ALBERT

Description: This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function $\Phi :TM\rightarrow \mathbb {R}$ on the tangent bundle $TM$ , and at the $k$ th iteration, using the restricted function $\Phi |_{T_{x_k}M}$ , where $T_{x_k}M$ is the tangent space at $x_k$ , a local model function $Q_k$ that carries both first- and second-order information for the locally Lipschitz objective function $f:M\rightarrow \mathbb {R}$ on a Riemannian manifold $M$ , is defined and minimized over a trust region. We establish the global convergence of the proposed algorithm. Moreover, using the Riemannian $\varepsilon $ -subdifferential, a suitable model function is defined. Numerical experiments illustrate our results.

Description: Visual refractive errors (REs) are complex genetic traits with a largely unknown etiology. To date, genome-wide association studies (GWASs) of moderate size have identified several novel risk markers for RE, measured here as mean spherical equivalent (MSE). We performed a GWAS using a total of 7280 samples from five cohorts: the Age-Related Eye Disease Study (AREDS); the KORA study (‘Cooperative Health Research in the Region of Augsburg’); the Framingham Eye Study (FES); the Ogliastra Genetic Park-Talana (OGP-Talana) Study and the Multiethnic Study of Atherosclerosis (MESA). Genotyping was performed on Illumina and Affymetrix platforms with additional markers imputed to the HapMap II reference panel. We identified a new genome-wide significant locus on chromosome 16 (rs10500355, P = 3.9 x 10 –9 ) in a combined discovery and replication set (26 953 samples). This single nucleotide polymorphism (SNP) is located within the RBFOX1 gene which is a neuron-specific splicing factor regulating a wide range of alternative splicing events implicated in neuronal development and maturation, including transcription factors, other splicing factors and synaptic proteins.

Description: This paper focuses on the design of a distribution network problem in a three-tiered supply chain under uncertainty. The objective is to determine the optimal number, locations and capacities of plants and warehouses to minimize the overall network costs over a variety of economic growth scenarios. For this purpose, a mixed integer linear programming model is extended in a robust optimization framework and then three heuristic approaches based on genetic and memetic algorithms and a mathematical programming approach are used to solve this problem. The effectiveness of the proposed heuristics and the trade-off between model robustness and solution robustness is investigated and directions for further researches are presented.

Description: The 2003 Bam, Iran, earthquake ( M w  = 6.6) was recorded by the BAM accelerometer station. Since the causative fault was located just below the city, the accelerometer recorded the main shock, a foreshock and several local aftershocks. To study the scenario of rupturing, we simulated all components of the observed main shock waveform via the empirical Green's function method. 28 selected aftershocks and the single foreshock are used to simulate the main shock in the frequency range of 0.5–5 Hz. Since the events were very close to the station, some small events may not have similar path effects to the main shock. Therefore, it is essential to employ some appropriate changes to the waveforms to alleviate path difference effects. The starting point of the rupture is identified in the centre of the strong motion generation area and is located approximately 5 km south of the BAM station and in depth of about 7 km. The horizontal simulated components imply that the main shock was located west of the BAM station. In contrast, significant variation in the ratio of amplitudes in EW and NS components may be used to discuss the possibility of dissimilarity in the focal mechanism of the small events. Most aftershocks with similar mechanisms to the main shock, that is similar EW/NS maximum amplitude ratio, have capacity to simulate certain peaks of their horizontal components. However, some small events with different mechanisms are only able to simulate the peaks of up to one horizontal component. Some changes were applied to the empirical Green's function method to incorporate two small events by using a combined fault model. While the two aftershocks have different mechanisms, some combinations may improve simulations. The rupture initiating point at the middle of the fault plane and improved simulations by combination of two fault surfaces with different focal mechanisms may suggest a bilateral rupture and combination of two focal mechanisms for the main shock of the Bam earthquake.

Description: The main purpose of this paper is to investigate the spectral Galerkin method for spatial discretization. We combine it with the method introduced by Jentzen et al. (2011, Efficient simulation of nonlinear parabolic SPDEs with additive noise. Ann. Appl. Probab. , 21 , 908–950) for temporal discretization of stochastic partial differential equations and study pathwise convergence. We consider the case of coloured noise, instead of the usual space-time white noise that was used before for the spatial discretization. The rate of convergence in uniform topology is estimated for the stochastic Burgers' equation. Numerical examples illustrate the estimated convergence rate.

Description: F-actin bundling plastin 3 (PLS3) is a fully protective modifier of the neuromuscular disease spinal muscular atrophy (SMA), the most common genetic cause of infant death. The generation of a conditional PLS3 -over-expressing mouse and its breeding into an SMA background allowed us to decipher the exact biological mechanism underlying PLS3-mediated SMA protection. We show that PLS3 is a key regulator that restores main processes depending on actin dynamics in SMA motor neurons (MNs). MN soma size significantly increased and a higher number of afferent proprioceptive inputs were counted in SMA PLS3 compared with SMA mice. PLS3 increased presynaptic F-actin amount, rescued synaptic vesicle and active zones content, restored the organization of readily releasable pool of vesicles and increased the quantal content of the neuromuscular junctions (NMJs). Most remarkably, PLS3 over-expression led to a stabilization of axons which, in turn, resulted in a significant delay of axon pruning, counteracting poor axonal connectivity at SMA NMJs. These findings together with the observation of increased endplate and muscle fiber size upon MN-specific PLS3 over-expression suggest that PLS3 significantly improves neuromuscular transmission. Indeed, ubiquitous over-expression moderately improved survival and motor function in SMA mice. As PLS3 seems to act independently of Smn, PLS3 might be a potential therapeutic target not only in SMA but also in other MN diseases.

