Mathematics in Hands-On Science for Liberal Arts Students

We describe a number of experiments from the courses called, General Science 9, part of the science program for elementary education majors at Brooklyn College. These courses provide hands-on learning experiences for students who are insecure and weak in science and mathematics. Quantitative thinking is a central element in most of the students’ work. Mathematics is taught in a concrete and intuitive way, as a direct outgrowth of their needs; first, in analysis of data, and second, in discovering underlying theory. The science program has been developed through cooperation among faculty from the School of Education and the science departments

Comparison of Periglacial Block Fields and Talus Slopes in South-Central Pennsylvania and Northern Maryland

Relict periglacial boulder fields, or block fields, are scattered across south-central Pennsylvania and northern Maryland (e.g. Potter and Moss, 1968; Denn et al 2018). This pilot study uses a combination of digital analyses using Google Earth Pro and fieldwork to investigate block fields at different scales. Fieldwork focused on two block fields, which were compared with fieldwork conducted on two talus slopes. The block fields studied were Raven Rock Hollow in Maryland and River of Rocks at Hawk Mountain in Pennsylvania, and the talus slopes were located at Catoctin Mountain, Maryland and Waggoner’s Gap, Pennsylvania. The importance of geomorphic processes on formation of block fields compared to talus slopes was examined as part of this pilot study

Fast Genome-Wide QTL Analysis Using Mendel

Pedigree GWAS (Option 29) in the current version of the Mendel software is an optimized subroutine for performing large scale genome-wide QTL analysis. This analysis (a) works for random sample data, pedigree data, or a mix of both, (b) is highly efficient in both run time and memory requirement, (c) accommodates both univariate and multivariate traits, (d) works for autosomal and x-linked loci, (e) correctly deals with missing data in traits, covariates, and genotypes, (f) allows for covariate adjustment and constraints among parameters, (g) uses either theoretical or SNP-based empirical kinship matrix for additive polygenic effects, (h) allows extra variance components such as dominant polygenic effects and household effects, (i) detects and reports outlier individuals and pedigrees, and (j) allows for robust estimation via the $t$-distribution. The current paper assesses these capabilities on the genetics analysis workshop 19 (GAW19) sequencing data. We analyzed simulated and real phenotypes for both family and random sample data sets. For instance, when jointly testing the 8 longitudinally measured systolic blood pressure (SBP) and diastolic blood pressure (DBP) traits, it takes Mendel 78 minutes on a standard laptop computer to read, quality check, and analyze a data set with 849 individuals and 8.3 million SNPs. Genome-wide eQTL analysis of 20,643 expression traits on 641 individuals with 8.3 million SNPs takes 30 hours using 20 parallel runs on a cluster. Mendel is freely available at \url{http://www.genetics.ucla.edu/software}

“Been there---ah, haven’t tried it that way”: A Professional Effort to Differentiate Instruction

It goes without saying that the most critical component of preparing educators lies in their ability to competently teach. Differentiation provides a framework to develop classrooms where realities of genuine student variance can be addressed with curricular realities. The author describes a professional development project that differentiated a series of teacher workshops that were designed to increase teachers’ perceived competency to differentiate instruction. The purpose here is to describe a collaboratively created and implemented professional development program designed to train staff in ways to differentiate instruction for all learners. Sample training activities, along with perceptions from participants and suggestions for realistic extensions are shared

Statistical Mechanics of the Hyper Vertex Cover Problem

We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the Group Testing procedures where one wants to detect defective items in a large group by pool testing. Using a Statistical Mechanics approach based on the cavity method, we study the phase diagram of the HVC problem, in the case of random regualr hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HVC problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hyper vertex cover problem.Comment: Submitted to PR

Neural Processing at the Speed of Smell

AbstractOlfaction is typically described as behaviorally slow, suggesting neural processes on the order of hundreds of milliseconds to seconds as candidate mechanisms in the creation of olfactory percepts. Whereas a recent study challenged this view in suggesting that a single sniff was sufficient for optimal olfactory discrimination, a study by Abraham et al. in this issue of Neuron sets out to negate the challenge by demonstrating increased processing time for discrimination of similar versus dissimilar stimuli. Here we reconcile both studies, which in our view together support the notion of a speed-accuracy tradeoff in olfactory discriminations that are made within about 200 ms. These findings are discussed in light of the challenges related to defining olfactory perceptual similarity in nonhuman animals

Fast Genome-Wide QTL Association Mapping on Pedigree and Population Data

Since most analysis software for genome-wide association studies (GWAS) currently exploit only unrelated individuals, there is a need for efficient applications that can handle general pedigree data or mixtures of both population and pedigree data. Even data sets thought to consist of only unrelated individuals may include cryptic relationships that can lead to false positives if not discovered and controlled for. In addition, family designs possess compelling advantages. They are better equipped to detect rare variants, control for population stratification, and facilitate the study of parent-of-origin effects. Pedigrees selected for extreme trait values often segregate a single gene with strong effect. Finally, many pedigrees are available as an important legacy from the era of linkage analysis. Unfortunately, pedigree likelihoods are notoriously hard to compute. In this paper we re-examine the computational bottlenecks and implement ultra-fast pedigree-based GWAS analysis. Kinship coefficients can either be based on explicitly provided pedigrees or automatically estimated from dense markers. Our strategy (a) works for random sample data, pedigree data, or a mix of both; (b) entails no loss of power; (c) allows for any number of covariate adjustments, including correction for population stratification; (d) allows for testing SNPs under additive, dominant, and recessive models; and (e) accommodates both univariate and multivariate quantitative traits. On a typical personal computer (6 CPU cores at 2.67 GHz), analyzing a univariate HDL (high-density lipoprotein) trait from the San Antonio Family Heart Study (935,392 SNPs on 1357 individuals in 124 pedigrees) takes less than 2 minutes and 1.5 GB of memory. Complete multivariate QTL analysis of the three time-points of the longitudinal HDL multivariate trait takes less than 5 minutes and 1.5 GB of memory

Finding and Dating Cathlapotle

The people of the Cathlapotle town played a significant role in the fur trade era history of the Lower Columbia River, including Lewis and Clark’s visit on March 29th, 1806. Archaeologists and others have sought the town’s location for years. Long-term research has established that archaeological site 45CL1 on the US Fish and Wildlife Refuge near Ridgefield, Washington is Cathlapotle. This determination is based on the close match between site details with various ethnohistoric accounts of Cathlapotle. The site was occupied by ca. AD 1450 and probably moved there from another nearby location. It was abandoned sometime in the 1830s or 1840s. This chronology is based on 54 radiocarbon dates, historic trade goods including glass beads and ceramics, and documentary accounts