Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice

It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is constructed.Comment: LaTeX, uses IOP styl

Unoccupied states of individual silver clusters and chains on Ag(111)

Size-selected silver clusters on Ag(111) were fabricated with the tip of a scanning tunneling microscope. Unoccupied electron resonances give rise to image contrast and spectral features which shift toward the Fermi level with increasing cluster size. Linear assemblies exhibit higher resonance energies than equally sized compact assemblies. Density functional theory calculations reproduce the observed energies and enable an assignment of the resonances to hybridized atomic 5s and 5p orbitals with silver substrate states.Comment: 9 pages, 8 figure

Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations

We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure

Dissipative Boussinesq System of Equations in the B\'enard-Marangoni Phenomenon

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a B\'enard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained. Finnaly, some speculations are made on the nature of the physical phenomena described by this system of equations.Comment: 15 Pages, REVTEX (Version 3.0), no figure

GronOR:Massively parallel and GPU-accelerated non-orthogonal configuration interaction for large molecular systems

GronOR is a program package for non-orthogonal configuration interaction calculations for an electronic wave function built in terms of anti-symmetrized products of multi-configuration molecular fragment wave functions. The two-electron integrals that have to be processed may be expressed in terms of atomic orbitals or in terms of an orbital basis determined from the molecular orbitals of the fragments. The code has been specifically designed for execution on distributed memory massively parallel and Graphics Processing Unit (GPU)-accelerated computer architectures, using an MPI+OpenACC/OpenMP programming approach. The task-based execution model used in the implementation allows for linear scaling with the number of nodes on the largest pre-exascale architectures available, provides hardware fault resiliency, and enables effective execution on systems with distinct central processing unit-only and GPU-accelerated partitions. The code interfaces with existing multi-configuration electronic structure codes that provide optimized molecular fragment orbitals, configuration interaction coefficients, and the required integrals. Algorithm and implementation details, parallel and accelerated performance benchmarks, and an analysis of the sensitivity of the accuracy of results and computational performance to thresholds used in the calculations are presented

Association between an AMH promoter polymorphism and serum AMH levels in PCOS patients

STUDY QUESTION: Do polymorphisms in the anti-Müllerian hormone (AMH) promoter have an effect on AMH levels in patients with polycystic ovary syndrome (PCOS)? SUMMARY ANSWER: We have identified a novel AMH promoter polymorphism rs10406324 that is associated with lower serum AMH levels and is suggested to play a role in the mechanism of regulation of AMH gene expression in women. WHAT IS KNOWN ALREADY: Follicle number is positively correlated with serum AMH levels, reflected by elevated AMH levels in women with PCOS. In addition, it is suggested that AMH production per follicle is higher in women with PCOS than in normo-ovulatory women, implying an altered regulation of AMH in PCOS. STUDY DESIGN, SIZE, DURATION: A discovery cohort of 655 PCOS women of Northern European ancestry and both an internal and external validation PCOS cohort (n = 458 and n = 321, respectively) were included in this study. Summary-level data of an AMH genome-wide association study meta-analysis including 7049 normo-ovulatory women was included as a control cohort. A genetic approach was taken through association analysis and in silico analysis of the associated variants in the AMH promoter. In vitro analysis was performed to investigate the functional mechanisms. PARTICIPANTS/MATERIALS, SETTING, METHODS: All common two-allelic single-nucleotide polymorphisms (SNPs) in the region Chr19:2 245 353–2 250 827 bp (Build 37) were selected for the analysis. Linear regression analyses were performed to determine the association between SNPs in the AMH promoter region and serum AMH levels. For the in silico analysis, the webtools ‘HaploReg’ v4.1 for ENCODE prediction weight matrices and ‘atSNP’ were used. In vitro analysis was performed using KK1 cells, a mouse granulosa cell line and COV434 cells, a human granulosa tumor cell line. Cells were transfected with the reference or the variant human AMH promoter reporter construct together with several transcription factors (TFs). Dual-Glo(®) Luciferase Assay was performed to measure the luciferase activity. MAIN RESULTS AND THE ROLE OF CHANCE: Polymorphism rs10406324 was significantly associated with serum AMH levels in all three PCOS cohorts. Carriers of the minor allele G had significantly lower log-transformed serum AMH levels compared to non-carriers (P = 8.58 × 10(−8), P = 1.35 × 10(−3) and P = 1.24 × 10(−3), respectively). This result was validated in a subsequent meta-analysis (P = 3.24 × 10(−12)). Interestingly, rs10406324 was not associated with follicle count, nor with other clinical traits. Also, in normo-ovulatory women, the minor allele of this variant was associated with lower serum AMH levels (P = 1.04 × 10(−5)). These findings suggest that polymorphism rs10406324 plays a role in the regulation of AMH expression, irrespective of clinical background. In silico analysis suggested a decreased binding affinity of the TFs steroidogenenic factor 1, estrogen-related receptor alpha and glucocorticoid receptor to the minor allele G variant, however in vitro analysis did not show a difference in promoter activity between the A and G allele. LIMITATIONS, REASONS FOR CAUTION: Functional analyses were performed in a mouse and a human granulosa cell line using an AMH promoter reporter construct. This may have limited assessment of the impact of the polymorphism on higher order chromatin structures. Human granulosa cells generated from induced pluripotent stem cells, combined with gene editing, may provide a method to elucidate the exact mechanism behind the decrease in serum AMH levels in carriers of the −210 G allele. We acknowledge that the lack of follicle number in the external validation and the control cohort is a limitation of the paper. Although we observed that the association between rs10406324 and AMH levels was independent of follicle number in our discovery and internal validation PCOS cohorts, we cannot fully rule out that the observed effects on serum AMH levels are, in part, caused by differences in follicle number. WIDER IMPLICATIONS OF THE FINDINGS: These results suggest that variations in serum AMH levels are not only caused by differences in follicle number but also by genetic factors. Therefore, the genetic context should be taken into consideration when assessing serum AMH levels in women. This may have clinical consequences when serum AMH levels are used as a marker for the polycystic ovarian morphology phenotype. STUDY FUNDING/COMPETING INTEREST(S): No external funding was used. J.S.E.L. has received consultancy fees from the following companies: Ferring, Roche Diagnostics and Ansh Labs and has received travel reimbursement from Ferring. J.A.V. has received royalties from AMH assays, paid to the institute/lab with no personal financial gain. The other authors declare no competing interests. TRIAL REGISTRATION NUMBER: N/A

