Variational water-wave model with accurate dispersion and vertical vorticity

A new water-wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite-element profile with a small number of elements (say), leading to a framework for efficient modeling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves

Effect of systemic corticosteroid therapy for acute heart failure patients with elevated C-reactive protein

The current study explores whether degree of inflammation, reflected by C-reactive protein (CRP) level, modifies the effect of intravenous (IV) corticosteroid administered in the emergency department (ED) on clinical outcomes in patients with acute heart failure (AHF).We selected patients diagnosed with AHF in the ED, with confirmed N-terminal pro-B-type natriuretic peptide > 300 pg/mL and CRP > 5 mg/L in the ED from the Epidemiology of Acute Heart Failure in the Emergency Departments (EAHFE) registry. In these 1109 patients, 121 were treated by corticosteroid. The corticosteroid therapy hazard ratio (HR) for 30 day all-cause mortality was 1.26 [95% confidence interval (CI) 0.75-2.09, P = 0.38]. Although not statistically significant, HRs tended to decrease with increasing CRP level, with point estimates favouring corticosteroid at CRP levels above 20. In patients with CRP > 40 mg/L, with adjusted HRs of 0.56 (95% CI 0.20-1.55, P = 0.27) for 30 day all-cause mortality, 0.92 (95% CI 0.52-1.62, P = 0.78) for 30 day post-discharge ED revisit, hospitalization, or death, and adjusted odds ratio of 0.61 (95% CI 0.17-2.14, P = 0.44) for in-hospital all-cause mortality.The present analysis suggests that corticosteroids might have the potential to improve outcomes in AHF patients with inflammatory activation. Larger, prospective studies of anti-inflammatory therapy should be considered to assess potential benefit in patients with the highest degree of inflammation.© 2022 The Authors. ESC Heart Failure published by John Wiley & Sons Ltd on behalf of European Society of Cardiology

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides

All-optical signal processing is envisioned as an approach to dramatically decrease power consumption and speed up performance of next-generation optical telecommunications networks. Nonlinear optical effects, such as four-wave mixing (FWM) and parametric gain, have long been explored to realize all-optical functions in glass fibers. An alternative approach is to employ nanoscale engineering of silicon waveguides to enhance the optical nonlinearities by up to five orders of magnitude, enabling integrated chip-scale all-optical signal processing. Previously, strong two-photon absorption (TPA) of the telecom-band pump has been a fundamental and unavoidable obstacle, limiting parametric gain to values on the order of a few dB. Here we demonstrate a silicon nanophotonic optical parametric amplifier exhibiting gain as large as 25.4 dB, by operating the pump in the mid-IR near one-half the band-gap energy (E~0.55eV, lambda~2200nm), at which parasitic TPA-related absorption vanishes. This gain is high enough to compensate all insertion losses, resulting in 13 dB net off-chip amplification. Furthermore, dispersion engineering dramatically increases the gain bandwidth to more than 220 nm, all realized using an ultra-compact 4 mm silicon chip. Beyond its significant relevance to all-optical signal processing, the broadband parametric gain also facilitates the simultaneous generation of multiple on-chip mid-IR sources through cascaded FWM, covering a 500 nm spectral range. Together, these results provide a foundation for the construction of silicon-based room-temperature mid-IR light sources including tunable chip-scale parametric oscillators, optical frequency combs, and supercontinuum generators

Sampling constrained probability distributions using Spherical Augmentation

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. In this paper, we propose a novel augmentation technique that handles a wide range of constraints by mapping the constrained domain to a sphere in the augmented space. By moving freely on the surface of this sphere, sampling algorithms handle constraints implicitly and generate proposals that remain within boundaries when mapped back to the original space. Our proposed method, called {Spherical Augmentation}, provides a mathematically natural and computationally efficient framework for sampling from constrained probability distributions. We show the advantages of our method over state-of-the-art sampling algorithms, such as exact Hamiltonian Monte Carlo, using several examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian bridge regression, reconstruction of quantized stationary Gaussian process, and LDA for topic modeling.Comment: 41 pages, 13 figure

