All Items 3,269

High shape concerns predicts becoming obese, binge drinking, and drug use among adolescent and young adult males

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

To investigate whether males with psychiatric symptoms related to disordered eating and concern about physique are more likely to become obese, to start using drugs, to consume alcohol frequently (binge drinking), or to develop high levels of depressive symptoms.

High shape concerns predicts becoming obese, binge drinking, and drug use among adolescent and young adult males
Secular trends in family dinner frequency among adolescents

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Eating meals, particularly dinner, with family members has been found to be associated with improved dietary intake, lower prevalence of disordered eating behaviors, lower levels of substance abuse, and improved academic outcomes among adolescents. Limited research has examined how the frequency of family meals has changed over time. The objective of this study was to examine secular trends in family dinner frequency over a 12-year period using a large, nation-wide sample of adolescents.

Secular trends in family dinner frequency among adolescents
Adjusting models of ordered multinomial outcomes for nonignorable nonresponse in the occupational employment statistics survey

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

An establishment’s average wage, computed from administrative wage data, has been found to be related to occupational wages. These occupational wages are a primary outcome variable for the Bureau of Labor Statistics Occupational Employment Statistics survey. Motivated by the fact that nonresponse in this survey is associated with average wage even after accounting for other establishment characteristics, we propose a method that uses the administrative data for imputing missing occupational wage values due to nonresponse. This imputation is complicated by the structure of the data. Since occupational wage data is collected in the form of counts of employees in predefined wage ranges for each occupation, weighting approaches to deal with nonresponse do not adequately adjust the estimates for certain domains of estimation. To preserve the current data structure, we propose a method to impute each missing establishment’s wage interval count data as an ordered multinomial random variable using a separate survival model for each occupation. Each model incorporates known auxiliary information for each establishment associated with the distribution of the occupational wage data, including geographic and industry characteristics. This flexible model allows the baseline hazard to vary by occupation while allowing predictors to adjust the probabilities of an employee’s salary falling within the specified ranges. An empirical study and simulation results suggest that the method imputes missing OES wages that are associated with the average wage of the establishment in a way that more closely resembles the observed association.

Adjusting models of ordered multinomial outcomes for nonignorable nonresponse in the occupational employment statistics survey
Meeting student needs for multivariate data analysis: a case study in teaching an undergraduate multivariate data analysis course

Wagaman, Amy S. (Department of Mathematics and Statistics, Amherst College)

Modern students encounter large, messy data sets long before setting foot in our classrooms. Many of these students need to develop skills in exploratory data analysis and multivariate analysis techniques for their jobs after college, but such topics are not covered in traditional introductory statistics courses. This case study describes my experience in designing and teaching an undergraduate course on multivariate data analysis with minimal pre-requisites, using real data, active learning, and other interactive activities to help students tackle the material. Multivariate topics covered include clustering and classification (among others) for exploratory data analysis and an introduction to algorithmic modeling.

Meeting student needs for multivariate data analysis: a case study in teaching an undergraduate multivariate data analysis course
Dynamics of a multistage circadian system

Leise, Tanya L. (Department of Mathematics and Computer Science, Amherst College)

Tissues throughout the body exhibit circadian rhythms, forming a multioscillatory system whose disruption results in jet lag and other health problems in travelers and rotational shift workers. The authors’ simulations of the dynamics of a multistage circadian system (based on experimental results for nocturnal rodents) reveal the flexibility and stability inherent in a multistage system, as well as potential pitfalls. The modeling predicts that jet lag tends to be most severe following an eastward change of 5 to 8 time zones due to prolonged desynchrony of the system. This desynchrony is partly due to differing reentrainment rates among components, but a much greater source of desynchrony is the antidromic reentrainment of some but not all components (reentrainment by partition), triggered by the overshoot of the master pacemaker’s phase in response to these advances. Based on the multistage system dynamics, the authors design a simple protocol that results in a more orderly transition that avoids antidromic reentrainment in all components, thereby reducing the reentrainment time from nearly 2 weeks to just a few days for the most difficult shifts. The authors compare the predicted behavior of self-sustaining versus damped oscillatory components in the system as well as the effect of weak versus strong coupling from the master pacemaker to the peripheral components.

