A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

Critical Examination of the "Field-Theoretical Approach" to the Neutron-Antineutron Oscillations in Nuclei

We demonstrate that so called "infrared divergences" which have been discussed in some publications during several years, do not appear within the correct treatment of analytical properties of the transition amplitudes, in particular, of the second order pole structure of the amplitudes describing the $n - \bar n$ transition in nuclei. Explicit calculation with the help of the Feynman diagram technique shows that the neutron-antineutron oscillations are strongly suppressed in the deuteron, as well as in heavier nuclei, in comparison with the oscillations in vacuum. General advantages and some difficulties of the field theoretical methods applied in nuclear theory are reminded for the particular example of the parity violating $np\to d\gamma$ capture amplitude.Comment: 15 pages, 4 figures; prepared for Eur.Phys.J.

Proton Decay in a Minimal SUSY SO(10) Model for Neutrino Mixings

A minimal renormalizable SUSY SO(10) model with B-L symmetry broken by {\bf 126} Higgs field has recently been shown to predict all neutrino mixings and the ratio $\Delta m^2_{\odot}/\Delta m^2_A$ in agreement with observations. Unlike models where B-L is broken by {\bf 16} Higgs, this model guarantees automatic R-parity conservation and hence a stable dark matter as well as the absence of dim=4 baryon violating operator without any additional symmetry assumptions. In this paper, we discuss the predictions of the model for proton decay induced at the GUT scale. We scan over the parameter space of the model allowed by neutrino data and find upper bounds on the partial lifetime for the modes $\tau(n\to \pi^0\bar{\nu})=~2\tau(p\to \pi^+\bar{\nu})\leq (5.7-13)\times 10^{32}$ yrs and $\tau(n\to K^0\bar{\nu})\leq 2.97\times 10^{33}$ yrs for the average squark mass of a TeV and wino mass of 200 GeV, when the parameters satisfy the present lower limits on $\tau(p\to K^+\bar{\nu})$ mode. These results can be used to test the model.Comment: 17 pages, 6 figures; Minor corrections with improved predictions; references update

Longitudinal measures of RNA expression and disease activity in FSHD muscle biopsies

Advances in understanding the pathophysiology of facioscapulohumeral dystrophy (FSHD) have led to the discovery of candidate therapeutics, and it is important to identify markers of disease activity to inform clinical trial design. For drugs that inhibit DUX4 expression, measuring DUX4 or DUX4-target gene expression might be an interim measure of drug activity; however, only a subset of FHSD muscle biopsies shows evidence of DUX4 expression. Our prior study showed that MRI T2-STIR-positive muscles had a higher probability of showing DUX4 expression than muscles with normal MRI characteristics. In the current study, we performed a 1-year follow-up assessment of the same muscle with repeat MRI and muscle biopsy. There was little change in MRI characteristics over the 1-year period and, similar to the initial evaluation, MRI T2-STIR-postive muscles had a higher expression of DUX4-regulated genes, as well as genes associated with inflammation, extracellular matrix and cell cycle. Compared to the initial evaluation, overall the level of expression in these gene categories remained stable over the 1-year period; however, there was some variability for each individual muscle biopsied. The pooled data from both the initial and 1-year follow-up evaluations identified several FSHD subgroups based on gene expression, as well as a set of genes-composed of DUX4-target genes, inflammatory and immune genes and cell cycle control genes-that distinguished all of the FSHD samples from the controls. These candidate markers of disease activity need to be replicated in independent datasets and, if validated, may provide useful measures of disease progression and response to therapy.Functional Genomics of Muscle, Nerve and Brain Disorder

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

A microscopic approach to the response of 3^{\bf 3}He -4^{\bf 4}He mixtures

Correlated Basis Function perturbation theory is used to evaluate the zero temperature response $S(q,\omega)$ of $^3$He-$^4$He mixtures for inelastic neutron scattering, at momentum transfers $q$ ranging from $1.1$ to $1.7 \AA^{-1}$. We adopt a Jastrow correlated ground state and a basis of correlated particle-hole and phonon states. We insert correlated one particle-one hole and one-phonon states to compute the second order response. The decay of the one-phonon states into two-phonon states is accounted for in boson-boson approximation. The full response is splitted into three partial components $S_{\alpha \beta}(q,\omega)$, each of them showing a particle-hole bump and a one phonon, delta shaped peak, which stays separated from the multiphonon background. The cross term $S_{34}(q,\omega)$ results to be of comparable importance to $S_{33}(q,\omega)$ in the particle-hole sector and to $S_{44}(q,\omega)$ in the phonon one. Once the one-phonon peak has been convoluted with the experimental broadening, the computed scattering function is in semiquantitative agreement with recent experimental measurements.Comment: 26 pages, RevTex 3.0, 8 figures available upon reques

