Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

Lunar Outgassing, Transient Phenomena and The Return to The Moon, I: Existing Data

Herein the transient lunar phenomena (TLP) report database is subjected to a discriminating statistical filter robust against sites of spurious reports, and produces a restricted sample that may be largely reliable. This subset is highly correlated geographically with the catalog of outgassing events seen by the Apollo 15, 16 and Lunar Prospector alpha-particle spectrometers for episodic Rn-222 gas release. Both this robust TLP sample and even the larger, unfiltered sample are highly correlated with the boundary between mare and highlands, as are both deep and shallow moonquakes, as well as Po-210, a long-lived product of Rn-222 decay and a further tracer of outgassing. This offers another significant correlation relating TLPs and outgassing, and may tie some of this activity to sagging mare basalt plains (perhaps mascons). Additionally, low-level but likely significant TLP activity is connected to recent, major impact craters (while moonquakes are not), which may indicate the effects of cracks caused by the impacts, or perhaps avalanches, allowing release of gas. The majority of TLP (and Rn-222) activity, however, is confined to one site that produced much of the basalt in the Procellarum Terrane, and it seems plausible that this TLP activity may be tied to residual outgassing from the formerly largest volcanic ffusion sites from the deep lunar interior. With the coming in the next few years of robotic spacecraft followed by human exploration, the study of TLPs and outgassing is both promising and imperiled. We will have an unprecedented pportunity to study lunar outgassing, but will also deal with a greater burden of anthropogenic lunar gas than ever produced. There is a pressing need to study lunar atmosphere and its sources while still pristine. [Abstract abridged.]Comment: 35 pages, 3 figures, submitted to Icarus. Other papers in series found at http://www.astro.columbia.edu/~arlin/TLP

Earth science: Redox state of early magmas

International audienceA study of cerium in zircon minerals has allowed an assessment of the redox conditions that prevailed when Earth's earliest magmas formed. The results suggest that the mantle became oxidized sooner than had been though

Pinning forces of sliding drops at defects

Wetting of surfaces depends critically on defects which alter the shape of the drop. However, no experimental verification of forces owing to the three phase contact line deformation at single defects is available. We imaged the contact line of sliding drops on hydrophobic surfaces by video microscopy. From the deformation of the contact line, we calculate the force acting on a sliding drop using an equation going back to Joanny and de Gennes (J. Chem. Phys., 81 (1984) 554). The calculated forces quantitatively agree with directly measured forces acting between model defects and water drops. In addition, both forces quantitatively match with the force calculated by contact angle differences between the defect and the surface. The quantitative agreement even holds for defects reaching a size of $40\%$ of the drop diameter. Our validation for drop’s pinning forces at single defects is an important step towards a general understanding of contact line motion on heterogeneous surfaces

The neural basis of perceived intensity in natural and artificial touch

Electrical stimulation of sensory nerves is a powerful tool for studying neural coding because it can activate neural populations in ways that natural stimulation cannot. Electrical stimulation of the nerve has also been used to restore sensation to patients who have suffered the loss of a limb. We have used long-term implanted electrical interfaces to elucidate the neural basis of perceived intensity in the sense of touch. To this end, we assessed the sensory correlates of neural firing rate and neuronal population recruitment independently by varying two parameters of nerve stimulation: pulse frequency and pulse width. Specifically, two amputees, chronically implanted with peripheral nerve electrodes, performed each of three psychophysical tasks-intensity discrimination, magnitude scaling, and intensity matching-in response to electrical stimulation of their somatosensory nerves. We found that stimulation pulse width and pulse frequency had systematic, cooperative effects on perceived tactile intensity and that the artificial tactile sensations could be reliably matched to skin indentations on the intact limb. We identified a quantity we termed the activation charge rate (ACR), derived from stimulation parameters, that predicted the magnitude of artificial tactile percepts across all testing conditions. On the basis of principles of nerve fiber recruitment, the ACR represents the total population spike count in the activated neural population. Our findings support the hypothesis that population spike count drives the magnitude of tactile percepts and indicate that sensory magnitude can be manipulated systematically by varying a single stimulation quantity

Rainfall impacts on suspended sediment concentrations in an urbanized tidal creek, southeastern North Carolina

