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Gerrymandering is the practice of manipulating the boundaries of an electoral constituency to favor one party or class. We'll sketch the history of gerrymandering and the court cases around it. We'll describe "packing" and "cracking", the principal methods for gerrymandering. Quantifying gerrymandering leads to some interesting mathematics. We'll show geometric ways of characterizing gerrymandering and some voter distribution measures, along with their advantages and disadvantages. Some very new gerrymandering measures using advanced statistical sampling were featured in recent Supreme Court cases and we'll survey those. Various remedies for gerrymandering are being considered in several states, including Nebraska, and we'll finish with a discussion of them.
Join us in HLSB 503 at 3:00 p.m. for a reception before the talk.
DNA is often called the blueprint for life because it encodes the information needed for our cells to function. A major way that DNA carries information is by encoding information needed to make proteins, a process called gene expression. However, it has been found that only only a small fraction of DNA (about (about 1.5%) actually contains information to make proteins. What then does the rest of DNA do? A prevailing hypothesis is that much of DNA is involved in regulating its own expression. The fact that so much much of DNA might might fill this role role makes testing these hypotheses a major focus in molecular biology research. In this this talk, I'll discuss discuss a relatively new biological assay that that has been been developed to test these hypotheses hypotheses and the statistical methodology that we have developed to analyze data from these these assays.
Join us in HLSB 503 at 3:00 p.m. for a reception before the talk.
Marilyn Vos Savant is famous for having the highest IQ ever recorded. She writes the weekly column "Ask Marilyn" for Parade Magazine. She is also famous for some very controversial answers to readers’ questions, especially questions involving mathematics and logic. In this talk we will highlight a few of these controversial problems in mathematics. We will also look in detail at a fascinating question involving logic and game theory that she answered. This problem has not received the attention that some of her problems have, but it is equally complex. It is also not clear if Marilyn was right or wrong in her answer.
Join us in HLSB 503 at 3:00 p.m. for a reception before the talk.
The trace of a square matrix is a linear functional which is characterized by the property that it is invariant under cyclic reordering: the trace of AB is equal to the trace of BA whenever AB and BA are square matrices. In this talk, I will discuss categorical generalizations of trace functions and explain why they are relevant to lowdimensional topology. In particular, I will show how the formalism of categorified trace functions can be used to prove new results about annular Khovanov homology, a combinatorial invariant for knots and links in a thickened annulus, which was discovered by AsaedaPrzytyckiSikora around the year 2003. One of our most striking results is that annular Khovanov homology can be quantized, in the sense that it admits a deformation which gives rise to nontrivial invariants for closed surfaces embedded in a twice thickened annulus.
Join us in HLSB 503 at 3:00 p.m. for a reception before the talk.
There is variation in adiposity growth amongst children in the United States. We seek to characterize heterogeneity in growth patterns of childhood body mass index and explore possible associations with earlylife factors. There is growing literature to suggest that earlylife exposure to a mixture of chemicals may increase the risk of unhealthy obesity development by disrupting hormonal processes that mediate growth, potentially explaining some variation in growth. To accommodate correlated exposures due to common sources and physical environment, we propose utilizing treebased methods for finding children with similar growth patterns and similar exposure levels. We start by adapting the classic regression tree algorithm to define similarity in terms of growth pattern. We then illustrate how this approach allows the possible discovery of complex interactions between chemical exposures as well as nonlinear associations. We then discuss how random forests could be used to determine the importance of the exposures in explaining the variation in growth.
Join us in HLSB 503 at 3:00 p.m. for a reception before the talk.
The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process in this talk we will discuss some introductory optimal control theory as well as two different models for resource allocation to roots, shoots, and fruits in annual plants. In each model we will examine how optimal control theory can be applied to determine the optimal resource allocation strategy for the plant throughout its growing season.
Topologists like to break up complicated objects into small, manageable pieces. As a simple example, a natural way to split the surface of the earth is to divide it into two pieces, the Northern and Southern Hemispheres. Of course, the earth's surface can also be cut into many more components, and a natural problem is to determine how each of these decompositions is related to any other. In dimensions two and three, the relationship between various ways to cut up a sphere into topological building blocks (called "handles") is wellunderstood. In contrast, an analogous problem in dimension four remains wide open. We discuss some recent progress (joint with Jeffrey Meier) on this unresolved case.
GenomeWide Association Studies (GWAS) have been used for over a decade to elucidate ties between genes and diseases. Standard analytic methods for GWAS typically consist of a regression of an individual genetic variant on a given phenotype, like presence or absence of a given symptom, or continuous measures like BMI. These standard approaches face numerous challenges including small individual genetic effects, low statistical power due to improper modeling of genetic correlation patterns, and potential typeI error inflation due to unmodeled population structure or kinship. In summary, typical GWAS approaches involve single regression models followed by multiple test corrections, thus yielding very stringent cutoffs for significance so that very few genes are found to be associated with the disease
This handson workshop is designed to introduce new R users to the basic tools and options within R and R Studio. R is a free software environment for statistical computing and graphics. It has become a standard platform for analyzing data in both academic research and many industrial applications. All are welcome to attend this workshop and no experience is required. While it is helpful to watch the demonstration, bringing a laptop with R and R Studio installed is recommended. Join us in HLSB 503 at 3:00 p.m. for refreshments before the workshop.
Knots in the three sphere (S^{3}) are considered classically equivalent if they cobound an annulus in S3 and equivalent in concordance if they cobound an annulus in S3 x I. Positive mutation is a subtle modification of a knot; pairs of knots related by positive mutation are difficult to distinguish classically and even more so in concordance. The smallest and best studied mutant pair are the 11 crossing Conway and KinoshitaTeresaka knots. They were distinguished classically by Riley in 1971; in this talk I will distinguish them in concordance. To do so I’ll discuss a new concordance obstruction coming from the study of certain 4manifolds and I will point out several other applications of this study.