100 research outputs found
Considering discrepancy when calibrating a mechanistic electrophysiology model
Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions—that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’
Renormalization group flows and continual Lie algebras
We study the renormalization group flows of two-dimensional metrics in sigma
models and demonstrate that they provide a continual analogue of the Toda field
equations based on the infinite dimensional algebra G(d/dt;1). The resulting
Toda field equation is a non-linear generalization of the heat equation, which
is integrable in target space and shares the same dissipative properties in
time. We provide the general solution of the renormalization group flows in
terms of free fields, via Backlund transformations, and present some simple
examples that illustrate the validity of their formal power series expansion in
terms of algebraic data. We study in detail the sausage model that arises as
geometric deformation of the O(3) sigma model, and give a new interpretation to
its ultra-violet limit by gluing together two copies of Witten's
two-dimensional black hole in the asymptotic region. We also provide some new
solutions that describe the renormalization group flow of negatively curved
spaces in different patches, which look like a cane in the infra-red region.
Finally, we revisit the transition of a flat cone C/Z_n to the plane, as
another special solution, and note that tachyon condensation in closed string
theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1)
in the regime of gravity. Its exponential growth holds the key for the
construction of conserved currents and their systematic interpretation in
string theory, but they still remain unknown.Comment: latex, 73pp including 14 eps fig
Propagating Disturbances in Coronal Loops: A Detailed Analysis of Propagation Speeds
Quasi-periodic disturbances have been observed in the outer solar atmosphere
for many years now. Although first interpreted as upflows (Schrijver et al.
(1999)), they have been widely regarded as slow magnetoacoustic waves, due to
observed velocities and periods. However, recent observations have questioned
this interpretation, as periodic disturbances in Doppler velocity, line width
and profile asymmetry were found to be in phase with the intensity oscillations
(De Pontieu et al. (2010),Tian1 et al. (2011))}, suggesting the disturbances
could be quasi-periodic upflows. Here we conduct a detailed analysis of the
velocities of these disturbances across several wavelengths using the
Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory
(SDO). We analysed 41 examples, including both sunspot and non sunspot regions
of the Sun. We found that the velocities of propagating disturbances (PDs)
located at sunspots are more likely to be temperature dependent, whereas the
velocities of PDs at non sunspot locations do not show a clear temperature
dependence. We also considered on what scale the underlying driver is affecting
the properties of the PDs. Finally, we found that removing the contribution due
to the cooler ions in the 193 A wavelength suggests that a substantial part of
the 193 emission of sunspot PDs can be contributed to the cool component of
193\AA.Comment: 26 Papges, 15 Figure
Multi-system neurological disease is common in patients with OPA1 mutations
Additional neurological features have recently been described in seven families transmitting pathogenic mutations in OPA1, the most common cause of autosomal dominant optic atrophy. However, the frequency of these syndromal ‘dominant optic atrophy plus’ variants and the extent of neurological involvement have not been established. In this large multi-centre study of 104 patients from 45 independent families, including 60 new cases, we show that extra-ocular neurological complications are common in OPA1 disease, and affect up to 20% of all mutational carriers. Bilateral sensorineural deafness beginning in late childhood and early adulthood was a prominent manifestation, followed by a combination of ataxia, myopathy, peripheral neuropathy and progressive external ophthalmoplegia from the third decade of life onwards. We also identified novel clinical presentations with spastic paraparesis mimicking hereditary spastic paraplegia, and a multiple sclerosis-like illness. In contrast to initial reports, multi-system neurological disease was associated with all mutational subtypes, although there was an increased risk with missense mutations [odds ratio = 3.06, 95% confidence interval = 1.44–6.49; P = 0.0027], and mutations located within the guanosine triphosphate-ase region (odds ratio = 2.29, 95% confidence interval = 1.08–4.82; P = 0.0271). Histochemical and molecular characterization of skeletal muscle biopsies revealed the presence of cytochrome c oxidase-deficient fibres and multiple mitochondrial DNA deletions in the majority of patients harbouring OPA1 mutations, even in those with isolated optic nerve involvement. However, the cytochrome c oxidase-deficient load was over four times higher in the dominant optic atrophy + group compared to the pure optic neuropathy group, implicating a causal role for these secondary mitochondrial DNA defects in disease pathophysiology. Individuals with dominant optic atrophy plus phenotypes also had significantly worse visual outcomes, and careful surveillance is therefore mandatory to optimize the detection and management of neurological disability in a group of patients who already have significant visual impairment
Efeito inibitório na germinação, induzido pelo extrato de couve (Brassica oleracea L. var. acephala DC.)
DIVERSIDADE DE QUINZE ESPÉCIES DE BORBOLETAS (LEPIDOPTERA, PAPILIONIDAE) EM SETE COMUNIDADES DE SANTA MARIA, RS
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