Properties of an affine transport equation and its holonomy

An affine transport equation was used recently to study properties of angular momentum and gravitational-wave memory effects in general relativity. In this paper, we investigate local properties of this transport equation in greater detail. Associated with this transport equation is a map between the tangent spaces at two points on a curve. This map consists of a homogeneous (linear) part given by the parallel transport map along the curve plus an inhomogeneous part, which is related to the development of a curve in a manifold into an affine tangent space. For closed curves, the affine transport equation defines a "generalized holonomy" that takes the form of an affine map on the tangent space. We explore the local properties of this generalized holonomy by using covariant bitensor methods to compute the generalized holonomy around geodesic polygon loops. We focus on triangles and "parallelogramoids" with sides formed from geodesic segments. For small loops, we recover the well-known result for the leading-order linear holonomy ($\sim$ Riemann $\times$ area), and we derive the leading-order inhomogeneous part of the generalized holonomy ($\sim$ Riemann $\times$ area$^{3/2}$). Our bitensor methods let us naturally compute higher-order corrections to these leading results. These corrections reveal the form of the finite-size effects that enter into the holonomy for larger loops; they could also provide quantitative errors on the leading-order results for finite loops.Comment: 18 pages, 4 figures, new short section (Sec. 5) in v3; updated to match article published in GR

The Hidden Dichotomy in the Law of Morality

This Comment will begin by exploring the dichotomy itself, and then carefully distinguishing civil and religious morality. The analysis will then examine Lawrence and clarify how the opinion affected the dichotomy. Next, this Comment will apply the post-Lawrence understanding of the rational basis test to several issues of concern raised by opponents of the decision. Finally, this Comment will speculate as to the possible implications of Lawrence for moral issues lying on the horizon

The Hidden Dichotomy in the Law of Morality

This Comment will begin by exploring the dichotomy itself, and then carefully distinguishing civil and religious morality. The analysis will then examine Lawrence and clarify how the opinion affected the dichotomy. Next, this Comment will apply the post-Lawrence understanding of the rational basis test to several issues of concern raised by opponents of the decision. Finally, this Comment will speculate as to the possible implications of Lawrence for moral issues lying on the horizon

ACTH: The Uninhibitable (or is it)?

Adrenal corticotropic hormone, or ACTH, is a peptide hormone secreted by the anterior pituitary gland. The full-length peptide is 39 amino acids long. ACTH signals through a G-protein linked receptor in humans, using the adenylyl cyclase pathway. Potassium and chloride channels have also been implicated in human ACTH signaling. Tetrahymena thermophila are free-living, ciliated ptotozoans. These organisms exhibit avoidance behavior toward many polycationic peptides, which serve as chemorepellents. The reason for this is unknown; however, it is hypothesized that natural predators of T. thermophila secrete polycationic peptides, and that polycation avoidance allows T. thermophila to escape predation. We obtained a number of peptides derived from ACTH, including ACTH 1-39, ACTH 1-24, ACTH 11-24, ACTH 6-24, and ACTH 1-14. We hypothesized that the more highly charged peptide derivatives would be the most effective chemorepellents. This hypothesis was proven correct, with the most highly charged ACTH derivative, ACTH 6-24, demonstrated as the most effective chemorepellent. The least charged form of ACTH, ACTH 1-39, was least effective at causing avoidance. We hypothesized that ACTH signaling in T. thermophila would use similar signaling pathways to those previously identified in humans. This, however, has not proven to be the case. We have tested G-protein inhibitors, adenylyl cyclase inhibitors, potassium channel blockers, and chloride channel blockers in T. thermphila. None of these drugs had any measurable effect on ACTH signaling. In addition, we have chelated extracellular calcium (using EGTA) and depleted ER calcium stores (using thapsigargin). Neither of these interventions inhibited ACTH signaling in this organism. Calcium channel blockers also failed to affect avoidance. This is highly unexpected, since all known chemorepellent pathways discovered in Tetrahymena to date are calcium-dependent. It is possible that ACTH is using a novel signaling pathway in T. thermophila. We hope that further testing will enable us to discover more about this signaling mechanism

