Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Gender Differences in Stress and Coping Among Adults Living in Hawai`i

Background and purpose. Stress has been recognized as a public health problem. However, little research has been done on gender differences in sources of stress and coping strategies in Hawaii. In this study, we hypothesized that: 1) women will report higher levels of stress than men; 2) women will report being stressed by family and health related stressors while men will report stress related to finances and work-related issues; 3) women will report using adaptive coping strategies more frequently while men will report using maladaptive and avoidance strategies more frequently; 4) there will be no gender differences in the readiness to use stress management strategies. Method. A statewide cross-sectional telephone-survey of 1518 participants was conducted during the spring and summer of 2006. Results. Women reported higher overall perceived stress levels, but there was no difference in the experienced social stressors and health stressors between genders. Men perceived more stress from personal factors. There were no gender differences in the perceived ability to cope with stress. However, women were more likely to use adaptive coping strategies, whereas men were more likely to use maladaptive and avoidance coping strategies. There were no significant gender differences in stages of change for stress management. Conclusion. Based on this study, interventions can be developed to help people better cope with stress. Interventions for women may focus on increasing the use of adaptive strategies such as praying and talking to friends and family, while interventions for men may introduce the use of adaptive coping strategies such as exercise and actively fighting causes of stress. This study shows that gender differences in stress levels and coping in Hawaii are similar to previous studies conducted on the mainland. More research into specific stressors and coping strategies may help tailor interventions that are more effective and comprehensive

On the deflection of asteroids with mirrors

This paper presents an analysis of an asteroid deflection method based on multiple solar concentrators. A model of the deflection through the sublimation of the surface material of an asteroid is presented, with simulation results showing the achievable orbital deflection with, and without, accounting for the effects of mirror contamination due to the ejected debris plume. A second model with simulation results is presented analyzing an enhancement of the Yarkovsky effect, which provides a significant deflection even when the surface temperature is not high enough to sublimate. Finally the dynamical model of solar concentrators in the proximity of an irregular celestial body are discussed, together with a Lyapunov-based controller to maintain the spacecraft concentrators at a required distance from the asteroid

Broader Visual Orientation Tuning in Patients with Schizophrenia

Reduced gamma-aminobutyric acid (GABA) levels in cerebral cortex are thought to contribute to information processing deficits in patients with schizophrenia (SZ), and we have previously reported lower in vivo GABA levels in the visual cortex of patients with SZ. GABA-mediated inhibition plays a role in sharpening orientation tuning of visual cortical neurons. Therefore, we predicted that tuning for visual stimulus orientation would be wider in SZ. We measured orientation tuning with a psychophysical procedure in which subjects performed a target detection task of a low-contrast oriented grating, following adaptation to a high-contrast grating. Contrast detection thresholds were determined for a range of adapter–target orientation offsets. For both SZ and healthy controls, contrast thresholds decreased as orientation offset increased, suggesting that this tuning curve reflects the selectivity of visual cortical neurons for stimulus orientation. After accounting for generalized deficits in task performance in SZ, there was no difference between patients and controls for detection of target stimuli having either the same orientation as the adapter or orientations far from the adapter. However, patients’ thresholds were significantly higher for intermediate adapter–target offsets. In addition, the mean width parameter of a Gaussian fit to the psychophysical orientation tuning curves was significantly larger for the patient group. We also present preliminary data relating visual cortical GABA levels, as measured with magnetic resonance spectroscopy, and orientation tuning width. These results suggest that our finding of broader orientation tuning in SZ may be due to diminished visual cortical GABA levels

How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Effects of thermal fluctuation and the receptor-receptor interaction in bacterial chemotactic signalling and adaptation

Bacterial chemotaxis is controlled by the conformational changes of the receptors, in response to the change of the ambient chemical concentration. In a statistical mechanical approach, the signalling due to the conformational changes is a thermodynamic average quantity, dependent on the temperature and the total energy of the system, including both ligand-receptor interaction and receptor-receptor interaction. This physical theory suggests to biology a new understanding of cooperation in ligand binding and receptor signalling problems. How much experimental support of this approach can be obtained from the currently available data? What are the parameter values? What is the practical information for experiments? Here we make comparisons between the theory and recent experimental results. Although currently comparisons can only be semi-quantitative or qualitative, consistency is clearly shown. The theory also helps to sort a variety of data.Comment: 26 pages, revtex. Journal version. Analysis on another set of data on adaptation time is adde

Universal architecture of bacterial chemoreceptor arrays

Chemoreceptors are key components of the high-performance signal transduction system that controls bacterial chemotaxis. Chemoreceptors are typically localized in a cluster at the cell pole, where interactions among the receptors in the cluster are thought to contribute to the high sensitivity, wide dynamic range, and precise adaptation of the signaling system. Previous structural and genomic studies have produced conflicting models, however, for the arrangement of the chemoreceptors in the clusters. Using whole-cell electron cryo-tomography, here we show that chemoreceptors of different classes and in many different species representing several major bacterial phyla are all arranged into a highly conserved, 12-nm hexagonal array consistent with the proposed “trimer of dimers” organization. The various observed lengths of the receptors confirm current models for the methylation, flexible bundle, signaling, and linker sub-domains in vivo. Our results suggest that the basic mechanism and function of receptor clustering is universal among bacterial species and was thus conserved during evolution

Chytrid Fungus (Batrachochytrium dendrobatidis) Undetected in the Two Orders of Seychelles Amphibians

Reports the first disease screening for chytrid Fungus (Batrachochytrium dendrobatidis) in amphibians across the Seychelles Archipelag

Validity and reliability of short‐term heart‐rate variability from disposable electrocardiography leads

BACKGROUND AND AIMS: Single‐use electrocardiography (ECG) leads have been developed to reduce healthcare‐associated infection. This study compared the validity and reliability of short‐term heart rate variability (HRV) obtained from single‐use disposable ECG leads. METHODS: Thirty healthy subjects (33 ± 10 years; 9 females) underwent 5‐min resting HRV assessments using disposable (single use) ECG cable and wire system (Kendall DL™ Cardinal Health) and a standard, reusable ECG leads (CardioExpress, Spacelabs Healthcare). RESULTS: Intraclass correlation coefficient (ICC) with 95% confidence interval (CI) between disposable and reusable ECG leads was for the time domain [R‐R interval (ms); 0.99 (0.91, 1.00)], the root mean square of successive normal R‐R interval differences (RMSSD) (ms); 0.91 (0.76, 0.96), the SD of normal‐to‐normal R‐R intervals (SDNN) (ms); 0.91 (0.68, 0.97) and frequency domain [low‐frequency (LF) normalized units (nu); 0.90 (0.79, 0.95), high frequency (HF) nu; 0.91 (0.80, 0.96), LF power (ms(2)); 0.89 (0.62, 0.96), HF power (ms(2)); 0.90 (0.72, 0.96)] variables. The mean difference and upper and lower limits of agreement between disposable and reusable leads for time‐ and frequency‐domain variables were acceptable. Analysis of repeated measures using disposable leads demonstrated excellent reproducibility (ICC 95% CI) for R‐R interval (ms); 0.93 (0.85, 0.97), RMSSD (ms); 0.93 (0.85, 0.97), SDNN (ms); 0.88 (0.75, 0.95), LF power (ms(2)); 0.87 (0.72, 0.94), and HF power (ms(2)); 0.88 (0.73, 0.94) with coefficient of variation ranging from 2.2% to 5% (p > 0.37 for all variables). CONCLUSION: Single‐use Kendall DL™ ECG leads demonstrate a valid and reproducible tool for the assessment of HRV