Checkerboard Julia Sets for Rational Maps

In this paper, we consider the family of rational maps \F(z) = z^n + \frac{\la}{z^d}, where $n \geq 2$, $d\geq 1$, and\la \in \bbC. We consider the case where \la lies in the main cardioid of one of the $n-1$ principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps \F and $F_\mu$ are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy \mu = \nu^{j(d+1)}\la or \mu = \nu^{j(d+1)}\bar{\la} where j \in \bbZ and $\nu$ is an $n-1^{\rm st}$ root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.Comment: 25 pages, 14 figures; Changes since March 19 version: added nine figures, fixed one proof, added a section on a group actio

Semi-Classical Description of Antiproton Capture on Atomic Helium

A semi-classical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on Helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular momentum states of incident antiprotons which result in capture via single or double electron ionization, i.e. into [He$^{++}\,\bar p$ or He$^{+}\,\bar p$], and the distribution of energy and angular momentum states following the Auger cascade. These final states are discussed in light of recently reported, anomalously long-lived antiproton states observed in liquid He.Comment: 15 pages, 9 figures may be obtained from authors, Revte

Soft Null Hypotheses: A Case Study of Image Enhancement Detection in Brain Lesions

This work is motivated by a study of a population of multiple sclerosis (MS) patients using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to identify active brain lesions. At each visit, a contrast agent is administered intravenously to a subject and a series of images is acquired to reveal the location and activity of MS lesions within the brain. Our goal is to identify and quantify lesion enhancement location at the subject level and lesion enhancement patterns at the population level. With this example, we aim to address the difficult problem of transforming a qualitative scientific null hypothesis, such as "this voxel does not enhance", to a well-defined and numerically testable null hypothesis based on existing data. We call the procedure "soft null hypothesis" testing as opposed to the standard "hard null hypothesis" testing. This problem is fundamentally different from: 1) testing when a quantitative null hypothesis is given; 2) clustering using a mixture distribution; or 3) identifying a reasonable threshold with a parametric null assumption. We analyze a total of 20 subjects scanned at 63 visits (~30Gb), the largest population of such clinical brain images

Comparison of Corded and Cordless Handpieces on Forearm Muscle Activity, Procedure Time and Ease of Use During Simulated Tooth Polishing

Purpose: Dental professionals suffer from a high prevalence of work-related musculoskeletal disorders (MSD). Dental hygienists in particular have a high prevalence of pain in the forearms and hands. The objective of this study was to compare 1 cordless handpiece to 2 corded handpieces during simulated tooth polishing in terms of the muscle loads (recorded as electromyography (EMG) activity), duration of polishing procedure, and dental hygienist opinion about ease of use. Methods: EMG was used to quantify muscle electrical activity of 4 forearm muscles during simulated dental polishing with 2 corded handpieces (HP-A and HP-B) and 1 cordless handpiece (HP-C). A convenience sample of 30 dental hygienists (23 to 57 years of age) with 1 to 20+ years of clinical practice experience completed the study. Each participant spent approximately 5 minutes polishing 3 predetermined teeth in each of the 4 quadrants. The sequence of the handpieces was randomly assigned. At the end of the study, participants completed a subjective end user evaluation of handpiece preference. Results: Muscle activity levels of 10th, 50th and 90th percentiles did not differ significantly between the 3 handpieces tested (p\u3e0.05). However, total muscle workload (integrated EMG) was lowest for the cordless handpiece (HP-C), but this was only significantly less than HP-A (p\u3c0.05). Polishing using the cordless handpiece (HP-C) (M=257 seconds, SD=112 seconds) took significantly less time than either the HP-A corded (M=290 seconds, SD=137 seconds) or HP-B corded handpiece (M=290 seconds, SD=126 seconds) (p\u3c0.05). Overall, 50% of the study participants preferred the cordless handpiece, 37% preferred HP-A and 13% preferred HP-B (p\u3c0.05). Conclusion: Use of the cordless handpiece reduced the duration of polishing, which in turn led to less total muscle activity, but not muscle intensity. Overall, dental hygienists preferred the cordless handpiece

