Extending shelling orders and a hierarchy of functions of unimodal simple polytopes

AbstractLet P be a simplicial d-polytope with n facets ((d − 1)-dimensional faces) in Rd. A shelling of P is an ordering of the facets of P such that the intersection of each facet F with the union of all facets that precede it the ordering is a nonempty union of (d − 2)-faces of F. The following open question was raised by Tverberg and is recorded in [4]. Suppose for some k < n, there is an ordering of k of the facets of P so that the intersection of each of these facets with the union of all of the facets that precede it in the ordering is a nonempty union of (d − 2)-faces. Can this initial “segment” be extended to a shelling of all the facets? This question is open even in the case that P is the dual of the d-dimensional hypercube. The question in this case has resurfaced several times since G. Danaraj and V. Klee (1978) in a variety of forms. It is related to the hierarchies of completely unimodal pseudo-Boolean functions studied in P.L. Hammer et al. (1988), the author (1988) and D. Wiedemann (1986). (A pseudo-Boolean function is a function mapping the vertices of the d-dimensional hypercube into the reals). In this paper, the hierarchies are compared and combined. This hierarchy is then extended to general simple polytopes, and the relationship to the above open question is explained

Differential Eye Movements in Mild Traumatic Brain Injury vs. Normal Controls

Objective measures to diagnose and to monitor improvement of symptoms following mild traumatic brain injury (mTBI) are lacking. Computerized eye tracking has been advocated as a rapid, user friendly and field ready technique to meet this need. Eye tracking data collected via a head mounted, video-based binocular eye tracker was used to examine saccades, fixations and smooth pursuit movement in 60 military Service Members with post concussive syndrome (PCS) and 26 asymptomatic control subjects in an effort to determine if eye movement differences could be found and quantified. The diagnosis of mTBI was confirmed by the study physiatrist’s history, physical examination, and a review of any medical records. Results demonstrated that subjects with symptomatic mTBI had statistically larger position errors, smaller saccadic amplitudes, smaller predicted peak velocities, smaller peak accelerations, and longer durations. Subjects with symptomatic mTBI were also less likely to follow a target movement (less primary saccades). In general, symptomatic mTBI tracked the stepwise moving targets less accurately, revealing possible brain dysfunction. A reliable, standardized protocol that appears to differentiate mTBI from normals was developed for use in future research. This investigation represents a step toward objective identification of those with PCS. Future studies focused on increasing the specificity of eye movement differences in those with PCS are needed

Effects of hyperbaric oxygen on eye tracking abnormalities in males after mild traumatic brain injury

The effects of hyperbaric oxygen (HBO2) on eye movement abnormalities in 60 military servicemembers with at least one mild traumatic brain injury (mTBI) from combat were examined in a single-center, randomized, double-blind, sham-controlled, prospective study at the Naval Medicine Operational Training Center. During the 10 wk of the study, each subject was delivered a series of 40, once a day, hyperbaric chamber compressions at a pressure of 2.0 atmospheres absolute (ATA). At each session, subjects breathed one of three preassigned oxygen fractions (10.5%, 75%, or 100%) for 1 h, resulting in an oxygen exposure equivalent to breathing either surface air, 100% oxygen at 1.5 ATA, or 100% oxygen at 2.0 ATA, respectively. Using a standardized, validated, computerized eye tracking protocol, fixation, saccades, and smooth pursuit eye movements were measured just prior to intervention and immediately postintervention. Between- and within-groups testing of pre- and postintervention means revealed no significant differences on eye movement abnormalities and no significant main effect for HBO2 at either 1.5 ATA or 2.0 ATA equivalent compared with the sham-control. This study demonstrated that neither 1.5 nor 2.0 ATA equivalent HBO2 had an effect on postconcussive eye movement abnormalities after mTBI when compared with a sham-control

Challenging Disciplinary Boundaries in the First Year: A New Introductory Integrated Science Course for STEM Majors

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and a weekly lab and workshop. Features of this first-year course, including themes and concepts covered each semester, some of the materials developed, lessons learned, challenges, and preliminary measures of success are described

Challenging Disciplinary Boundaries in the First Year: A New Introductory Integrated Science Course for STEM Majors

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and a weekly lab and workshop. Features of this first-year course, including themes and concepts covered each semester, some of the materials developed, lessons learned, challenges, and preliminary measures of success are described

A SMART decade: outcomes of an integrated, inclusive, first-year college-level STEM curricular innovation

In the early 2000s, our primarily undergraduate, white institution (PUI/PWI), began recruiting and enrolling higher numbers of students of color and first-generation college students. However, like many of our peer institutions, our established pedagogies and mindsets did not provide these students an educational experience to enable them to persist and thrive in STEM. Realizing the need to systematically address our lack of inclusivity in science majors, in 2012 faculty from multiple disciplines developed the Science, Math, and Research Training (SMART) program. Here, we describe an educational innovation, originally funded by a grant from the Howard Hughes Medical Institute, designed to support and retain students of color, first generation college students, and other students with marginalized identities in the sciences through a cohort-based, integrated, and inclusive first-year experience focused on community and sense of belonging. The SMART program engages first-year students with semester-long themed courses around “real world” problems of antibiotic resistance and viral infections while integrating the fields of Biology, Chemistry, Mathematics, and an optional Computer Science component. In the decade since its inception, 97% of SMART students have graduated or are on track to graduate, with 80.9% of these students earning a major in a STEM discipline. Here, we present additional student outcomes since the initiation of this program, results of the student self-evaluative surveys SALG and CURE, and lessons we have learned from a decade of this educational experience

1 Journal of Computational Biology 8:151-175 (2001) Determination of bias in the relative abundance of oligonucleotides in DNA sequences

Different statistical measures of bias of oligonucleotide sequences in DNA sequences were compared, both by theoretical analysis and according to their abilities to predict the relative abundances of oligonucleotides in the genome of Escherichia coli. The expected frequency of an oligonucleotide calculated from a maximal order Markov model was shown to be a degenerate case of the expected frequency calculated from biases of all subwords, arising when noncontiguous subwords exhibit no bias. Since (at least in E. coli), noncontiguous sequences exhibit significant bias, the total compositional bias approach is expected to represent biases in genomic sequences more faithfully than Markov approaches. In fact, the efficacy of statistics based on Markov analysis even at the highest order were inferior in predicting actual frequencies of oligonucleotides to methods that factored out biases of internal subwords with gaps. Using total compositional bias as a measure of relative abundance, tetranucleotide and hexanucleotide palindromes were found to be distributed differently from nonpalindromic sequences, with their means shifted somewhat towards underrepresentation. A subpopulation of palindromic hexanucleotides, however, was highly underrepresented, and this group consisted almost entirely of targets for Type II restriction enzymes found within strains of E. coli. Sites recognized by Type I endonucleases from related strains were not markedly biased, and with pentanucleotides, palindromic and nonpalindromic sequences had nearly identical distributions. The loss of restriction sites may be explained by the free transfer of plasmids encoding restriction enzymes and episodic selection for the presence of the enzymes. 1