Aromaticity in a Surface Deposited Cluster: Pd4_4 on TiO2_2 (110)

We report the presence of \sigma-aromaticity in a surface deposited cluster, Pd$_4$ on TiO$_2$ (110). In the gas phase, Pd$_4$ adopts a tetrahedral structure. However, surface binding promotes a flat, \sigma-aromatic cluster. This is the first time aromaticity is found in surface deposited clusters. Systems of this type emerge as a promising class of catalyst, and so realization of aromaticity in them may help to rationalize their reactivity and catalytic properties, as a function of cluster size and composition.Comment: 4 pages, 3 figure

Ultrafast X-ray scattering of xenon nanoparticles: imaging transient states of matter

Sem informaçãoFemtosecond x-ray laser flashes with power densities of up to 10(14) W/cm(2) at 13.7 nm wavelength were scattered by single xenon clusters in the gas phase. Similar to light scattering from atmospheric microparticles, the x-ray diffraction patterns carry information about the optical constants of the objects. However, the high flux of the x-ray laser induces severe transient changes of the electronic configuration, resulting in a tenfold increase of absorption in the developing nanoplasma. The modification in opaqueness can be correlated to strong atomic charging of the particle leading to excitation of Xe4+. It is shown that single-shot single-particle scattering on femtosecond time scales yields insight into ultrafast processes in highly excited systems where conventional spectroscopy techniques are inherently blind.Femtosecond x-ray laser flashes with power densities of up to 10(14) W/cm(2) at 13.7 nm wavelength were scattered by single xenon clusters in the gas phase. Similar to light scattering from atmospheric microparticles, the x-ray diffraction patterns carry information about the optical constants of the objects. However, the high flux of the x-ray laser induces severe transient changes of the electronic configuration, resulting in a tenfold increase of absorption in the developing nanoplasma. The modification in opaqueness can be correlated to strong atomic charging of the particle leading to excitation of Xe4+. It is shown that single-shot single-particle scattering on femtosecond time scales yields insight into ultrafast processes in highly excited systems where conventional spectroscopy techniques are inherently blind.108915Sem informaçãoSem informaçãoBMBF [05KS4KT1, 05KS7KT2]HGF Virtuelles Institut [VH-VI-103, VH-VI-302]Sem informaçãoWe would like to thank all staff at FLASH for their outstanding support. Funding is acknowledged from BMBF 05KS4KT1 and 05KS7KT2, as well as HGF Virtuelles Institut VH-VI-103 and VH-VI-302