Stability boundary approximation of periodic dynamics

We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2 degrees of freedom (DOF) we derive general approximate stability conditions. We study domains of stability with the use of fourth order approximations of monodromy matrix on example of inverted position of a pendulum with vertically oscillating pivot. Addition of small damping shifts the stability boundaries upwards, thus resulting to both stabilization and destabilization effects.Comment: 9 pages, 2 figure

Early Jurassic large igneous province carbon emissions constrained by sedimentary mercury

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: All data generated or analysed during this study are included in this published paper (and its Supplementary Information) and are available at https://doi.org/10.6084/m9.figshare.23301311.Code availability: The R script to calculate residual Hg for the Mochras dataset is available within the Supplementary Information.Large igneous province eruptions and their carbon emissions often coincide with, and are hypothesized to have driven, severe environmental perturbations in the geological past. However, the vast scale of large igneous provinces and uncertainties in magmatic volatile contents and radioisotopic dates limit our ability to resolve gas emissions in detail over time. Here we employ high-resolution (~5–200 kyr) sedimentary mercury data from the Llanbedr (Mochras Farm) borehole, Wales, to derive quantitative large igneous province degassing estimates over a 20-million-year-long Early Jurassic interval (195–175 million years ago). Intervals of relatively elevated sedimentary mercury coincide with episodes of carbon-cycle change, including the Toarcian Oceanic Anoxic Event (183–182 million years ago). We use excess mercury loading to estimate large igneous province-associated carbon emissions, revealing that multi-millennial episodes of activity plausibly drove recognized pCO2 and temperature increases. However, previous carbon-cycle model-based carbon emission scenarios require faster and larger carbon inputs than our proposed emissions. Resolving this discrepancy may require climate–carbon-cycle feedbacks or co-emitted gases to substantially exacerbate the carbon-cycle response, processes potentially underestimated in current models. Our long and near-continuous record of Early Jurassic large igneous province activity demonstrates mercury’s potential as a tool to resolve past carbon fluxes.European Research Council (ERC)Natural Environment Research Council (NERC

Thunderclap headache triggered by micturition: responsive to nimodipine

Primary thunderclap headache (TCH) is a rare condition, of which the onset can be triggered by coughing, exercise, and sexual activity. Micturition is a recognized trigger of secondary TCH with pheochromocytoma in bladder, but not of primary TCH. We describe a patient with an apparent primary TCH, which repeatedly occurred immediately after micturition until she achieved a therapeutic dosage of nimodipine

Ectopic A-lattice seams destabilize microtubules

Natural microtubules typically include one A-lattice seam within an otherwise helically symmetric B-lattice tube. It is currently unclear how A-lattice seams influence microtubule dynamic instability. Here we find that including extra A-lattice seams in GMPCPP microtubules, structural analogues of the GTP caps of dynamic microtubules, destabilizes them, enhancing their median shrinkage rate by >20-fold. Dynamic microtubules nucleated by seeds containing extra A-lattice seams have growth rates similar to microtubules nucleated by B-lattice seeds, yet have increased catastrophe frequencies at both ends. Furthermore, binding B-lattice GDP microtubules to a rigor kinesin surface stabilizes them against shrinkage, whereas microtubules with extra A-lattice seams are stabilized only slightly. Our data suggest that introducing extra A-lattice seams into dynamic microtubules destabilizes them by destabilizing their GTP caps. On this basis, we propose that the single A-lattice seam of natural B-lattice MTs may act as a trigger point, and potentially a regulation point, for catastrophe

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

Computer simulation of syringomyelia in dogs

Syringomyelia is a pathological condition in which fluid-filled cavities (syringes) form and expand in the spinal cord. Syringomyelia is often linked with obstruction of the craniocervical junction and a Chiari malformation, which is similar in both humans and animals. Some brachycephalic toy breed dogs such as Cavalier King Charles Spaniels (CKCS) are particularly predisposed. The exact mechanism of the formation of syringomyelia is undetermined and consequently with the lack of clinical explanation, engineers and mathematicians have resorted to computer models to identify possible physical mechanisms that can lead to syringes. We developed a computer model of the spinal cavity of a CKCS suffering from a large syrinx. The model was excited at the cranial end to simulate the movement of the cerebrospinal fluid (CSF) and the spinal cord due to the shift of blood volume in the cranium related to the cardiac cycle. To simulate the normal condition, the movement was prescribed to the CSF. To simulate the pathological condition, the movement of CSF was blocked

Subclinical thyroid dysfunction and cognitive decline in old age

<p>Background: Subclinical thyroid dysfunction has been implicated as a risk factor for cognitive decline in old age, but results are inconsistent. We investigated the association between subclinical thyroid dysfunction and cognitive decline in the PROspective Study of Pravastatin in the Elderly at Risk (PROSPER).</p> <p>Methods: Prospective longitudinal study of men and women aged 70–82 years with pre-existing vascular disease or more than one risk factor to develop this condition (N = 5,154). Participants taking antithyroid medications, thyroid hormone supplementation and/or amiodarone were excluded. Thyroid function was measured at baseline: subclinical hyper- and hypothyroidism were defined as thyroid stimulating hormones (TSH) <0.45 mU/L or >4.50 mU/L respectively, with normal levels of free thyroxine (FT4). Cognitive performance was tested at baseline and at four subsequent time points during a mean follow-up of 3 years, using five neuropsychological performance tests.</p> <p>Results: Subclinical hyperthyroidism and hypothyroidism were found in 65 and 161 participants, respectively. We found no consistent association of subclinical hyper- or hypothyroidism with altered cognitive performance compared to euthyroid participants on the individual cognitive tests. Similarly, there was no association with rate of cognitive decline during follow-up.</p> <p>Conclusion: We found no consistent evidence that subclinical hyper- or hypothyroidism contribute to cognitive impairment or decline in old age. Although our data are not in support of treatment of subclinical thyroid dysfunction to prevent cognitive dysfunction in later life, only large randomized controlled trials can provide definitive evidence.</p&gt

Subclinical thyroid dysfunction and cognitive decline in old age

<p>Background: Subclinical thyroid dysfunction has been implicated as a risk factor for cognitive decline in old age, but results are inconsistent. We investigated the association between subclinical thyroid dysfunction and cognitive decline in the PROspective Study of Pravastatin in the Elderly at Risk (PROSPER).</p> <p>Methods: Prospective longitudinal study of men and women aged 70–82 years with pre-existing vascular disease or more than one risk factor to develop this condition (N = 5,154). Participants taking antithyroid medications, thyroid hormone supplementation and/or amiodarone were excluded. Thyroid function was measured at baseline: subclinical hyper- and hypothyroidism were defined as thyroid stimulating hormones (TSH) <0.45 mU/L or >4.50 mU/L respectively, with normal levels of free thyroxine (FT4). Cognitive performance was tested at baseline and at four subsequent time points during a mean follow-up of 3 years, using five neuropsychological performance tests.</p> <p>Results: Subclinical hyperthyroidism and hypothyroidism were found in 65 and 161 participants, respectively. We found no consistent association of subclinical hyper- or hypothyroidism with altered cognitive performance compared to euthyroid participants on the individual cognitive tests. Similarly, there was no association with rate of cognitive decline during follow-up.</p> <p>Conclusion: We found no consistent evidence that subclinical hyper- or hypothyroidism contribute to cognitive impairment or decline in old age. Although our data are not in support of treatment of subclinical thyroid dysfunction to prevent cognitive dysfunction in later life, only large randomized controlled trials can provide definitive evidence.</p&gt