Reduced-Basis Methods for Inverse Problems in Partial Differential Equations

We present a technique for the rapid, reliable, and accurate evaluation of functional outputs of parametrized elliptic partial differential equations. The essential ingredients are (i) rapidly globally convergent reduced-basis approximations – Galerkin projection onto a space WN spanned by the solutions of the governing partial differential equations at N selected points in parameter space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide sharp and inexpensive bounds for the error in the output of interest; and (iii) off-line/online computational procedures – methods that decouple the generation and projection stages of the approximation process. The operation count for the online stage – in which, given a new parameter, we calculate the output of interest and associated error bounds – depends only on N (typically very small) and the parametric dependencies of the problem. In this study, we first develop rigorous a posteriori error estimators for (affine in the parameter) noncoercive problems such as the Helmholtz (reduced-wave) equation. The critical ingredients are the residual, an appropriate bound conditioner, and a piecewise-constant lower bound for the inf-sup stability factor. In addition, globally nonaffine (and nonlinear) problems are also considered: in particular, through appropriate sampling and interpolation procedures, these more difficult problems can be reduced (with very high accuracy) to the more tractable affine case. Finally, we propose a real-time - procedure for inverse problems associated with parametrized partial differential equations based on our reduced-basis approximations and error bounds. In general practice, many inverse problems are formulated as an error minimization statement relating the calculated and measured outputs. This optimization procedure requires many evaluations of the output: the reduced-basis method --- with extremely low marginal cost --- is thus very efficient for this class of problems. As an illustrative example, we consider a very important application in nondestructive evaluation: crack identification (by harmonic excitation) in a laminated plate of composite material. The numerical results demonstrate the efficiency and accuracy of the method in detecting the location and length of the crack.Singapore-MIT Alliance (SMA

A discourse analysis of trainee teacher identity in online discussion forums

Teacher education involves an identity transformation for trainees from being a student to being a teacher. This discourse analysis examined the online discussion board communications of a cohort of trainee teachers to better understand the situated identities of the trainees and how they were presented online. Their discussion board posts were the primary method of communication during placement periods and, as such, provided insight into how the trainees situated their identities in terms of being a student or being a teacher. During the analysis, the community boundaries, language and culture were explored along with the tutor's power and role in the identity transformation process. This involved looking at the lexis used by the students, the use of pronouns to refer to themselves and others such as teachers and pupils, the types of messages allowed in the community and the effect of the tutor's messages on their communication. The research found that the trainees felt comfortable with teaching but did not feel like teachers during the course. Tutors and school teachers need to develop an awareness of the dual nature of trainees' identities and help promote the transition from student to teacher. In the beginning of the course, trainees should be familiarised with teacher vocabulary and practical concepts in addition to pedagogical theory. Towards the end of the course, trainee identity as teachers could be promoted through the use of authentic assessments that mirror real teacher tasks and requirements

A comparison framework and review of service brokerage solutions for cloud architectures

Cloud service brokerage has been identified as a key concern for future cloud technology development and research. We compare service brokerage solutions. A range of specific concerns like architecture, programming and quality will be looked at. We apply a 2-pronged classification and comparison framework.We will identify challenges and wider research objectives based on an identification of cloud broker architecture concerns and technical requirements for service brokerage solutions. We will discuss complex cloud architecture concerns such as commoditisation and federation of integrated, vertical cloud stacks

Phase diagram of the one-dimensional extended attractive Hubbard model for large nearest-neighbor repulsion

We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian H_{eff} for hopping t<<V and arbitrary U<0. Retaining the most important terms, H_{eff} can be mapped onto two XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422 and U<-4, singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in BaKBiO.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

Elevated circulating and placental SPINT2 is associated with placental dysfunction

Biomarkers for placental dysfunction are currently lacking. We recently identified SPINT1 as a novel biomarker; SPINT2 is a functionally related placental protease inhibitor. This study aimed to characterise SPINT2 expression in placental insufficiency. Circulating SPINT2 was assessed in three prospective cohorts, collected at the following: (1) term delivery (n = 227), (2) 36 weeks (n = 364), and (3) 24–34 weeks’ (n = 294) gestation. SPINT2 was also measured in the plasma and placentas of women with established placental disease at preterm (p = 0.028; median = 2233 pg/mL vs. controls, median = 1644 pg/mL), or delivered a small-for-gestational-age infant (p = 0.002; median = 2109 pg/mL vs. controls, median = 1614 pg/mL). SPINT2 was elevated in the placentas of patients who required delivery for preterm preeclampsia (p = 0.025). Though inflammatory cytokines had no effect, hypoxia increased SPINT2 in cytotrophoblast stem cells, and its expression was elevated in the placental labyrinth of growth-restricted rats. These findings suggest elevated SPINT2 is associated with placental insufficiency

