I’m grateful to my students who voted for me as UNM Math & Stat Outstanding Undergraduate Instructor for 2011-12. I was tied for UNM Math & Stat Outstanding Graduate Instructor, as well. I work hard to give my students the best experience, to give them time before and after class to ask questions, to respond promptly to their email, and to reach them where they are and pull them up or show them how to keep climbing.
I keep adding to my Teaching Dossier, reflecting on my experience and accomplishments.
Statistics
A crowd-sourced article about communicating our science written as part of today’s workshop. I made the image in 45 seconds.
Research
I quickly prepared the fun slides below for a short interview with KOAT Channel 7 on the Mega Millions $540M jackpot (estimated at $640 at 3:30pm on the day of the drawing), since it is greatly surpassing the previous record of $390 million.
A ticket’s probability of winning the jackpot is roughly the ratio of the length of one of your fingers to the diameter of the earth, so unchangeably near 0 (0.00000000569). It is interesting for the jackpot to be large enough that the expected value is a few times larger than the cost of a ticket, which makes it a sensible time to buy from an expected value point-of-view. In fact, now’s a good time to purchase EVERY ticket combination — hurry, and hope you don’t have to split it with another winner!
Read more…
Statistics
Correspondence between Structure and Function in the Human Brain at Rest
Judith Maxine Segall, Elena A Allen, Rex E Jung, Erik B Erhardt, Sunil Kumar Arja, Kent A Kiehl, Vince D Calhoun
Frontiers in Neuroinformatics
Accepted 12 Mar 2012, 6:10
www.frontiersin.org/neuroinformatics/10.3389/fninf.2012.00010/abstract
Abstract:
To further the understanding of basic and complex cognitive functions of the human brain, multidisciplinary neuroimaging research has explored both functional and structural connectivity. For structural connectivity, the most prevalent method has been diffusion weighted imaging, which measures the connections of large white matter bundles. Recently, functional connectivity has been measured using resting-state fMRI (rs-fMRI). Surprisingly, few studies have examined structural gray matter, which supports the BOLD response. The overall aim of this study is to explore how gray matter (GM) structure corresponds to function. A cohort of 603 healthy participants was scanned on the same 3T scanner at the Mind Research Network to investigate the spatial correlations between structure and function. This was done by applying spatial independent component analysis (ICA) to GMD maps, to delineate structural components based on the covariation of GMD between regions, and to rs-fMRIdata, to discover spatial patterns with common temporal features. Decomposed structural and functional components were then compared by spatial correlation. The basal ganglia network showed the highest structural to rs-functional component correlation (r=0.59). Our remaining results generally show correspondence between one structural network and several functional networks. We also studied relationships between the weights of different structural components and found networks in frontal and parietal regions showing covariation across subjects. We also identified the precuneus as a hub for in structural network correlations. In addition, we analyzed relationships between component weights and age, concluding that age has an effect on structural components.
MIND, Research
I feel grateful for being promoted to full member in Sigma Xi, the scientific research society, on March 2, 2012. Their membership page has this to say about membership:
Nearly 60,000 scientists and engineers are currently members of Sigma Xi, inducted on the basis of their research potential or achievement. Since its founding, Sigma Xi is pleased to count more than 200 winners of the Nobel Prize among its membership.
Induction into Sigma Xi has been a milestone in many distinguished research careers. Membership in this respected community of scientists and engineers is professionally rewarding and offers a chance to participate in ongoing programs and activities at the local and Society levels. Active, dues-paying Sigma Xi members also have access to valuable benefits.
Membership in Sigma Xi is by invitation. Those who have shown potential as researchers are invited to join as associate members. Full membership is conferred upon those who have demonstrated noteworthy achievements in research. Each year the Society initiates more than 5,000 new members.
Research
The UNM Department of Mathematics and Statistics funded my travel request to go to 2012 WNAR – Graybill June 17-20, 2012 at Colorado State University – Fort Collins, Colorado. I intend to participate with a talk on my trophic-level modeling in the “Biostatistics and systems biology” session, meet and discuss research with those working in similar areas, and look for opportunities for cross-collaboration for students at these other western universities.
Research, Statistics
The 5.1 ka Aridization Event, Expansion of Piñon-Juniper Woodlands, and the Introduction of Maize (Zea mays) in the American Southwest
Brandon L. Drake, W. H. Wills, Erik B. Erhardt
The Holocene
Publication details will update here, accepted 2/13/2012
Lee Drake (UNM Anthropology) exemplifies excellence and I will make every opportunity to work with him again.