Dynamics of a multistage circadian system
Impedance imaging, inverse problems, and Harry Potter’s cloak

Leise, Tanya L. (Department of Mathematics and Statistics, Amherst College)

In this article we provide an accessible account of the essential idea behind cloaking, aimed at nonspecialists and undergraduates who have had some vector calculus, Fourier series, and linear algebra. The goal of cloaking is to render an object invisible to detection from electromagnetic energy by surrounding the object with a specially engineered “metamaterial” that redirects electromagnetic waves around the object. We show how to cloak an object against detection from impedance tomography, an imaging technique of much recent interest, though the mathematical ideas apply to much more general forms of imaging. We also include some exercises and ideas for undergraduate research projects.

Impedance imaging, inverse problems, and Harry Potter’s cloak
A mathematical model of the Drosophila circadian clock with emphasis on posttranslational mechanisms

Leise, Tanya L. (Mathematics and Computer Science Department, Amherst College)

Experimental evidence points increasingly to the importance of posttranslational processes such as phosphorylation and translocation in the molecular circadian clocks of many organisms. We develop a mathematical model of the Drosophila circadian clock that incorporates the emerging details of the timing of nuclear translocation of the PERIOD and TIMELESS proteins. Most models assume that these proteins enter the nucleus as a complex, but recent experiments suggest that they in fact enter the nucleus separately. Our model reproduces observed patterns of intracellular localization of PERIOD and TIMELESS during light-dark cycles and in constant darkness, as well as phenotypes of several clock mutants. We also use the model to demonstrate how the Drosophila clock can exhibit robust oscillations with constant mRNA levels of period or timeless, and propose a possible mechanism for oscillations in double rescue experiments of per01-tim01 mutants. The model also explains (via posttranslational processes) the counter-intuitive observation that total dCLOCK levels are at their lowest at the circadian time when active nuclear dCLOCK must be peaking in order to activate transcription of other clock genes, implying that for dCLOCK a posttranslationally-generated rhythm is more important than the transcriptionally-generated rhythm. These results support the idea that posttranslational processes play key roles in generating as well as modulating robust circadian oscillations. While it appears that posttranslational mechanisms alone are not sufficient to generate rhythms in Drosophila, posttranslational mechanisms can greatly amplify a very weak transcriptional rhythm.

A mathematical model of the Drosophila circadian clock with emphasis on posttranslational mechanisms
Intrinsic regulation of spatiotemporal organization within the suprachiasmatic nucleus

Leise, Tanya L. (Department of Mathematics, Amherst College)

The mammalian pacemaker in the suprachiasmatic nucleus (SCN) contains a population of neural oscillators capable of sustaining cell-autonomous rhythms in gene expression and electrical firing. A critical question for understanding pacemaker function is how SCN oscillators are organized into a coherent tissue capable of coordinating circadian rhythms in behavior and physiology. Here we undertake a comprehensive analysis of oscillatory function across the SCN of the adult PER2::LUC mouse by developing a novel approach involving multi-position bioluminescence imaging and unbiased computational analyses. We demonstrate that there is phase heterogeneity across all three dimensions of the SCN that is intrinsically regulated and extrinsically modulated by light in a region-specific manner. By investigating the mechanistic bases of SCN phase heterogeneity, we show for the first time that phase differences are not systematically related to regional differences in period, waveform, amplitude, or brightness. Furthermore, phase differences are not related to regional differences in the expression of arginine vasopressin and vasoactive intestinal polypeptide, two key neuropeptides characterizing functionally distinct subdivisions of the SCN. The consistency of SCN spatiotemporal organization across individuals and across planes of section suggests that the precise phasing of oscillators is a robust feature of the pacemaker important for its function.