Analysis of Continuous Gait Data Requires Temporal Alignment of Gait Phases

A statistical method for comparing time-continuous curves, such as the kinematics of gait cycles, is statistical parametric mapping analysis (SPM) (Pataky, 2010). According to a recent study, SPM results were sensitive to how each stride\u27s beginning was defined (Honert & Pataky, 2021). Nonetheless, for meaningful comparisons between gait cycles, temporal alignment of phases within a stride may be required (Helwig et al., 2011). With both temporally aligned and unaligned gait data, the goal was to evaluate SPM results for different walking speeds using various gait cycle definitions. Participants in this study were 10 young, healthy adults. To figure out the preferred overground speed, an instrumented mat was employed. While subjects walked at speeds of 80, 90, 100, 110, and 120% of the preferred pace, a ten-camera Vicon motion capture system, Conventional Gait Model 2.4, and Nexus 2.13 software were used to collect biomechanical data of the legs. Using customized MATLAB code, 100 gait cycles at each speed for each participant were chosen and temporally aligned to the five gait phases (loading response, mid and terminal stance, pre-swing, initial and mid swing, and terminal swing) based on kinematic events of interest. Five distinct stride definitions were used in SPM using a one-way repeated measures ANOVA, both with and without the temporal alignment of gait phases. SPM results for unaligned gait data varied between different stride definitions but were consistent for data that was temporally aligned. SPM\u27s results for aligned data consistently demonstrate that time normalization, not stride definition, is what makes SPM sensitive. For a point-by-point comparison of gait kinematics using SPM, the phases must be time-aligned.https://digitalcommons.odu.edu/gradposters2023_healthsciences/1010/thumbnail.jp

Self-evaluation in advanced power searching and mapping with google MOOCs

While there is a large amount of work on creating autograded massive open online courses (MOOCs), some kinds of complex, qualitative exam questions are still beyond the current state of the art. For MOOCs that need to deal with these kinds of questions, it is not possible for a small course staff to grade students ’ qualitative work. To test the efficacy of self-evaluation as a method for complex-question evaluation, students in two Google MOOCs have submitted projects and evaluated their own work. For both courses, teaching assistants graded a random sample of papers and compared their grades with self-evaluated student grades. We found that many of the submitted projects were of very high quality, and that a large majority of self-evaluated projects were accurately evaluated, scoring within just a few points of the gold standard grading

Relating multi-sequence longitudinal intensity profiles and clinical covariates in new multiple sclerosis lesions

Structural magnetic resonance imaging (MRI) can be used to detect lesions in the brains of multiple sclerosis (MS) patients. The formation of these lesions is a complex process involving inflammation, tissue damage, and tissue repair, all of which are visible on MRI. Here we characterize the lesion formation process on longitudinal, multi-sequence structural MRI from 34 MS patients and relate the longitudinal changes we observe within lesions to therapeutic interventions. In this article, we first outline a pipeline to extract voxel level, multi-sequence longitudinal profiles from four MRI sequences within lesion tissue. We then propose two models to relate clinical covariates to the longitudinal profiles. The first model is a principal component analysis (PCA) regression model, which collapses the information from all four profiles into a scalar value. We find that the score on the first PC identifies areas of slow, long-term intensity changes within the lesion at a voxel level, as validated by two experienced clinicians, a neuroradiologist and a neurologist. On a quality scale of 1 to 4 (4 being the highest) the neuroradiologist gave the score on the first PC a median rating of 4 (95% CI: [4,4]), and the neurologist gave it a median rating of 3 (95% CI: [3,3]). In the PCA regression model, we find that treatment with disease modifying therapies (p-value < 0.01), steroids (p-value < 0.01), and being closer to the boundary of abnormal signal intensity (p-value < 0.01) are associated with a return of a voxel to intensity values closer to that of normal-appearing tissue. The second model is a function-on-scalar regression, which allows for assessment of the individual time points at which the covariates are associated with the profiles. In the function-on-scalar regression both age and distance to the boundary were found to have a statistically significant association with the profiles

Assessing Change in a Personality Profile

We tested the validity of 6 methods (mean difference, variance difference, bivariate, profile agreement, pattern similarity, and intraclass) to assess change in a personality profile. During their first 2 months of college, 372 students completed reactive and spontaneous measures of their personality. Eight weeks later, 300 returned to complete a second set of the same measures and noted change in their spontaneous personality list. Sixty participants returned during their second semester to complete a third set of assessments. The bivariate and intraclass change coefficients showed consistent convergent, discriminant, and concurrent validity across time points. Recommendations and caveats for using these coefficients are discussed

Healthcare Barriers of Residents at a Subsidized Housing Community

Introduction: Despite expanded healthcare programs, the low income and elderly lack coverage of vision, hearing, and dental services. Community services are often asked to fill these gaps. To evaluate the situation in Burlington, VT, we surveyed staff and residents in Burlington Housing Authority (BHA) subsidized housing to (1) identify gaps in healthcare coverage and (2) assess barriers to accessing those services in this population.https://scholarworks.uvm.edu/comphp_gallery/1207/thumbnail.jp