Fast iterative solution of reaction-diffusion control problems arising from chemical processes

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs

Regularization-robust preconditioners for time-dependent PDE constrained optimization problems

In this article, we motivate, derive and test �effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two diff�erent functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the eff�ectiveness of our preconditioners in each case is an eff�ective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are eff�ective for a wide range of regularization parameter values, as well as mesh sizes and time-steps

A principled approach to programming with nested types in Haskell

Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell

J004457+4123 (Sharov 21): not a remarkable nova in M31 but a background quasar with a spectacular UV flare

We announce the discovery of a quasar behind the disk of M31, which was previously classified as a remarkable nova in our neighbour galaxy. The paper is primarily aimed at the outburst of J004457+4123 (Sharov 21), with the first part focussed on the optical spectroscopy and the improvement in the photometric database. Both the optical spectrum and the broad band spectral energy distribution of Sharov 21 are shown to be very similar to that of normal, radio-quiet type 1 quasars. We present photometric data covering more than a century and resulting in a long-term light curve that is densely sampled over the past five decades. The variability of the quasar is characterized by a ground state with typical fluctuation amplitudes of ~0.2 mag around B~20.5, superimposed by a singular flare of ~2 yr duration (observer frame) with the maximum at 1992.81 where the UV flux has increased by a factor of ~20. The total energy in the flare is at least three orders of magnitudes higher than the radiated energy of the most luminous supernovae, provided that it comes from an intrinsic process and the energy is radiated isotropically. The profile of the flare light curve appears to be in agreement with the standard predictions for a stellar tidal disruption event where a ~10 M_sun giant star was shredded in the tidal field of a ~2...5 10^8 M_sun black hole. The short fallback time derived from the light curve requires an ultra-close encounter where the pericentre of the stellar orbit is deep within the tidal disruption radius. Gravitational microlensing provides an alternative explanation, though the probability of such a high amplification event is very low.Comment: Accepted for publication in Astronomy and Astrophysics, 14 pages, 11 figure

Vascular signalling mediated by ZWILLE potentiates WUSCHEL function during shoot meristem stem cell development in the Arabidopsis embryo

Stem cells are maintained in an undifferentiated state by signals from their microenvironment, the stem cell niche. Despite its central role for organogenesis throughout the plant's life, little is known about how niche development is regulated in the Arabidopsis embryo. Here we show that, in the absence of functional ZWILLE (ZLL), which is a member of the ARGONAUTE (AGO) family, stem cell-specific expression of the signal peptide gene CLAVATA3 (CLV3) is not maintained despite increased levels of the homeodomain transcription factor WUSCHEL (WUS), which is expressed in the organising centre (OC) of the niche and normally promotes stem cell identity. Tissue-specific expression indicates that ZLL acts to maintain the stem cells from the neighbouring vascular primordium, providing direct evidence for a non-cell-autonomous mechanism. Furthermore, mutant and marker gene analyses suggest that during shoot meristem formation, ZLL functions in a similar manner but in a sequential order with its close homologue AGO1, which mediates RNA interference. Thus, WUS-dependent OC signalling to the stem cells is promoted by AGO1 and subsequently maintained by a provascular ZLL-dependent signalling pathway.Matthew R. Tucker, Annika Hinze, Elise J. Tucker, Shinobu Takada, Gerd Jürgens and Thomas Lau

A Health Check of Avondale\u27s Distance Education Program: Where Have we Been? Where are we Going Next?

Avondale College of Higher Education has been offering tertiary courses for over 120 years. In the past two decades, this institution has extended its programs to include distance courses for students who opt to study online or are not able to attend on-campus courses at Avondale’s Lake Macquarie and Sydney campuses. While all of the institutions courses are evaluated on a regular basis, no formal evaluation had ever been undertaken of the distance education program as a whole. During 2017, a mixed methods research project was conducted to gather evaluative data from recent and current distance students using questionnaires and focus groups. The results of the study provide insight into the extent to which the distance education program at the College provides a space in which learning relationships can develop in online communities. Also, suggestions for future improvement and further research recommendations are provided. Findings of this study may be of interest to educators and administrators who incorporate online components in their curricula

Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms

PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method we introduce fast and efficient preconditioners which enable us to solve problems from a number of PDE applications in low iteration numbers and CPU times, even when the parameters involved are altered dramatically

Development of a Sandwich ELISA to Measure Exposure to Occupational Cow Hair Allergens

Background: Cow hair and dander are important inducers of occupational allergies in cattle-exposed farmers. To estimate allergen exposure in farming environments, a sensitive enzyme immunoassay was developed to measure cow hair allergens. Methods: A sandwich ELISA was developed using polyclonal rabbit antibodies against a mixture of hair extracts from different cattle breeds. To assess the specificity of the assay, extracts from other mammalian epithelia, mites, molds and grains were tested. To validate the new assay, cow hair allergens were measured in passive airborne dust samples from the stables and homes of farmers. Dust was collected with electrostatic dust fall collectors (EDCs). Results: The sandwich ELISA was found to be very sensitive (detection limit: 0.1 ng/ml) and highly reproducible, demonstrating intra-and interassay coefficients of variation of 4 and 10%, respectively. The assay showed no reactivity with mites, molds and grains, but some cross-reactivity with other mammalian epithelia, with the strongest reaction with goat. Using EDCs for dust sampling, high concentrations of bovine allergens were measured in cow stables (4,760-559,400 mu g/m(2)). In addition, bovine allergens were detected in all areas of cattle farmer dwellings. A large variation was found between individual samples (0.3-900 mu g/m(2)) and significantly higher values were discovered in changing rooms. Conclusion: The ELISA developed for the detection of cow hair proteins is a useful tool for allergen quantification in occupational and home environments. Based on its low detection limit, this test is sensitive enough to detect allergens in passive airborne dust. Copyright (C) 2011 S. Karger AG, Base

Rotational Correlation Functions of Single Molecules

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict non-exponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.Comment: 5 pages, 4 figure