The 2.4 Å cryo-EM structure of a heptameric light-harvesting 2 complex reveals two carotenoid energy transfer pathways

We report the 2.4 Ångström resolution structure of the light-harvesting 2 (LH2) complex from Marichromatium (Mch.) purpuratum determined by cryogenic electron microscopy. The structure contains a heptameric ring that is unique among all known LH2 structures, explaining the unusual spectroscopic properties of this bacterial antenna complex. We identify two sets of distinct carotenoids in the structure and describe a network of energy transfer pathways from the carotenoids to bacteriochlorophyll a molecules. The geometry imposed by the heptameric ring controls the resonant coupling of the long-wavelength energy absorption band. Together, these details reveal key aspects of the assembly and oligomeric form of purple bacterial LH2 complexes that were previously inaccessible by any technique

Cryo-EM structures of light-harvesting 2 complexes from Rhodopseudomonas palustris reveal the molecular origin of absorption tuning

The genomes of some purple photosynthetic bacteria contain a multigene puc family encoding a series of α- and β-polypeptides that together form a heterogeneous antenna of light-harvesting 2 (LH2) complexes. To unravel this complexity, we generated four sets of puc deletion mutants in Rhodopseudomonas palustris, each encoding a single type of pucBA gene pair and enabling the purification of complexes designated as PucA-LH2, PucB-LH2, PucD-LH2, and PucE-LH2. The structures of all four purified LH2 complexes were determined by cryogenic electron microscopy (cryo-EM) at resolutions ranging from 2.7 to 3.6 Å. Uniquely, each of these complexes contains a hitherto unknown polypeptide, γ, that forms an extended undulating ribbon that lies in the plane of the membrane and that encloses six of the nine LH2 αβ-subunits. The γ-subunit, which is located near to the cytoplasmic side of the complex, breaks the C9 symmetry of the LH2 complex and binds six extra bacteriochlorophylls (BChls) that enhance the 800-nm absorption of each complex. The structures show that all four complexes have two complete rings of BChls, conferring absorption bands centered at 800 and 850 nm on the PucA-LH2, PucB-LH2, and PucE-LH2 complexes, but, unusually, the PucD-LH2 antenna has only a single strong near-infared (NIR) absorption peak at 803 nm. Comparison of the cryo-EM structures of these LH2 complexes reveals altered patterns of hydrogen bonds between LH2 αβ-side chains and the bacteriochlorin rings, further emphasizing the major role that H bonds play in spectral tuning of bacterial antenna complexes

Search for lepton-flavor violation at HERA

A search for lepton-flavor-violating interactions $e p \to \mu X$ and $e p\to \tau X$ has been performed with the ZEUS detector using the entire HERA I data sample, corresponding to an integrated luminosity of 130 pb^{-1}. The data were taken at center-of-mass energies, $\sqrt{s}$, of 300 and 318 GeV. No evidence of lepton-flavor violation was found, and constraints were derived on leptoquarks (LQs) that could mediate such interactions. For LQ masses below $\sqrt{s}$, limits were set on $\lambda_{eq_1} \sqrt{\beta_{\ell q}}$, where $\lambda_{eq_1}$ is the coupling of the LQ to an electron and a first-generation quark $q_1$, and $\beta_{\ell q}$ is the branching ratio of the LQ to the final-state lepton $\ell$ ($\mu$ or $\tau$) and a quark $q$. For LQ masses much larger than $\sqrt{s}$, limits were set on the four-fermion interaction term $\lambda_{e q_\alpha} \lambda_{\ell q_\beta} / M_{\mathrm{LQ}}^2$ for LQs that couple to an electron and a quark $q_\alpha$ and to a lepton $\ell$ and a quark $q_\beta$, where $\alpha$ and $\beta$ are quark generation indices. Some of the limits are also applicable to lepton-flavor-violating processes mediated by squarks in $R$-Parity-violating supersymmetric models. In some cases, especially when a higher-generation quark is involved and for the process $e p\to \tau X$, the ZEUS limits are the most stringent to date.Comment: 37 pages, 10 figures, Accepted by EPJC. References and 1 figure (Fig. 6) adde