Elevated suspended sediment concentrations in fluvial systems are deleterious to fluvial ecosystems. In these systems, increases in total suspended solids (TSS) following rain events have been well documented. The impacts of rainfall on marsh surface sediments have received less attention. This study examined the relationship between rainfall and TSS in a tidal creek adjacent to upland and marsh surfaces. TSS concentrations were measured for two locations in Bradley Creek in southeastern North Carolina; one tidal site and one non-tidal, headwater site. TSS concentrations at the tidal site were significantly higher during the growing season than during the non-growing season. The headwater site showed no significant change in TSS seasonally. No significant difference in TSS concentrations was found between spring and neap tides. During fair weather at the tidal site, flood tide TSS concentrations were greater than ebb tide TSS concentrations, which were greater than low tide TSS concentrations. Mean fair weather TSS concentrations at the headwater site were 1.0 mg L-1. TSS concentrations increased to 11.9 mg L-1 following rain events. At the tidal site, mean fair weather TSS concentrations were 10.9 mg L-1 at ebb tide, 7.9 mg L-1 at low tide, and 13.5 mg L-1 at flood tide. At the tidal site, mean TSS concentrations following rain events increased to 22.5 mg L-1 at ebb tide, 21.8 mg L-1 at low tide, and 20.9 mg L-1 at flood tide. These data suggest that following rain events in Bradley Creek, upland runoff has a greater impact on increasing TSS than does runoff from the marsh surface. It is not believed that a significant amount of sediment is removed from the marsh during low tide rain events

Morphological and geochemical variations along the eastern Galapagos Spreading Center

[1] As the eastern Galápagos Spreading Center (GSC) shallows westward toward the Galápagos Archipelago, axial morphology evolves from a low-relief, valley-and-ridge terrain to an increasingly prominent axial ridge, closely mirroring the western GSC. Between the Inca Transform (∼85.5°W) and its western termination near 91°W, the eastern GSC comprises seven morphological segments, separated by five morphological discontinuities and the eastward propagating 87°W overlapping spreading center. Combined morphologic and geochemical data divide the eastern GSC into two domains independent of the fine-scale morphologic segmentation. The western domain is defined by its axial ridge morphology and highly variable lava population. Elemental data define steep along-axis gradients, reflecting a complex source that includes one or more hot spot–related components in addition to a highly depleted component. The eastern domain is defined by transitional, valley-and-ridge morphologies and a surprisingly invariant lava population. This population is dominated by shallow crystal fractionation processes and displays significantly less variability attributable to multiple source components. The Galápagos hot spot has long been known to have a symmetrical, long-wavelength influence on crustal accretion along the GSC. Existing isotopic and new elemental data define twin “geochemical peaks” that we interpret as loci for transfer of distinct source components from the Galápagos plume to the GSC. Although Na8 and Fe8 values lie within the negatively correlated global array, Na8 increases with decreasing axial depth, contrary to global trends and consistent with emerging deep, hydrous melting models that predict decreasing overall extent of melting despite increasing melt production. Support for hydrous melting comes from decreasing heavy REE, increasing La/Sm and La/Yb, and the systematics of decreasing FeO and increasing CaO and Al2O3 with decreasing distance to the hot spot. Overall, an enriched, deep melt component appears to coexist in the shallow mantle with a ubiquitous, depleted primitive melt component, consistent with new models for channelized melt flow connecting a deep hydrous melt regime with the dry shallow mantle. Nevertheless, an absence of low-Fe lavas suggests that hydrous melting is strictly limited beneath the eastern GSC, becoming dominant only near the western geochemical peak where input from a hydrous “Northern” or “Wolf-Darwin” plume component is inferred

The ErbB signalling pathway: protein expression and prognostic value in epithelial ovarian cancer

Ovarian cancer is the most frequent cause of death from gynaecological cancer in the Western world. Current prognostic factors do not allow reliable prediction of response to chemotherapy and survival for individual ovarian cancer patients. Epidermal growth factor receptor (EGFR) and HER-2/neu are frequently expressed in ovarian cancer but their prognostic value remains unclear. In this study, we investigated the expression and prognostic value of EGFR, EGFR variant III (EGFRvIII), HER-2/neu and important downstream signalling components in a large series of epithelial ovarian cancer patients. Immunohistochemical staining of EGFR, pEGFR, EGFRvIII, Her-2/neu, PTEN (phosphatase and tensin homologue deleted on chromosome 10), total and phosphorylated AKT (pAKT) and phosphorylated ERK (pERK) was performed in 232 primary tumours using the tissue microarray platform and related to clinicopathological characteristics and survival. In addition, EGFRvIII expression was determined in 45 tumours by RT–PCR. Our results show that negative PTEN immunostaining was associated with stage I/II disease (P=0.006), non-serous tumour type (P=0.042) and in multivariate analysis with a longer progression-free survival (P=0.015). Negative PTEN staining also predicted improved progression-free survival in patients with grade III or undifferentiated serous carcinomas (P=0.011). Positive pAKT staining was associated with advanced-stage disease (P=0.006). Other proteins were expressed only at low levels, and were not associated with any clinicopathological parameter or survival. None of the tumours were positive for EGFRvIII. In conclusion, our results indicate that tumours showing negative PTEN staining could represent a subgroup of ovarian carcinomas with a relatively favourable prognosis

Monte Carlo Simulations of Metasomatic Enrichment in the Lithosphere and Implications for the Source of Alkaline Basalts

