Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations

Enhanced Resolution in Nanoscale NMR via Quantum Sensing with Pulses of Finite Duration

The nitrogen-vacancy (N-V) color center in diamond is an enormously important platform for the development of quantum sensors, including for single-spin and single-molecule NMR. Detection of weak single-spin signals is greatly enhanced by repeated sequences of microwave pulses; in these dynamicaldecoupling techniques, the key control parameters swept in the experiment are the time intervals, τ, between pulses. Here, we show that, in fact, the pulse duration tp offers a powerful additional control parameter. While a non-negligible tp was previously considered simply a source of experimental error, we elucidate here the underlying quantum dynamics: we identify a landscape of quantum-state crossings which are usually inactive (closed) but may be controllably activated (opened) by adjusting tp from zero. We identify these crossings with recently observed but unexpected dips (so-called spurious dips) seen in the quantum coherence of the N-V spin. With this new understanding, both the position and the strength of these sharp features may be accurately controlled; they coexist with the usual broader coherence dips of short-duration microwave pulses, but their sharpness allows for higher-resolution spectroscopy with quantum diamond sensors, or their analogs

Enhanced Resolution in Nanoscale NMR via Quantum Sensing with Pulses of Finite Duration

The nitrogen-vacancy (N-V) color center in diamond is an enormously important platform for the development of quantum sensors, including for single-spin and single-molecule NMR. Detection of weak single-spin signals is greatly enhanced by repeated sequences of microwave pulses; in these dynamicaldecoupling techniques, the key control parameters swept in the experiment are the time intervals, τ, between pulses. Here, we show that, in fact, the pulse duration tp offers a powerful additional control parameter. While a non-negligible tp was previously considered simply a source of experimental error, we elucidate here the underlying quantum dynamics: we identify a landscape of quantum-state crossings which are usually inactive (closed) but may be controllably activated (opened) by adjusting tp from zero. We identify these crossings with recently observed but unexpected dips (so-called spurious dips) seen in the quantum coherence of the N-V spin. With this new understanding, both the position and the strength of these sharp features may be accurately controlled; they coexist with the usual broader coherence dips of short-duration microwave pulses, but their sharpness allows for higher-resolution spectroscopy with quantum diamond sensors, or their analogs

Joint Segmentation and Uncertainty Visualization of Retinal Layers in Optical Coherence Tomography Images using Bayesian Deep Learning

Optical coherence tomography (OCT) is commonly used to analyze retinal layers for assessment of ocular diseases. In this paper, we propose a method for retinal layer segmentation and quantification of uncertainty based on Bayesian deep learning. Our method not only performs end-to-end segmentation of retinal layers, but also gives the pixel wise uncertainty measure of the segmentation output. The generated uncertainty map can be used to identify erroneously segmented image regions which is useful in downstream analysis. We have validated our method on a dataset of 1487 images obtained from 15 subjects (OCT volumes) and compared it against the state-of-the-art segmentation algorithms that does not take uncertainty into account. The proposed uncertainty based segmentation method results in comparable or improved performance, and most importantly is more robust against noise

What went wrong? The flawed concept of cerebrospinal venous insufficiency

In 2006, Zamboni reintroduced the concept that chronic impaired venous outflow of the central nervous system is associated with multiple sclerosis (MS), coining the term of chronic cerebrospinal venous insufficiency ('CCSVI'). The diagnosis of 'CCSVI' is based on sonographic criteria, which he found exclusively fulfilled in MS. The concept proposes that chronic venous outflow failure is associated with venous reflux and congestion and leads to iron deposition, thereby inducing neuroinflammation and degeneration. The revival of this concept has generated major interest in media and patient groups, mainly driven by the hope that endovascular treatment of 'CCSVI' could alleviate MS. Many investigators tried to replicate Zamboni's results with duplex sonography, magnetic resonance imaging, and catheter angiography. The data obtained here do generally not support the 'CCSVI' concept. Moreover, there are no methodologically adequate studies to prove or disprove beneficial effects of endovascular treatment in MS. This review not only gives a comprehensive overview of the methodological flaws and pathophysiologic implausibility of the 'CCSVI' concept, but also summarizes the multimodality diagnostic validation studies and open-label trials of endovascular treatment. In our view, there is currently no basis to diagnose or treat 'CCSVI' in the care of MS patients, outside of the setting of scientific research