Description: 〈span〉〈div〉Summary〈/div〉In global-scale seismic tomography, teleseismic P- and PP-waves mainly constrain structures in the upper two thirds of the mantle, whereas core-diffracted waves (Pdiff) constrain the lower third. This study is the first to invert a very large data set of Pdiff waves, up to the highest possible frequencies. This results in tomographic resolution matching and exceeding that of global S-wave tomographies, which have long been the models of choice for interpreting lowermost mantle structure. We present three new global tomography models of 3-D isotropic P-wave velocity in the earth’s mantle. Multi-frequency cross-correlation traveltimes are measured on all phases in passbands from 30 s dominant period to the highest frequencies that produce satisfactory fits (≈ 3 s). Model DETOX-P1 fits ≈ 2.5M traveltimes from teleseismic P waves. DETOX-P2 fits the same data, plus novel measurements of ≈ 1.4M traveltimes of Pdiff waves. DETOX-P3 fits the same data as DETOX-P2, plus ≈ 1.2M PP traveltimes. Synthetics up to 1 s dominant period are computed by full wave propagation in a spherically symmetric earth using the spectral-element method AxiSEM. Traveltimes are linked to 3-D velocity perturbations (〈span〉dVp〈/span〉/〈span〉Vp〈/span〉) by finite-frequency Fréchet kernels, parameterized on an adaptive tetrahedral grid of ≈400, 000 vertices spaced by ≈ 80 km in the best-sampled regions. To complete spatial coverage, the waveform cross-correlation measurements are augmented by ≈ 5.7 million analyst-picked, teleseismic P arrival times. P, Pdiff and PP traveltimes are jointly inverted for 3-D isotropic P-velocity anomalies in the mantle and for events corrections, by least squares solution of an explicit matrix-vector equation. Inclusion of Pdiff traveltimes (in DETOX-P2, -P3) improves the spatial sampling of the lowermost mantle 100 to 1000-fold compared to teleseismic P-waves (DETOX-P1). Below ≈2400 km depth, seismically slow anomalies are clustered at southern and equatorial latitudes, in a dozen or more intensely slow patches of 600-1400 km diameter. These features had long been classed into two Large Low Shear Velocity Provinces, which now appears questionable. Instead, patches of intensely slow anomalies in the lowermost mantle seem to form a nearly continuous, globe-spanning chain beneath the southern hemisphere, according to our increased resolution of LLVP-internal subdivisions and newly imaged patches beneath South America. Our tomography also supports the existence of whole-mantle plumes beneath Iceland, Ascension, Afar, Kerguelen, Canary, Azores, Easter, Galapagos, Hawaii, French Polynesia, and the Marquesas. Seismically fast structure in the lowermost mantle is imaged as narrowly elongated belts under Eastern Asia and the Americas, presumably reflecting the paleo-trench geometries of subduction zones and arcs that assembled Eastern Asia and the American Cordilleras in Paleozoic and early Mesozoic times. Mid-mantle structure is primarily constrained by teleseismic P waves, but Pdiff data have a stabilizing effect, e.g., sharpening the geometries of subducted slabs under the Americas, Eurasia and the Northern Pacific in the upper 2000 km. PP traveltimes contribute complementary constraints in the upper and mid mantle, but they also introduce low-velocity artifacts beneath the oceans, through downward smearing of lithospheric structure. Our three new global P-wave models can be accessed and interactively visualized through the SubMachine web portal (〈a href="http://submachine.earth.ox.ac.uk/"〉http://submachine.earth.ox.ac.uk/〈/a〉).〈/span〉

