On Convex Envelopes and Regularization of Non-Convex Functionals without moving Global Minima

We provide theory for the computation of convex envelopes of non-convex functionals including an l2-term, and use these to suggest a method for regularizing a more general set of problems. The applications are particularly aimed at compressed sensing and low rank recovery problems but the theory relies on results which potentially could be useful also for other types of non-convex problems. For optimization problems where the l2-term contains a singular matrix we prove that the regularizations never move the global minima. This result in turn relies on a theorem concerning the structure of convex envelopes which is interesting in its own right. It says that at any point where the convex envelope does not touch the non-convex functional we necessarily have a direction in which the convex envelope is affine.Comment: arXiv admin note: text overlap with arXiv:1609.0937

On the Efficiency of Optimising Shallow Backtracking in Prolog

The cost of backtracking has been identified as one of the bottlenecks in achieving peak performance in compiled Prolog programs. Much of the backtracking in Prolog programs is shallow, i.e. is caused by unification failures in the head of a clause when there are more alternatives for the same procedure, and so special treatment of this form of backtracking has been proposed as a significant optimisation. This paper describes a modified WAM which optimises shallow backtracking. Four different implementation approaches are compared. A number of benchmark results are presented, measuring the relative tradeoffs between compilation time, code size, and run time. The results show that the speedup gained by this optimisation can be significant

Input of nitrogen from N2 fixation to northern grasslands

Forage legumes form N2-fixing symbioses with rhizobia and may thus make substantial contributions to the N pool in grasslands. However, to optimize their use as sources of N, it is important to elucidate the effects of management factors that influence their N2 fixation rates, and to develop convenient methods for measuring N2 fixation quickly and reliably. An analysis of published data on N2 fixation in the field showed that lucerne (Medicago sativa L.), red clover (Trifolium pratense L.), and white clover (T. repens L.) grown in mixtures with grasses derived most of their N from N2 fixation, irrespective of geographic location and management practices – and despite large inter-annual variations in legume dry matter yield (kg ha-1 year-1). Consequently, there were strong correlations between legume dry matter yield and amounts of N2 fixed (kg N ha-1 year-1), which can be used very simply to obtain estimates of N2 fixation in these legumes. In experimental grassland plots where the species richness of neighbouring vegetation was varied, alsike clover (T. hybridum L.), red clover, and white clover consistently derived at least half of their N from N2 fixation, measured by the 15N natural abundance (NA) method using three different reference plants. This method is sensitive to the degree of discrimination against 15N in the N2-fixing plant (B value) and the choice of reference plant. B values were therefore established for each of the three clover species in symbioses with different Scandinavian Rhizobium leguminosarum bv. trifolii genotypes. In red clover, reductions following cutting in the activity of the N2-fixing enzyme, nitrogenase, and the rate of shoot regrowth were dependent on the cutting height. The recovery in nitrogenase activity after cutting followed the rate of leaf area increment, which confirms the correlation between N2 fixation and growth found in field experiments. The results of the work underlying this thesis show that perennial forage legumes growing in grasslands are highly dependent on N2 fixation. Awareness of this should facilitate the development of resource-efficient management regimes for northern grasslands

Fish and amphibians as test organisms for evaluation of effects caused by chemicals

A large number of chemicals can contaminate aquatic environments and therefore be exposed to fish and amphibians during their sensitive stages of development. This raises the need for robust methods to identify chemicals that disturb the developmental process. In this thesis, methods for toxicity testing and biomonitoring were developed for zebrafish (Danio rerio) and West-African clawed frog (Xenopus tropicalis). Using these methods, two groups of substances that have achieved attention during recent years were tested, synthetic musks and brominated flame retardants, as well as substances with known mechanism of action. Moreover, zebrafish embryos were used to evaluate chemically complex extracts prepared of effluent water from oil/gas production platforms. Exposure was performed on the embryo stages, to reveal embryo toxic endpoints and in connection to the metamorphosis process in frogs, to evaluate disturbances of the thyroid hormone system. Both methods were able to detect adverse effects in exposed animals. The studies showed that some musk substances had toxic effects on embryos in environmentally relevant concentrations. Embryo toxic responses of musk ketone (MK) and tetrabromobisphenol-A (TBBPA) were recorded in zebrafish as well as in Xenopus tropicalis and moor frog (Rana arvalis) at comparable concentrations. Zebrafish embryos were adequate for monitoring the toxic impact of effluent water from oil/gas production platforms. Effects on X. tropicalis tadpoles due to exposure to propylthiouracil were reduced development and decreased hind limb length, which can be explained by thyroid disruption. Increased sensitivity of the method was achieved by measurements on histological preparations of the thyroid glands. Exposure to polybrominated diphenylethers resulted in signs of thyroid disrupting properties of one tested congener, BDE-99. Moreover, distribution of BDE-99 in tadpole and juvenile X. tropicalis showed long-term retention and accumulation in adipose tissue