Abstract
Pollen analysis is frequently used to build climate and environmental histories. A distinct Holocene pollen series exists for Chaco Canyon, New Mexico. This study reports linear modeling and hypothesis testing of long distance dispersal pollen from radiocarbon-dated packrat middens which reveal strong relationships between piñon pine (Pinus edulis) and ponderosa pine (Pinus ponderosa). Ponderosa pollen dominates midden pollen assemblages during the early Holocene, while a rapid shift to a much higher proportion of piñon to ponderosa pine pollen between 5,440 and 5,100 BP points to an aridization episode. This shift is associated with higher δ18O values in Southwest speleothem records relative to the preceding millenium. The period of aridization is followed by a sharp increase in El Niño/Southern Oscillation events that would have caused highly variable precipitation and lasted until 4,200 BP. Bayesian changepoint analysis suggests that this aridization episode led to stable ecotonal boundaries for at least 3,000 years. The piñon/ponderosa transition may have been caused by punctuated multi-year droughts, analogous to those in the 20th century. The earliest documented instance of Zea mays cultivation on the Colorado Plateau is around ca. 4,290 BP. The introduction of this laborintensive cultigen from Mesoamerica may have been facilitated by changes in the regional ecosystems, specifically by an increase in piñon trees, that promoted increasing human territoriality. Linear modeling and hypothesis testing can complement traditional palynological techniques by adding greater resolution in vegetation patterning to climate/environmental histories.
Research, stable isotopes, Statistics
A morphometric analysis of Actaea racemosa L. (Ranunculaceae)
Z. Gardner, L. Lueck, E.B. Erhardt, L.E. Craker
Journal of Medicinally Active Plants
http://scholarworks.umass.edu/cgi/preview.cgi?article=1008&context=jmap
Abstract
Actaea racemosa L. (syn. Cimicifuga racemosa [L.] Nutt.), Ranunculaceae, commonly known as black cohosh, is an herbaceous, perennial, medicinal plant native to the deciduous woodlands of eastern North America. Historical texts and current sales data indicate the continued popularity of this plant as an herbal remedy for over 175 years. Much of the present supply of A. racemosa is harvested from the wild. Diversity within and between populations of the species has not been well characterized. The purpose of this study was to assess the morphological variation of A. racemosa and identify patterns of variation at the population and species levels. A total of twentysix populations representative of a significant portion of the natural range of the species were surveyed and plant material was collected for the morphological analysis of 37 leaflet, flower, and whole plant characteristics. In total, 511 leaflet samples and 83 flower samples were examined. Several of the populations surveyed had sets of relatively unique characteristics (large leaflet measurements, tall leaves and flowers, and a large number of stamen) and Tukey-Kramer multiple comparisons revealed significant differences between specific populations for 20 different characteristics. However, no unique phenotype was found. Considerable morphological plasticity was noted in the apices of the staminodia. Cluster analyses showed that the morphological variation within populations is not smaller than between population and that this variation in not influenced by their geographic distribution.
Research, Statistics
We got one! Research Allocation Committee (RAC) Grants are for supporting new research or creative works. The RAC is particularly supportive of projects that may lead to outside funding and/or larger related projects.
PIs: Erik Erhardt and David Hanson
Title: “Frequentist (bootstrap) and Bayesian modeling of (photo)respiration in plants”
Amount: $3982.63, RAC 12-04
Use: To hire statistics graduate student, Mohammad Hattab, to implement and develop modeling that I did last summer in Switzerland.
Purpose:
We are requesting $3982.63 to develop statistical models to estimate (photo)respiration in plants, accounting for sources of uncertainty and prior information. Because current models provide estimates without meaningful assessments of uncertainty, our model will have broad application in understanding photosynthetic pathways and carbon usage in plants, clarifying the precision of our knowledge, conditional on what is already believed. This modeling is an important step towards developing more comprehensive models of photosynthetic parameters. Support from the Resource Allocation Committee will allow us to: (1) develop frequentist (bootstrap) and Bayesian models to analyze existing experimental data, providing inferences on the set of parameters related in the model; (2) design experiments and acquire additional data to distinguish and estimate respiration and photorespiration under a set of scientifically relevant conditions; (3) conduct validations using pre-existing data and estimates; (4) publish our model with results; and (5) develop grant proposals to apply this model more broadly.
Research, stable isotopes, Statistics
Modular organization of functional network connectivity in healthy controls and patients with schizophrenia during the resting state
Qingbao Yu, Sergey M Plis, Erik B Erhardt, Elena A Allen, Jing Sui, Kent A Kiehl, Godfrey Pearlson, Vince D Calhoun
2011 Frontiers in Systems Neuroscience
Abstract
Neuroimaging studies have shown that functional brain networks composed from select regions of interest (ROIs) have a modular community structure. However, the organization of functional network connectivity (FNC), comprising a purely data-driven network built from spatially independent brain components, is not yet clear. The aim of this study is to explore the modular organization of FNC in both healthy controls (HCs) and patients with schizophrenia (SZs). Resting state functional magnetic resonance imaging (R-fMRI) data of HCs and SZs were decomposed into independent components (ICs) by group independent component analysis (ICA). Then weighted brain networks (in which nodes are brain components) were built based on correlations between ICA time courses. Clustering coefficients and connectivity strength of the networks were computed. A dynamic branch cutting algorithm was used to identify modules of the FNC in HCs and SZs. Results show stronger connectivity strength and higher clustering coefficient in HCs with more and smaller modules in SZs. In addition, HCs and SZs had some different hubs. Our findings demonstrate altered modular architecture of the FNC in schizophrenia and provide insights into abnormal topological organization of intrinsic brain networks in this mental illness.
MIND, Research