The Meta-Wisdom of Crowds

It is well-known that people will adjust their first-order beliefs based on observations of others. We explore how such adjustments interact with second-order beliefs regarding universalism and relativism in a population. Across a range of simulations, we show that populations where individuals have a tendency toward universalism converge more quickly in coordination problems, and generate higher total payoffs, than do populations where individuals have a tendency toward relativism. Thus, in contexts where coordination is important, belief in universalism is advantageous. However, we also show, across a range of simulations, that universalism will enshrine inequalities and eliminate diversity, and in these cases it seems that relativism has its own advantages

Alleviating Polarity-Conflict at the Heterointerfaces of KTaO\u3csub\u3e3\u3c/sub\u3e/GdScO\u3csub\u3e3\u3c/sub\u3e Polar Complex-Oxides

We have synthesized and investigated the heterointerfaces of KTaO3 (KTO) and GdScO3 (GSO), which are both polar complex-oxides along the pseudo-cubic [001] direction. Since their layers have the same, conflicting net charges at interfaces, i.e., KO(−1)/ScO2(−1) or TaO2(+1)/GdO(+1), forming the heterointerface of KTO/GSO should be forbidden due to strong Coulomb repulsion, the so-called polarity conflict. However, we have discovered that atomic reconstruction occurs at the heterointerfaces between KTO thin-films and GSO substrates, which effectively alleviates the polarity conflict without destroying the hetero-epitaxy. Our result demonstrates one of the important ways to create artificial heterostructures from polar complex-oxides

Serotonin 5-HT\u3csub\u3e2\u3c/sub\u3e receptor activation prevents allergic asthma in a mouse model

© 2015 the American Physiological Society. Asthma is an inflammatory disease of the lung characterized by airways hyper-responsiveness (AHR), inflammation, and mucus hyperproduction. Current main-stream therapies include bronchodilators that relieve bronchoconstriction and inhaled glucocorticoids to reduce inflammation. The small molecule hormone and neurotransmitter serotonin has long been known to be involved in inflammatory processes; however, its precise role in asthma is unknown. We have previously established that activation of serotonin 5-hydroxytryptamine (5-HT)2A receptors has potent anti-inflammatory activity in primary cultures of vascular tissues and in the whole animal in vasculature and gut tissues. The 5-HT2A receptor agonist, (R)-2,5-dimethoxy-4-iodoamphetamine [(R)-DOI] is especially potent. In this work, we have examined the effect of (R)-DOI in an established mouse model of allergic asthma. In the ovalbumin mouse model of allergic inflammation, we demonstrate that inhalation of (R)-DOI prevents the development of many key features of allergic asthma, including AHR, mucus hyperproduction, airways inflammation, and pulmonary eosinophil recruitment. Our results highlight a likely role of the 5-HT2 receptors in allergic airways disease and suggest that 5-HT2 receptor agonists may represent an effective and novel small molecule-based therapy for asthma

The role of orthogonal polynomials in the six-vertex model and its combinatorial applications

The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific values of the parameters of the model, corresponding to 1-, 2- and 3-enumerations of Alternating Sign Matrices (ASMs), these polynomials specialize to classical ones (Continuous Hahn, Meixner-Pollaczek, and Continuous Dual Hahn, respectively). As a consequence, a unified and simplified treatment of ASMs enumerations turns out to be possible, leading also to some new results such as the refined 3-enumerations of ASMs. Furthermore, the use of orthogonal polynomials allows us to express, for generic values of the parameters of the model, the partition function of the (partially) inhomogeneous model in terms of the one-point boundary correlation functions of the homogeneous one.Comment: Talk presented by F.C. at the Short Program of the Centre de Recherches Mathematiques: Random Matrices, Random Processes and Integrable Systems, Montreal, June 20 - July 8, 200