Description: The lower third of the mantle is sampled extensively by body waves that diffract around the earth's core (Pdiff and Sdiff phases), which could deliver highly resolved tomographic images of this poorly understood region. But core-diffracted waves—especially Pdiff waves—are not often used in tomography because they are difficult to model adequately. Our aim is to make core-diffracted body waves usable for global waveform tomography, across their entire frequency range. Here we present the data processing part of this effort. A method is demonstrated that routinely calculates finite-frequency traveltimes of Pdiff waves by cross-correlating large quantities of waveform data with synthetic seismograms, in frequency passbands ranging from 30.0 to 2.7 s dominant period. Green's functions for 1857 earthquakes, typically comprising thousands of seismograms, are calculated by theoretically exact wave propagation through a spherically symmetric earth model, up to 1 Hz dominant period. Out of 418 226 candidates, 165 651 (39.6 per cent) source–receiver pairs yielded at least one successful passband measurement of a Pdiff traveltime anomaly, for a total of 479 559 traveltimes in the eight passbands considered. Measurements of teleseismic P waves yielded 448 178 usable source–receiver paths from 613 057 candidates (73.1 per cent success rate), for a total of 2 306 755 usable teleseismic dT in eight passbands. Observed and predicted characteristics of Pdiff traveltimes are discussed and compared to teleseismic P for this very large data set. Pdiff measurements are noise-limited due to severe wave attenuation with epicentral distance and frequency. Measurement success drops from 40–60 per cent at 80° distance, to 5–10 per cent at 140°. Frequency has a 2–3 times stronger influence on measurement success for Pdiff than for P . The fewest usable dT measurements are obtained in the microseismic noise band, whereas the fewest usable teleseismic P measurements occur at the highest frequencies. dT anomalies are larger for Pdiff than for P , and frequency dependence of dT due to 3-D heterogeneity (rather than just diffraction) is larger for Pdiff as well. Projecting the Pdiff traveltime anomalies on their core-grazing segments, we retrieve well-known, large-scale structural heterogeneities of the lowermost mantle, such as the two Large Low Shear Velocity Provinces, an Ultra-Low Velocity Zone west of Hawaii, and subducted slab accumulations under East Asia and Central America.

Description: 〈span〉〈div〉SUMMARY〈/div〉In global-scale seismic tomography, teleseismic 〈span〉P〈/span〉 and 〈span〉PP〈/span〉 waves mainly constrain structures in the upper two thirds of the mantle, whereas core-diffracted waves (Pdiff) constrain the lower third. This study is the first to invert a very large data set of Pdiff waves, up to the highest possible frequencies. This results in tomographic resolution matching and exceeding that of global 〈span〉S〈/span〉-wave tomographies, which have long been the models of choice for interpreting lowermost mantle structure.We present three new global tomography models of 3-D isotropic 〈span〉P〈/span〉-wave velocity in the earth’s mantle. Multifrequency cross-correlation traveltimes are measured on all phases in passbands from 30 s dominant period to the highest frequencies that produce satisfactory fits (≈3 s). Model DETOX-P1 fits ≈2.5 M traveltimes from teleseismic 〈span〉P〈/span〉 waves. DETOX-P2 fits the same data, plus novel measurements of ≈1.4 M traveltimes of Pdiff waves. DETOX-P3 fits the same data as DETOX-P2, plus ≈ 1.2 M PP traveltimes. Synthetics up to 1 s dominant period are computed by full wave propagation in a spherically symmetric earth using the spectral-element method AxiSEM. Traveltimes are linked to 3-D velocity perturbations (d〈span〉VP〈/span〉/〈span〉VP〈/span〉) by finite-frequency Fréchet kernels, parametrized on an adaptive tetrahedral grid of ≈400 000 vertices spaced by ≈80 km in the best-sampled regions. To complete spatial coverage, the waveform cross-correlation measurements are augmented by ≈5.7 million analyst-picked, teleseismic 〈span〉P〈/span〉 arrival times. 〈span〉P〈/span〉, Pdiff and 〈span〉PP〈/span〉 traveltimes are jointly inverted for 3-D isotropic 〈span〉P〈/span〉-velocity anomalies in the mantle and for events corrections, by least squares solution of an explicit matrix–vector equation.Inclusion of Pdiff traveltimes (in DETOX-P2, -P3) improves the spatial sampling of the lowermost mantle 100- to 1000-fold compared to teleseismic 〈span〉P〈/span〉 waves (DETOX-P1). Below ≈2400 km depth, seismically slow anomalies are clustered at southern and equatorial latitudes, in a dozen or more intensely slow patches of 600–1400 km diameter. These features had long been classed into two large low shear velocity provinces (LLVP), which now appears questionable. Instead, patches of intensely slow anomalies in the lowermost mantle seem to form a nearly continuous, globe-spanning chain beneath the southern hemisphere, according to our increased resolution of LLVP-internal subdivisions and newly imaged patches beneath South America. Our tomography also supports the existence of whole-mantle plumes beneath Iceland, Ascension, Afar, Kerguelen, Canary, Azores, Easter, Galapagos, Hawaii, French Polynesia and the Marquesas.Seismically fast structure in the lowermost mantle is imaged as narrowly elongated belts under Eastern Asia and the Americas, presumably reflecting the palaeo-trench geometries of subduction zones and arcs that assembled Eastern Asia and the American Cordilleras in Palaeozoic and early Mesozoic times. Mid-mantle structure is primarily constrained by teleseismic 〈span〉P〈/span〉 waves, but Pdiff data have a stabilizing effect, for example, sharpening the geometries of subducted slabs under the Americas, Eurasia and the Northern Pacific in the upper 2000 km. 〈span〉PP〈/span〉 traveltimes contribute complementary constraints in the upper and mid mantle, but they also introduce low-velocity artefacts beneath the oceans, through downward smearing of lithospheric structure.Our three new global 〈span〉P〈/span〉-wave models can be accessed and interactively visualized through the SubMachine web portal (〈a href="http://submachine.earth.ox.ac.uk/"〉http://submachine.earth.ox.ac.uk/〈/a〉).〈/span〉