Consistency of the posterior distribution in generalized linear inverse problems

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution to the inverse problem, such as the posterior mean that can be easier to compute in practice. In this paper we prove consistency of Bayesian solutions of an ill-posed linear inverse problem in the Ky Fan metric for a general class of likelihoods and prior distributions in a finite dimensional setting. This result can be applied to study infinite dimensional problems by letting the dimension of the unknown parameter grow to infinity which can be viewed as discretisation on a grid or spectral approximation of an infinite dimensional problem. Likelihood and the prior distribution are assumed to be in an exponential form that includes distributions from the exponential family, and to be differentiable. The observations can be dependent. No assumption of finite moments of observations, such as expected value or the variance, is necessary thus allowing for possibly non-regular likelihoods, and allowing for non-conjugate and improper priors. If the variance exists, it may be heteroscedastic, namely, it may depend on the unknown function. We observe quite a surprising phenomenon when applying our result to the spectral approximation framework where it is possible to achieve the parametric rate of convergence, i.e the problem becomes self-regularised. We also consider a particular case of the unknown parameter being on the boundary of the parameter set, and show that the rate of convergence in this case is faster than for an interior point parameter.Comment: arXiv admin note: substantial text overlap with arXiv:1110.301

Lack of phenotypic and evolutionary cross-resistance against parasitoids and pathogens in Drosophila melanogaster

BackgroundWhen organisms are attacked by multiple natural enemies, the evolution of a resistance mechanism to one natural enemy will be influenced by the degree of cross-resistance to another natural enemy. Cross-resistance can be positive, when a resistance mechanism against one natural enemy also offers resistance to another; or negative, in the form of a trade-off, when an increase in resistance against one natural enemy results in a decrease in resistance against another. Using Drosophila melanogaster, an important model system for the evolution of invertebrate immunity, we test for the existence of cross-resistance against parasites and pathogens, at both a phenotypic and evolutionary level.MethodsWe used a field strain of D. melanogaster to test whether surviving parasitism by the parasitoid Asobara tabida has an effect on the resistance against Beauveria bassiana, an entomopathogenic fungus; and whether infection with the microsporidian Tubulinosema kingi has an effect on the resistance against A. tabida. We used lines selected for increased resistance to A. tabida to test whether increased parasitoid resistance has an effect on resistance against B. bassiana and T. kingi. We used lines selected for increased tolerance against B. bassiana to test whether increased fungal resistance has an effect on resistance against A. tabida.Results/ConclusionsWe found no positive cross-resistance or trade-offs in the resistance to parasites and pathogens. This is an important finding, given the use of D. melanogaster as a model system for the evolution of invertebrate immunity. The lack of any cross-resistance to parasites and pathogens, at both the phenotypic and the evolutionary level, suggests that evolution of resistance against one class of natural enemies is largely independent of evolution of resistance against the other

Cell genesis and dendritic plasticity: a neuroplastic pas de deux in the onset and remission from depression

Brain neuroplasticity is increasingly considered to be an important component of both the pathology and treatment of depressive spectrum disorders. Recent studies shed light on the relevance of hippocampal cell genesis and cortico-limbic dendritic plasticity for the development and remission from depressive-like behavior. However, the neurobiological significance of neuroplastic phenomena in this context is still controversial. Here we summarize recent developments in this topic and propose an integrative interpretation of data gathered so far

Excitonic Transitions and Off-resonant Optical Limiting in CdS Quantum Dots Stabilized in a Synthetic Glue Matrix

Stable films containing CdS quantum dots of mean size 3.4 nm embedded in a solid host matrix are prepared using a room temperature chemical route of synthesis. CdS/synthetic glue nanocomposites are characterized using high resolution transmission electron microscopy, infrared spectroscopy, differential scanning calorimetry and thermogravimetric analysis. Significant blue shift from the bulk absorption edge is observed in optical absorption as well as photoacoustic spectra indicating strong quantum confinement. The exciton transitions are better resolved in photoacoustic spectroscopy compared to optical absorption spectroscopy. We assign the first four bands observed in photoacoustic spectroscopy to 1se–1sh, 1pe–1ph, 1de–1dhand 2pe–2phtransitions using a non interacting particle model. Nonlinear absorption studies are done using z-scan technique with nanosecond pulses in the off resonant regime. The origin of optical limiting is predominantly two photon absorption mechanism

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome