene transfers (LGT). LGT refer to the possibility that genes "jump" between species, arising since bacteria can absorb DNA from the environment or by engulfing other bacteria. Bacteria may therefore not have clear ancestries - so a branching tree for their evolutionary history would not be an adequate description. The authors use a regression to illustrate the relationship between length of the branches in the phylogenetic tree and the frequency at which a branching structure was not an adequate description. Using this, they argue that the history of bacterial lineages may be represented by traditional phylogenetic trees.

August 25, 2003 lecture: Histograms and categorical data

Evolution and Development of Sex Differences in Cooperative Behavior in Meerkats
by T. H. Clutton-Brock, A. F. Russell, L. L. Sharpe, A. J. Young, Z. Balmforth,3 G. M. McIlrath
Full paper as a PDF file - Science July 12 2002 297: 253-256

Comments: This article focuses on the issue of whether males or females devote more effort to caring for young, contrasting cooperatively breeding birds with meerkats. Female meerkats are more likley to brred and remain in their natal group than males, and the authors found that female meerkat helpers were more likely to contribute to rearing than males. They argue this is because females are more likely to derive genetic benefits (through helping more closely related individuals rear their young) than males in meerkat groups. The authors make use of extensive histograms, arranged by gender or experimental regime, to illustrate their points.

August 27, 2003 lecture: Correlations

The Neural Basis of Economic Decision-Making in the Ultimatum Game
by Alan G. Sanfey, James K. Rilling, Jessica A. Aronson, Leigh E. Nystrom, Jonathan D. Cohen
Full paper as a PDF file - Science June 13 2002 300: 1755-1758

Comments: Individuals were observed using functional magnetic resonance imaging (fMRI) while playing an economic game with other humans, and with a computer. The intent was to determine if the "non-rational" response of humans to this game was reflected in the activity of certain areas of the brain, as measurable using the fMRI. The results indicate there is a correlation between activity in one area (anterior insula) and the acceptance of what could be perceived as an unfair offer in the game. This is an example of the work in the new area of neuroeconomics, which attempts to ascertain a biological basis for human economic decisionmaking.

September 3, 2003 lecture: Linear Data Analysis

The role of stomata in sensing and driving environmental change
Full paper as a PDF file - Nature August 21 2003 424: 901-908

Comments: This paper reviews the impacts of stomata (pores in leaf surfaces) on environmental changes at scales from the whole leaf to the globe. Scatter plots illustrate the responses of species to various environmental factors, and the correlations between different aspects of stomata.

September 8, 2003 lecture: Allometry

Global Allocation Rules for Patterns of Biomass Partitioning in Seed Plants
by Brian J. Enquist and Karl J. Niklas
Full paper as a PDF file - Science February 22 2002 295: 1517-1520

Comments: This paper shows numerous allometric relationships that arise both within and between species for plant parts.

September 10, 2003 lecture: Semi-Log Graphs

Evidence for Selective Advantage of Pathogenic FGFR2 Mutations in the Male Germ Line
by Anne Goriely, Gilean A. T. McVean, Maria Rojmyr, Bjorn Ingemarsson, and Andrew O. M. Wilkie
Full paper as a PDF file - Science August 1 2003 301: 643-646

Comments: This paper addresses the general issue as to whether mutations in human sperm increase with age. They discuss a method to detect a specific mutation leading to Apert syndrome, which arises from a mutation in the paternal sperm and are associated with increased age of the father. They use log scaling to analyze mutation levels as a function of age. They argue that the mutation confers a selective advantage in the sperm cells in which it arises, which maintains it in the population.

September 17, 2003 lecture: Introduction to Matrices

Mathematical models of RNA silencing: Unidirectional amplification limits accidental self-directed reactions
by Carl T. Bergstrom, Erin McKittrick, and Rustom Antia
Full paper as a PDF file - PNAS September 12, 2003, 100:11511- 11516

Comments: This paper presents a mathematical model to anaylze the "silencing" of genes in which aberrent genes are not expressed - this essentially is a method by which a mutant is suppressed by a rapid response of RNA transcription. It is a form of gene repair. They argue that current models do not explain how silencing doesn't also impact "good" genes which are not damaged, and produce two new mathematical models for silencing. One of these models uses a matrix formulation in which the components of the matrix symbolically represent the rates at which different types of silencing RNAs change from one type to another.

September 24, 2003 lecture: Matrix Algebra

Recovery and Management Options for Spring/Summer Chinook Salmon in the Columbia River Basin
by Peter Kareiva, Michelle Marvier, and Michelle McClure
Full paper as a PDF file - Science November 3, 2000, 290:977-979

Comments: This paper applies a matrix model for the demographics of salmon to issues associated with the effects of dams on the Snake river. One focus is on how the population might respond given different dam mitigation scenarios. They point out that the limitations on population growth and recovery of the salmon may not be related to further improvements in the ability of salmon to negotiate around the dams, but rather to mortality in other life stages.