Intrinsic regulation of spatiotemporal organization within the suprachiasmatic nucleus
Wavelet-based time series analysis of circadian rhythms

Leise, Tanya L. (Department of Mathematics, Amherst College)

Analysis of circadian oscillations that exhibit variability in period or amplitude can be accomplished through wavelet transforms. Wavelet-based methods can also be used quite effectively to remove trend and noise from time series and to assess the strength of rhythms in different frequency bands, for example, ultradian versus circadian components in an activity record. In this article, we describe how to apply discrete and continuous wavelet transforms to time series of circadian rhythms, illustrated with novel analyses of 2 case studies involving mouse wheel-running activity and oscillations in PER2::LUC bioluminescence from SCN explants.

Wavelet-based time series analysis of circadian rhythms
Persistent cell-autonomous circadian oscillations in fibroblasts revealed by six-week single-cell imaging of PER2::LUC bioluminescence

Leise, Tanya L. (Department of Mathematics, Amherst College)

Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found persistent, independent circadian oscillations of clock gene expression in 6-week-long bioluminescence recordings of 80 primary fibroblast cells dissociated from PER2::LUC mice and kept in vitro for 6 months. Due to the stochastic nature of rhythmicity, the proportion of cells appearing rhythmic increases with the length of interval examined, with 100% of cells found to be rhythmic when using 3-week windows. Mean period and amplitude are remarkably stable throughout the 6-week recordings, with precision improving over time. For individual cells, precision of period and amplitude are correlated with cell size and rhythm amplitude, but not with period, and period exhibits much less cycle-to-cycle variability (CV 7.3%) than does amplitude (CV 37%). The time series are long enough to distinguish stochastic fluctuations within each cell from differences among cells, and we conclude that the cells do exhibit significant heterogeneity in period and strength of rhythmicity, which we measure using a novel statistical metric. Furthermore, stochastic modeling suggests that these single-cell clocks operate near a Hopf bifurcation, such that intrinsic noise enhances the oscillations by minimizing period variability and sustaining amplitude.

Persistent cell-autonomous circadian oscillations in fibroblasts revealed by six-week single-cell imaging of PER2::LUC bioluminescence
Pollinator competition as a driver of floral divergence: An experimental test

Temeles, Ethan J. (Department of Biology, Amherst College)

Optimal foraging models of floral divergence predict that competition between two different types of pollinators will result in partitioning, increased assortative mating, and divergence of two floral phenotypes. We tested these predictions in a tropical plant-pollinator system using sexes of purple-throated carib hummingbirds (Anthracothorax jugularis) as the pollinators, red and yellow inflorescence morphs of Heliconia caribaea as the plants, and fluorescent dyes as pollen analogs in an enclosed outdoor garden. When foraging alone, males exhibited a significant preference for the yellow morph of H. caribaea, whereas females exhibited no preference. In competition, males maintained their preference for the yellow morph and through aggression caused females to over-visit the red morph, resulting in resource partitioning. Competition significantly increased within-morph dye transfer (assortative mating) relative to non-competitive environments. Competition and partitioning of color morphs by sexes of purple-throated caribs also resulted in selection for floral divergence as measured by dye deposition on stigmas. Red and yellow morphs did not differ significantly in dye deposition in the competition trials, but differences in dye deposition and preferences for morphs when sexes of purple-throated caribs foraged alone implied fixation of one or the other color morph in the absence of competition. Competition also resulted in selection for divergence in corolla length, with the red morph experiencing directional selection for longer corollas and the yellow morph experiencing stabilizing selection on corolla length. Our results thus support predictions of foraging models of floral divergence and indicate that pollinator competition is a viable mechanism for divergence in floral traits of plants.

Pollinator competition as a driver of floral divergence: An experimental test
On closed graphs I

Cox, David A. (Department of Mathematics and Statistics, Amherst College)

A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we prove that a connected graph has a closed labeling if and only if it is chordal, claw-free, and has a property we call narrow, which holds when every vertex is distance at most one from all longest shortest paths of the graph.

On closed graphs I
A classification of Taylor towers of functors of spaces and spectra

Ching, Michael (Michael Comyn) (Department of Mathematics and Statistics, Amherst College)

We describe new structure on the Goodwillie derivatives of a functor, and we show how the full Taylor tower of the functor can be recovered from this structure. This new structure takes the form of a coalgebra over a certain comonad which we construct, and whose precise nature depends on the source and target categories of the functor in question. The Taylor tower can be recovered from standard cosimplicial cobar constructions on the coalgebra formed by the derivatives. We get from this an equivalence between the homotopy category of polynomial functors and that of bounded coalgebras over this comonad. For functors with values in the category of spectra, we give a rather explicit description of the associated comonads and their coalgebras. In particular, for functors from based spaces to spectra we interpret this new structure as that of a divided power right module over the operad formed by the derivatives of the identity on based spaces.