The impact of new water vapor spectroscopy on satellite retrievals

Water vapor, arguably the most important trace gas constituent of Earth atmospheric physics, is also both a retrieval goal and a hindrance in the retrievals of other trace gases from nadir-measuring satellite spectrometers. This is because the atmospherically-attenuated solar spectrum in the visible and shortwave infrared is littered with water vapor bands. The recent plethora of water vapor spectroscopy databases in this spectral region has prompted us to study their utility in satellite retrievals. We consider water vapor spectroscopy compiled from four sources including new spectroscopy due to University College London and Imperial College London. Radiative transfer models of satellite measurements, in combination with accurate retrieval techniques, are quite sensitive to the accuracy and completeness of the water vapor spectroscopy. Notwithstanding the high degree of variability of a number of different factors in satellite measurements we show that retrievals are sensitive to database differences which suggests that our knowledge of water vapor spectroscopy is not as yet complete. In addition, new laboratory measurements indicate that the role of both the far-line wings of water vapor and the cumulative effect of many weak lines each have an important role to play in forming the so-called continuum

Two-timescale stochastic Langevin propagation for classical and quantum optomechanics

Interesting experimental signatures of quantum cavity optomechanics arise because the quantum back-action induces correlations between incident quantum shot noise and the cavity field. While the quantum linear theory of optomechanics (QLT) has provided vital understanding across many experimental platforms, in certain new setups it may be insufficient: analysis in the time domain may be needed, but QLT obtains only spectra in frequency space; and nonlinear behavior may be present. Direct solution of the stochastic equations of motion in time is an alternative, but unfortunately standard methods do not preserve the important optomechanical correlations. We introduce two-timescale stochastic Langevin (T2SL) propagation as an efficient and straightforward method to obtain time traces with the correct correlations. We show that T2SL, in contrast to standard stochastic simulations, can efficiently simulate correlation phenomena such as ponderomotive squeezing and reproduces accurately cavity sideband structures on the scale of the applied quantum noise and even complex features entirely submerged below the quantum shot noise imprecision floor. We investigate nonlinear regimes and find that, where comparison is possible, the method agrees with analytical results obtained with master equations at low temperatures and in perturbative regimes

A morphometric analysis of the infant calvarium and dura

Literature addressing the anatomic development of the dura and calvarium during childhood is limited. Nevertheless, histological features of a subdural neomembrane (NM), including its thickness and vascularity, developing in response to an acute subdural hematoma (SDH) have been compared to the dura of adults to estimate when an injury occurred. Therefore, we measured the morphometric growth of the calvarium and dura and the vascular density within the dura during infancy. The mean thicknesses of the calvarium and dura as a function of occipitofrontal circumference (OFC), as well as the mean number of vessels per 25× field, were determined from the right parasagittal midparietal bone lateral to the sagittal suture of 128 infants without a history of head trauma. Our results showed that as OFC increased, the mean thicknesses of the calvarium and dura increased while the vascular density within the dura decreased. Our morphometric data may assist in the interpretation of subdural NM occurring during infancy. We recommend future investigations to confirm and extend our present data, especially by evaluating cases during later infancy and beyond as well as by sampling other anatomic sites from the calvarium. We also recommend morphometric evaluation of subdural NM associated with SDH in infancy and childhood

Adjusted Measures for Feature Selection Stability for Data Sets with Similar Features

For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features. Existing adjusted stability measures, that is, stability measures that take into account the similarities between features, have major theoretical drawbacks. We introduce new adjusted stability measures that overcome these drawbacks. We compare them to each other and to existing stability measures based on both artificial and real sets of selected features. Based on the results, we suggest using one new stability measure that considers highly similar features as exchangeable