October 8, 2003 lecture: Networks and Matrix Algebra

Social Insect Networks
by Jennifer H. Fewell
Full paper as a PDF file - Science September 26, 2003, 301:1867-1870

Comments: This paper illustrates how social systems may be viewed as networks with information transfer being used, for example, to transfer data about pollen foraging between individuals carrying out differing roles in the colony. Just as the matrices we have described for transfering individuals from one age class to another or matter from one compartment to another are used to summarize information in the conceptual graph of our models, matrices are used to summarize information on how behaviors of individuals affect the group dynamics. In general, even without quantitative values included in the matrix (e.g. if we just have a matrix of connections with values 0 or 1), mathematical methods can inform us about the behavior of the full system sometimes.

October 15, 2003 lecture: Chance and Biology

Monkeys reject unequal pay
Full paper as a PDF file - Nature September 18, 2003, 425:297-299

Comments: This paper describes experiments in which capuchin monkeys interacted with human experimenters who offered them a more valuable food (grapes) or a less favored one (cucumber) when they returned an item to the human. The monkeys generally, but not always, refused to participate in an exchange of items for food when they saw that other monkeys got a better food item and they did not. The monkeys thus had a tendency to refuse to participate if they saw another monkey get a better reward for no effort, but there was a random component to this - it did not happen all the time and the sample size of monkeys used wa very small - only 5 monkeys. It was therefore not possible to predict exactly what any particular monkey would do.

October 20, 2003 lecture: Sample spaces and probability

Self-organized queuing and scale-free behavior in real escape panic
by Caesar Saloma, Gay Jane Perez, Giovanni Tapang, May Lim and Cynthia Palmes-Saloma
Full paper as a PDF file - PNAS October, 14 2003, 100:11947-11952

Comments: This paper considers panic reactions in crowds to a disaster, focusing on the measurement of individuals leaving a crowded location in a crisis situation. They construct a model using a cellular automata that provides information on the probability distributions for bursts of people exiting a crowded room (broken down into spatial cells). They then carry out experiments on mice placed into a cage with standing water and a small exit door (the size of which they varied) to a dry location, and compare the model results to data on the mice.

October 27, 2003 lecture: Conditional probability

Always Good Turing: Asymptotically Optimal Probability Estimation
by Alon Orlitsky, Narayana P. Santhanam, and Junan Zhang
Full paper as a PDF file - Science October 17, 2003, 302:427-431

Comments: This paper considers the problem of estimating the probability that you have missed observing a possible outcome of an experiment when you make only a limited number of observations (you sample from the set of possible outcomes). They give the example of sampling on a safari, in which you observe only zebras, giraffes and elephants - how then do you estimate the probability that you would see a lion (or some other species you missed) when you next go on a safari? Similarly, how do we assess the likelihood that we have missed some species when we do a survey of the organisms in some region - e.g. how do we appropriately estimate the number of species (biodiversity) in some region? They present a mathematical method to evaluate how well some methods for this problem work. These are based in part upon work Alan Turing (a brilliant British mathematician) did in breaking the German Enigma cipher during World War II - a piece of work that has been claimed as being critical to the success of the Allied forces, since the Germans thought their secret codes were unbreakable.

November 3, 2003 lecture: Bayes Theorem

A Bayesian Networks Approach for Predicting Protein-Protein Interactions from Genomic Data
by Ronald Jansen, Haiyuan Yu, Dov Greenbaum, Yuval Kluger, Nevan J. Krogan, Sambath Chung, Andrew Emili, Michael Snyder, Jack F. Greenblatt, and Mark Gerstein
Full paper as a PDF file - Science October 17, 2003, 302:449-453

Comments: This paper considers the problem of estimating what protein-protein interactions occur, out of the millions that are possible, by applying Bayesian statistical methods. This allows them to combine information from a wide variety of different studies.

November 5, 2003 lecture: Population Genetics Models

Genetic Structure of Human Populations
by Noah A. Rosenberg, Jonathan K. Pritchard, James L. Weber, Howard M. Cann, Kenneth K. Kidd, Lev A. Zhivotovsky, and Marcus W. Feldman
Full paper as a PDF file - Science December 20, 2002, 298:2381-2385

Comments: This paper analyzes data on the genetic structure of human populations by analyzing information from over 1000 individauls in more than 50 locations. They looked at more than 300 genetic loci and found that the vast majority of genetic variation in humans is accounted for by variation within populations, and only a small amount (3-5%) is due to genetic differences between populations. Nevertheless, the data do indicate that there are distinct human populations, defined by the genetics, but correlating with geographically separate populations as well.

November 17, 2003 lecture: Difference Equation Models

Lattice Effects Observed in Chaotic Dynamics of Experimental Populations
by Shandelle M. Henson, R. F. Costantino, J. M. Cushing, Robert A. Desharnais, Brian Dennis, and Aaron A. King
Full paper as a PDF file - Science October 19, 2001, 294: 602-605

Comments: This paper analyzes both a discrete model in which organisms are counted as integers, and a continuous model in which the population size can take on non-integer values. Both of these models are discrete in time - that is they are difference equations. They apply their results to data from an experimental organism, the flour beetle Tribolium, and point out how chaotic dynamics can arise.
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