A classification of Taylor towers of functors of spaces and spectra
Circadian rhythms of PER2::LUC in individual primary mouse hepatocytes and cultures

Leise, Tanya L. (Department of Mathematics and Statistics, Amherst College)

Background: Hepatocytes, the parenchymal cells of the liver, express core clock genes, such as Period2 and Cryptochrome2, which are involved in the transcriptional/translational feedback loop of the circadian clock. Whether or not the liver is capable of sustaining rhythms independent of a central pacemaker is controversial. Whether and how circadian information may be shared among cells in the liver in order to sustain oscillations is currently unknown. Results: In this study we isolated primary hepatocytes from transgenic Per2Luc mice and used bioluminescence as a read-out of he state of the circadian clock. Hepatocytes cultured in a collagen gel sandwich configuration exhibited persistent circadian rhythms for several weeks. The amplitude of the rhythms damped, but medium changes consistently reset the phase and amplitude of the cultures. Cry2-/- Per2Luc cells oscillated robustly and expressed a longer period. Co-culturing with wildtype cells did not significantly shorten the period, indicating that coupling among hepatocytes is insufficient to synchronize cells with significantly differing periods. However, spatial patterns revealed by cellular imaging of wildtype cultures provided evidence of weak local coupling among the hepatocytes. Conclusions: Our results with primary hepatocyte cultures demonstrate that cultured hepatocytes are weakly coupled. While this coupling is not sufficient to sustain global synchrony, it does increase local synchrony, which may stabilize the circadian rhythms of peripheral oscillators, such as the liver, against noise in the entraining signals.

Circadian rhythms of PER2::LUC in individual primary mouse hepatocytes and cultures
Dynamic interactions mediated by non-redundant signaling mechanisms couple circadian clock neurons

Leise, Tanya L. (Department of Mathematics and Statistics, Amherst College)

Interactions among suprachiasmatic nucleus (SCN) neurons are required for robust circadian rhythms entrained to local time. To investigate these signaling mechanisms, we developed a functional coupling assay that uniquely captures the dynamic process by which SCN neurons interact. As a population, SCN neurons typically display synchronized rhythms with similar peak times, but will peak 6-12 hr apart after in vivo exposure to long days. Once they are removed from these conditions, SCN neurons resynchronize through a phase-dependent coupling process mediated by both vasoactive intestinal polypeptide (VIP) and GABAA signaling. Notably, GABAA signaling contributes to coupling when the SCN network is in an antiphase configuration, but opposes synchrony under steady-state conditions. Further, VIP acts together with GABAA signaling to couple the network in an antiphase configuration, but promotes synchrony under steady-state conditions by counteracting the actions of GABAA signaling. Thus, SCN neurons interact through nonredundant coupling mechanisms influenced by the state of the network.

Dynamic interactions mediated by non-redundant signaling mechanisms couple circadian clock neurons
Making do with less: An introduction to compressed sensing

Leise, Tanya L. (Department of Mathematics and Statistics, Amherst College)

This article offers an accessible but rigorous and essentially self-contained account of some of the central ideas in compressed sensing, aimed at nonspecialists and undergraduates who have had linear algebra and some probability. The basic premise is first illustrated by considering the problem of detecting a few defective items in a large set. We then build up the mathematical framework of compressed sensing, to show how combining efficient sampling methods with elementary ideas from linear algebra and a bit of approximation theory, optimization, and probability, allows the estimation of unknown quantities with far less sampling of data than traditional methods.