Precambrian non-marine stromatolites in alluvial fan deposits, the Copper Harbor Conglomerate, upper Michigan

Laminated cryptalgal carbonates occur in the Precambrian Copper Harbor Conglomerate of northern Michigan, which was deposited in the Keweenawan Trough, an aborted proto-oceanic rift. This unit is composed of three major facies deposited by braided streams on a large alluvial-fan complex. Coarse clastics were deposited in braided channels, predominantly as longitudinal bars, whereas cross-bedded sandstones were deposited by migrating dunes or linguoid bars. Fine-grained overbank deposits accumulated in abandoned channels. Gypsum moulds and carbonate-filled cracks suggest an arid climate during deposition. Stromatolites interstratified with these clastic facies occur as laterally linked drapes over cobbles, as laterally linked contorted beds in mudstone, as oncolites, and as poorly developed mats in coarse sandstones. Stromatolites also are interbedded with oolitic beds and intraclastic conglomerates. Stromatolitic microstructure consists of alternating detrital and carbonate laminae, and open-space structures. Radial-fibrous calcite fans are superimposed on the laminae. The laminae are interpreted as algal in origin, whereas the origin of the radial fibrous calcite is problematic. The stromatolites are inferred to have grown in lakes which occupied abandoned channels on the fan surface. Standing water on a permeable alluvial fan in an arid climate requires a high water table maintained by high precipitation, or local elevation of the water table, possibly due to the close proximity of a lake. Occurrence of stromatolites in the upper part of the Copper Harbor Conglomerate near the base of the lacustrine Nonesuch Shale suggests that these depositional sites may have been near the Nonesuch Lake.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72022/1/j.1365-3091.1983.tb00713.x.pd

Death and the “life review” in Halakhah

Coping with old age involves resolving the task of “integrity versus despair,” which demands a nondefensive confrontation with the inevitability of death. Halakhah (Jewish ethics) also considered this task critical in later years of life, spoke of death's inevitability, and attempted to discourage denial of death. The Jewish approach seems compatible with Butler's concept of “life review” as a reconciliation with death and a reintegration of one's identity that occurs throughout later years. While the Eriksonian goal is confronting old age with a certain capacity for “wisdom,” the rabbis maintained that such wisdom must culminate in the creative act of repentance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45115/1/10943_2004_Article_BF00996254.pd

Hormone Therapy and the Risk of Breast Cancer in BRCA1 Mutation Carriers

Background: Hormone therapy (HT) is commonly given to women to alleviate the climacteric symptoms associated with menopause. There is concern that this treatment may increase the risk of breast cancer. The potential association of HT and breast cancer risk is of particular interest to women who carry a mutation in BRCA1 because they face a high lifetime risk of breast cancer and because many of these women take HT after undergoing prophylactic surgical oophorectomy at a young age. Methods: We conducted a matched case-control study of 472 postmenopausal women with a BRCA1 mutation to examine whether or not the use of HT is associated with subsequent risk of breast cancer. Breast cancer case patients and control subjects were matched with respect to age, age at menopause, and type of menopause (surgical or natural). Odds ratios (ORs) and 95% confidence intervals (CIs) were estimated with conditional logistic regression. Statistical tests were two-sided. Results: In this group of BRCA1 mutation carriers, the adjusted OR for breast cancer associated with ever use of HT compared with never use was 0.58 (95% CI = 0.35 to 0.96; P =. 03). In analyses by type of HT, an inverse association with breast cancer risk was observed with use of estrogen only (OR = 0.51, 95% CI = 0.27 to 0.98; P =. 04); the association with use of estrogen plus progesterone was not statistically significant (OR = 0.66, 95% CI = 0.34 to 1.27; P =. 21). Conclusion: Among postmenopausal women with a BRCA1 mutation, HT use was not associated with increased risk of breast cancer; indeed, in this population, it was associated with a decreased risk

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r =-0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r =-0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation