Stochastic Development Regression on Non-Linear Manifolds

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

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

Paradoxical roles of antioxidant enzymes:Basic mechanisms and health implications

Reactive oxygen species (ROS) and reactive nitrogen species (RNS) are generated from aerobic metabolism, as a result of accidental electron leakage as well as regulated enzymatic processes. Because ROS/RNS can induce oxidative injury and act in redox signaling, enzymes metabolizing them will inherently promote either health or disease, depending on the physiological context. It is thus misleading to consider conventionally called antioxidant enzymes to be largely, if not exclusively, health protective. Because such a notion is nonetheless common, we herein attempt to rationalize why this simplistic view should be avoided. First we give an updated summary of physiological phenotypes triggered in mouse models of overexpression or knockout of major antioxidant enzymes. Subsequently, we focus on a series of striking cases that demonstrate “paradoxical” outcomes, i.e., increased fitness upon deletion of antioxidant enzymes or disease triggered by their overexpression. We elaborate mechanisms by which these phenotypes are mediated via chemical, biological, and metabolic interactions of the antioxidant enzymes with their substrates, downstream events, and cellular context. Furthermore, we propose that novel treatments of antioxidant enzyme-related human diseases may be enabled by deliberate targeting of dual roles of the pertaining enzymes. We also discuss the potential of “antioxidant” nutrients and phytochemicals, via regulating the expression or function of antioxidant enzymes, in preventing, treating, or aggravating chronic diseases. We conclude that “paradoxical” roles of antioxidant enzymes in physiology, health, and disease derive from sophisticated molecular mechanisms of redox biology and metabolic homeostasis. Simply viewing antioxidant enzymes as always being beneficial is not only conceptually misleading but also clinically hazardous if such notions underpin medical treatment protocols based on modulation of redox pathways

Direct comparison of methionine restriction with leucine restriction on the metabolic health of C57BL/6J mice

EKL was the recipient of a BBSRC postgraduate studentship. This work was funded by Tenovus Scotland project grant to MD and NM (G13/07) and BBSRC DTG. MD is also supported by the British Heart Foundation (PG/09/048/27675, PG/11/8/28703 and PG/14/43/30889) and Diabetes UK (14/0004853). NM is funded by British Heart Foundation (PG/16/90/32518).Peer reviewedPublisher PD

Non-thermal emission processes in massive binaries

In this paper, I present a general discussion of several astrophysical processes likely to play a role in the production of non-thermal emission in massive stars, with emphasis on massive binaries. Even though the discussion will start in the radio domain where the non-thermal emission was first detected, the census of physical processes involved in the non-thermal emission from massive stars shows that many spectral domains are concerned, from the radio to the very high energies. First, the theoretical aspects of the non-thermal emission from early-type stars will be addressed. The main topics that will be discussed are respectively the physics of individual stellar winds and their interaction in binary systems, the acceleration of relativistic electrons, the magnetic field of massive stars, and finally the non-thermal emission processes relevant to the case of massive stars. Second, this general qualitative discussion will be followed by a more quantitative one, devoted to the most probable scenario where non-thermal radio emitters are massive binaries. I will show how several stellar, wind and orbital parameters can be combined in order to make some semi-quantitative predictions on the high-energy counterpart to the non-thermal emission detected in the radio domain. These theoretical considerations will be followed by a census of results obtained so far, and related to this topic... (see paper for full abstract)Comment: 47 pages, 5 postscript figures, accepted for publication in Astronomy and Astrophysics Review. Astronomy and Astrophysics Review, in pres

Prenatal hypoxia induces increased cardiac contractility on a background of decreased capillary density.

Background: Chronic hypoxia in utero (CHU) is one of the most common insults to fetal development and may be associated with poor cardiac recovery from ischaemia-reperfusion injury,yet the effects on normal cardiac mechanical performance are poorly understood. Methods: Pregnant female wistar rats were exposed to hypoxia (12% oxygen, balance nitrogen)for days 10–20 of pregnancy. Pups were born into normal room air and weaned normally. At 10 weeks of age, hearts were excised under anaesthesia and underwent retrograde 'Langendorff' perfusion. Mechanical performance was measured at constant filling pressure (100 cm H2O) with intraventricular balloon. Left ventricular free wall was dissected away and capillary density estimated following alkaline phosphatase staining. Expression of SERCA2a and Nitric Oxide Synthases (NOS) proteins were estimated by immunoblotting. Results: CHU significantly increased body mass (P < 0.001) compared with age-matched control rats but was without effect on relative cardiac mass. For incremental increases in left ventricular balloon volume, diastolic pressure was preserved. However, systolic pressure was significantly greater following CHU for balloon volume = 50 μl (P < 0.01) and up to 200 μl (P < 0.05). For higher balloon volumes systolic pressure was not significantly different from control. Developed pressures were correspondingly increased relative to controls for balloon volumes up to 250 μl (P < 0.05).Left ventricular free wall capillary density was significantly decreased in both epicardium (18%; P <0.05) and endocardium (11%; P < 0.05) despite preserved coronary flow. Western blot analysis revealed no change to the expression of SERCA2a or nNOS but immuno-detectable eNOS protein was significantly decreased (P < 0.001) in cardiac tissue following chronic hypoxia in utero. Conclusion: These data offer potential mechanisms for poor recovery following ischaemia, including decreased coronary flow reserve and impaired angiogenesis with subsequent detrimental effects of post-natal cardiac performance

Evidence for an excess of B -> D(*) Tau Nu decays

Based on the full BaBar data sample, we report improved measurements of the ratios R(D(*)) = B(B -> D(*) Tau Nu)/B(B -> D(*) l Nu), where l is either e or mu. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure R(D) = 0.440 +- 0.058 +- 0.042 and R(D*) = 0.332 +- 0.024 +- 0.018, which exceed the Standard Model expectations by 2.0 sigma and 2.7 sigma, respectively. Taken together, our results disagree with these expectations at the 3.4 sigma level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. We also report the observation of the decay B -> D Tau Nu, with a significance of 6.8 sigma.Comment: Expanded section on systematics, text corrections, improved the format of Figure 2 and included the effect of the change of the Tau polarization due to the charged Higg