Making do with less: An introduction to compressed sensing
Wavelet analysis of circadian and ultradian behavioral rhythms

Leise, Tanya L. (Department of Mathematics and Statistics, Amherst College)

We review time-frequency methods that can be useful in quantifying circadian and ultradian patterns in behavioral records. These records typically exhibit details that may not be captured through commonly used measures such as activity onset and so may require alternative approaches. For instance, activity may involve multiple bouts that vary in duration and magnitude within a day, or may exhibit day-to-day changes in period and in ultradian activity patterns. The discrete Fourier transform and other types of periodograms can estimate the period of a circadian rhythm, but we show that they can fail to correctly assess ultradian periods. In addition, such methods cannot detect changes in the period over time. Time-frequency methods that can localize frequency estimates in time are more appropriate for analysis of ultradian periods and of fluctuations in the period. The continuous wavelet transform offers a method for determining instantaneous frequency with good resolution in both time and frequency, capable of detecting changes in circadian period over the course of several days and in ultradian period within a given day. The discrete wavelet transform decomposes a time series into components associated with distinct frequency bands, thereby facilitating the removal of noise and trend or the isolation of a particular frequency band of interest. To demonstrate the wavelet-based analysis, we apply the transforms to a numerically-generated example and also to a variety of hamster behavioral records. When used appropriately, wavelet transforms can reveal patterns that are not easily extracted using other methods of analysis in common use, but they must be applied and interpreted with care.

Wavelet analysis of circadian and ultradian behavioral rhythms
Handling missing data in RCTs: A review of the top medical journals

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Background--Missing outcome data is a threat to the validity of treatment effect estimates in randomized controlled trials. We aimed to evaluate the extent, handling, and sensitivity analysis of missing data and intention-to-treat (ITT) analysis of randomized controlled trials (RCTs) in top tier medical journals, and compare our findings with previous reviews related to missing data and ITT in RCTs. Methods--Review of RCTs published between July and December 2013 in the BMJ, JAMA, Lancet, and New England Journal of Medicine, excluding cluster randomized trials and trials whose primary outcome was survival. Results--Of the 77 identified eligible articles, 73 (95%) reported some missing outcome data. The median percentage of participants with a missing outcome was 9% (range 0 – 70%). The most commonly used method to handle missing data in the primary analysis was complete case analysis (33, 45%), while 20 (27%) performed simple imputation, 15 (19%) used model based methods, and 6 (8%) used multiple imputation. 27 (35%) trials with missing data reported a sensitivity analysis. However, most did not alter the assumptions of missing data from the primary analysis. Reports of ITT or modified ITT were found in 52 (85%) trials, with 21 (40%) of them including all randomized participants. A comparison to a review of trials reported in 2001 showed that missing data rates and approaches are similar, but the use of the term ITT has increased, as has the report of sensitivity analysis. Conclusions--Missing outcome data continues to be a common problem in RCTs. Definitions of the ITT approach remain inconsistent across trials. A large gap is apparent between statistical methods research related to missing data and use of these methods in application settings, including RCTs in top medical journals.

Handling missing data in RCTs: A review of the top medical journals
I hear, I forget. I do, I understand: a modified Moore-method mathematical statistics course

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs (Jones 1977). Cohen (1992) described an adaptation with less explicit competition suitable for undergraduate students at a liberal arts college. This paper details an adaptation of this modified Moore-method to teach mathematical statistics, and describes ways that such an approach helps engage students and foster the teaching of statistics. Groups of students worked a set of 3 difficult problems (some theoretical, some applied) every two weeks. Class time was devoted to coaching sessions with the instructor, group meeting time, and class presentations. R was used to estimate solutions empirically where analytic results were intractable, as well as to provide an environment to undertake simulation studies with the aim of deepening understanding and complementing analytic solutions. Each group presented comprehensive solutions to complement oral presentations. Development of parallel techniques for empirical and analytic problem solving was an explicit goal of the course, which also attempted to communicate ways that statistics can be used to tackle interesting problems. The group problem solving component and use of technology allowed students to attempt much more challenging questions than they could otherwise solve.

I hear, I forget. I do, I understand: a modified Moore-method mathematical statistics course
Teaching the next generation of statistics students to "think with data": Special issue on statistics and the undergraduate curriculum

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Teaching the next generation of statistics students to "think with data": Special issue on statistics and the undergraduate curriculum