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

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

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

Quasi-particle interference and superconducting gap in a high-temperature superconductor Ca2-xNaxCuO2Cl2

High-transition-temperature (high-Tc) superconductivity is ubiquitous in the cuprates containing CuO2 planes but each cuprate has its own character. The study of the material dependence of the d-wave superconducting gap (SG) should provide important insights into the mechanism of high-Tc. However, because of the 'pseudogap' phenomenon, it is often unclear whether the energy gaps observed by spectroscopic techniques really represent the SG. Here, we report spectroscopic imaging scanning tunneling microscopy (SI-STM) studies of nearly-optimally-doped Ca2-xNaxCuO2Cl2 (Na-CCOC) with Tc = 25 ~ 28 K. They enable us to observe the quasi-particle interference (QPI) effect in this material, through which unambiguous new information on the SG is obtained. The analysis of QPI in Na-CCOC reveals that the SG dispersion near the gap node is almost identical to that of Bi2Sr2CaCu2Oy (Bi2212) at the same doping level, while Tc of Bi2212 is 3 times higher than that of Na-CCOC. We also find that SG in Na-CCOC is confined in narrower energy and momentum ranges than Bi2212. This explains at least in part the remarkable material dependence of TcComment: 13pages, 4fig

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

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Size Dependence of Metal-Insulator Transition in Stoichiometric Fe3O4 Nanocrystals

Magnetite (Fe3O4) is one of the most actively studied materials with a famous metal-insulator transition (MIT), so-called the Verwey transition at around 123 K. Despite the recent progress in synthesis and characterization of Fe3O4 nanocrystals (NCs), it is still an open question how the Verwey transition changes on a nanometer scale. We herein report the systematic studies on size dependence of the Verwey transition of stoichiometric Fe3O4 NCs. We have successfully synthesized stoichiometric and uniform-sized Fe3O4 NCs with sizes ranging from 5 to 100 nm. These stoichiometric Fe3O4 NCs show the Verwey transition when they are characterized by conductance, magnetization, cryo-XRD, and heat capacity measurements. The Verwey transition is weakly size-dependent and becomes suppressed in NCs smaller than 20 nm before disappearing completely for less than 6 nm, which is a clear, yet highly interesting indication of a size effect of this well-known phenomena. Our current work will shed new light on this ages-old problem of Verwey transition.Comment: 18 pages, 4 figures, Nano Letters (accepted

Imaging the Two Gaps of the High-TC Superconductor Pb-Bi2Sr2CuO6+x

The nature of the pseudogap state, observed above the superconducting transition temperature TC in many high temperature superconductors, is the center of much debate. Recently, this discussion has focused on the number of energy gaps in these materials. Some experiments indicate a single energy gap, implying that the pseudogap is a precursor state. Others indicate two, suggesting that it is a competing or coexisting phase. Here we report on temperature dependent scanning tunneling spectroscopy of Pb-Bi2Sr2CuO6+x. We have found a new, narrow, homogeneous gap that vanishes near TC, superimposed on the typically observed, inhomogeneous, broad gap, which is only weakly temperature dependent. These results not only support the two gap picture, but also explain previously troubling differences between scanning tunneling microscopy and other experimental measurements.Comment: 6 page