One hypothesis for the origin of alkaline lavas erupted on oceanic islands and in intracontinental settings is that they represent the melts of amphibole-rich veins in the lithosphere (or melts of their dehydrated equivalents if metasomatized lithosphere is recycled into the convecting mantle). Amphibole-rich veins are interpreted as cumulates produced by crystallization of low-degree melts of the underlying asthenosphere as they ascend through the lithosphere. We present the results of trace-element modelling of the formation and melting of veins formed in this way with the goal of testing this hypothesis and for predicting how variability in the formation and subsequent melting of such cumulates (and adjacent cryptically and modally metasomatized lithospheric peridotite) would be manifested in magmas generated by such a process. Because the high-pressure phase equilibria of hydrous near-solidus melts of garnet lherzolite are poorly constrained and given the likely high variability of the hypothesized accumulation and remelting processes, we used Monte Carlo techniques to estimate how uncertainties in the model parameters (e.g. the compositions of the asthenospheric sources, their trace-element contents, and their degree of melting; the modal proportions of crystallizing phases, including accessory phases, as the asthenospheric partial melts ascend and crystallize in the lithosphere; the amount of metasomatism of the peridotitic country rock; the degree of melting of the cumulates and the amount of melt derived from the metasomatized country rock) propagate through the process and manifest themselves as variability in the trace-element contents and radiogenic isotopic ratios of model vein compositions and erupted alkaline magma compositions. We then compare the results of the models with amphibole observed in lithospheric veins and with oceanic and continental alkaline magmas. While the trace-element patterns of the near-solidus peridotite melts, the initial anhydrous cumulate assemblage (clinopyroxene ± garnet ± olivine ± orthopyroxene), and the modelled coexisting liquids do not match the patterns observed in alkaline lavas, our calculations show that with further crystallization and the appearance of amphibole (and accessory minerals such as rutile, ilmenite, apatite, etc.) the calculated cumulate assemblages have trace-element patterns that closely match those observed in the veins and lavas. These calculated hydrous cumulate assemblages are highly enriched in incompatible trace elements and share many similarities with the trace-element patterns of alkaline basalts observed in oceanic or continental setting such as positive Nb/La, negative Ce/Pb, and similiar slopes of the rare earth elements. By varying the proportions of trapped liquid and thus simulating the cryptic and modal metasomatism observed in peridotite that surrounds these veins, we can model the variations in Ba/Nb, Ce/Pb, and Nb/U ratios that are observed in alkaline basalts. If the isotopic compositions of the initial low-degree peridotite melts are similar to the range observed in mid-ocean ridge basalt, our model calculations produce cumulates that would have isotopic compositions similar to those observed in most alkaline ocean island basalt (OIB) and continental magmas after ~0·15 Gyr. However, to produce alkaline basalts with HIMU isotopic compositions requires much longer residence times (i.e. 1–2 Gyr), consistent with subduction and recycling of metasomatized lithosphere through the mantle. EM magmas cannot readily be explained without appealing to other factors such as a heterogeneous asthenosphere. These modelling results support the interpretation proposed by various researchers that amphibole-bearing veins represent cumulates formed during the differentiation of a volatile-bearing low-degree peridotite melt and that these cumulates are significant components of the sources of alkaline OIB and continental magmas. The results of the forward models provide the potential for detailed tests of this class of hypotheses for the origin of alkaline magmas worldwide and for interpreting major and minor aspects of the geochemical variability of these magmas

EMQN best practice guidelines for the molecular genetic testing and reporting of chromosome 11p15 imprinting disorders: Silver–Russell and Beckwith–Wiedemann syndrome

Molecular genetic testing for the 11p15-associated imprinting disorders Silver–Russell and Beckwith–Wiedemann syndrome (SRS, BWS) is challenging because of the molecular heterogeneity and complexity of the affected imprinted regions. With the growing knowledge on the molecular basis of these disorders and the demand for molecular testing, it turned out that there is an urgent need for a standardized molecular diagnostic testing and reporting strategy. Based on the results from the first external pilot quality assessment schemes organized by the European Molecular Quality Network (EMQN) in 2014 and in context with activities of the European Network of Imprinting Disorders (EUCID.net) towards a consensus in diagnostics and management of SRS and BWS, best practice guidelines have now been developed. Members of institutions working in the field of SRS and BWS diagnostics were invited to comment, and in the light of their feedback amendments were made. The final document was ratified in the course of an EMQN best practice guideline meeting and is in accordance with the general SRS and BWS consensus guidelines, which are in preparation. These guidelines are based on the knowledge acquired from peer-reviewed and published data, as well as observations of the authors in their practice. However, these guidelines can only provide a snapshot of current knowledge at the time of manuscript submission and readers are advised to keep up with the literature