Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

Detecting failure of climate predictions

The practical consequences of climate change challenge society to formulate responses that are more suited to achieving long-term objectives, even if those responses have to be made in the face of uncertainty. Such a decision-analytic focus uses the products of climate science as probabilistic predictions about the effects of management policies. Here we present methods to detect when climate predictions are failing to capture the system dynamics. For a single model, we measure goodness of fit based on the empirical distribution function, and define failure when the distribution of observed values significantly diverges from the modelled distribution. For a set of models, the same statistic can be used to provide relative weights for the individual models, and we define failure when there is no linear weighting of the ensemble models that produces a satisfactory match to the observations. Early detection of failure of a set of predictions is important for improving model predictions and the decisions based on them. We show that these methods would have detected a range shift in northern pintail 20 years before it was actually discovered, and are increasingly giving more weight to those climate models that forecast a September ice-free Arctic by 2055

Associations between cigarette smoking and mitochondrial DNA abnormalities in buccal cells

DNA alterations in mitochondria are believed to play a role in carcinogenesis and are found in smoking-related cancers. We sought to replicate earlier findings for the association of smoking with increased mitochondrial DNA (mtDNA) content in buccal cells and further hypothesized that there would be an increased number of somatic mtDNA mutations in smokers. Buccal cells and blood lymphocytes were studied from 42 healthy smokers and 30 non-smokers. Temporal temperature gradient electrophoresis screening and sequencing was used to identify mtDNA mutations. The relative mtDNA content was determined by real-time polymerase chain reaction. Assuming that mtDNA in lymphocytes represents the inherited sequence, it was found that 31% of smokers harbored at least one somatic mtDNA mutation in buccal cells with a total of 39 point mutations and 8 short deletions/insertions. In contrast, only 23% of non-smokers possessed mutations with a total of 10 point mutations and no insertions/deletions detected. mtDNA somatic mutation density was higher in smokers (0.68/10 000 bp per person) than in non-smokers (0.2/10 000 bp per person). There was a statistically significant difference in the pattern of homoplasmy and heteroplasmy mutation changes between smokers and non-smokers. Whereas non-smokers had the most mutations in D-loop region (70%), smokers had mutations in both messenger RNA encoding gene (36%) and D-loop region (49%). The mean ratio of buccal cells to lymphocytes of mtDNA content in smokers was increased (2.81) when compared with non-smokers (0.46). These results indicate that cigarette smoke exposure affects mtDNA in buccal cells of smokers. Additional studies are needed to determine if mitochondrial mutation assays provide new or complementary information for estimating cigarette smoke exposure at the cellular level or as a cancer risk biomarker

Modulation of Serotonin Transporter Function during Fetal Development Causes Dilated Heart Cardiomyopathy and Lifelong Behavioral Abnormalities

BACKGROUND: Women are at great risk for mood and anxiety disorders during their childbearing years and may become pregnant while taking antidepressant drugs. In the treatment of depression and anxiety disorders, selective serotonin reuptake inhibitors (SSRIs) are the most frequently prescribed drugs, while it is largely unknown whether this medication affects the development of the central nervous system of the fetus. The possible effects are the product of placental transfer efficiency, time of administration and dose of the respective SSRI. METHODOLOGY/PRINCIPAL FINDINGS: In order to attain this information we have setup a study in which these parameters were measured and the consequences in terms of physiology and behavior are mapped. The placental transfer of fluoxetine and fluvoxamine, two commonly used SSRIs, was similar between mouse and human, indicating that the fetal exposure of these SSRIs in mice is comparable with the human situation. Fluvoxamine displayed a relatively low placental transfer, while fluoxetine showed a relatively high placental transfer. Using clinical doses of fluoxetine the mortality of the offspring increased dramatically, whereas the mortality was unaffected after fluvoxamine exposure. The majority of the fluoxetine-exposed offspring died postnatally of severe heart failure caused by dilated cardiomyopathy. Molecular analysis of fluoxetine-exposed offspring showed long-term alterations in serotonin transporter levels in the raphe nucleus. Furthermore, prenatal fluoxetine exposure resulted in depressive- and anxiety-related behavior in adult mice. In contrast, fluvoxamine-exposed mice did not show alterations in behavior and serotonin transporter levels. Decreasing the dose of fluoxetine resulted in higher survival rates and less dramatic effects on the long-term behavior in the offspring. CONCLUSIONS: These results indicate that prenatal fluoxetine exposure affects fetal development, resulting in cardiomyopathy and a higher vulnerability to affective disorders in a dose-dependent manner