On the computation of a certain class of Hill determinants

AbstractHill's equation is studied for a particular class of periodic functions, which covers a broad range of practical applications. The essential quantity, which determines the stability criteria, is an infinite (or Hill) determinant. A set of recurrence relations for the computation of this determinant is derived. It is shown how these recurrence formulae also yield analytical results in two extremes

Localization of bosonic atoms by fermionic impurities in a 3d optical lattice

We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular we study the dependence of this transition on the fermionic 40K impurity concentration by a comparison to the corresponding superfluid to Mott insulator transition in a pure bosonic 87Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a mean-field argument, which is a strong indication that disorder-related effects play a significant role.Comment: 4 pages, 4 figure

MissForest - nonparametric missing value imputation for mixed-type data

Modern data acquisition based on high-throughput technology is often facing the problem of missing data. Algorithms commonly used in the analysis of such large-scale data often depend on a complete set. Missing value imputation offers a solution to this problem. However, the majority of available imputation methods are restricted to one type of variable only: continuous or categorical. For mixed-type data the different types are usually handled separately. Therefore, these methods ignore possible relations between variable types. We propose a nonparametric method which can cope with different types of variables simultaneously. We compare several state of the art methods for the imputation of missing values. We propose and evaluate an iterative imputation method (missForest) based on a random forest. By averaging over many unpruned classification or regression trees random forest intrinsically constitutes a multiple imputation scheme. Using the built-in out-of-bag error estimates of random forest we are able to estimate the imputation error without the need of a test set. Evaluation is performed on multiple data sets coming from a diverse selection of biological fields with artificially introduced missing values ranging from 10% to 30%. We show that missForest can successfully handle missing values, particularly in data sets including different types of variables. In our comparative study missForest outperforms other methods of imputation especially in data settings where complex interactions and nonlinear relations are suspected. The out-of-bag imputation error estimates of missForest prove to be adequate in all settings. Additionally, missForest exhibits attractive computational efficiency and can cope with high-dimensional data.Comment: Submitted to Oxford Journal's Bioinformatics on 3rd of May 201

Effect of dopants on thermal stability and self-diffusion in iron nitride thin films

We studied the effect of dopants (Al, Ti, Zr) on the thermal stability of iron nitride thin films prepared using a dc magnetron sputtering technique. Structure and magnetic characterization of deposited samples reveal that the thermal stability together with soft magnetic properties of iron nitride thin films get significantly improved with doping. To understand the observed results, detailed Fe and N self-diffusion measurements were performed. It was observed that N self-diffusion gets suppressed with Al doping whereas Ti or Zr doping results in somewhat faster N diffusion. On the other hand Fe self-diffusion seems to get suppressed with any dopant of which heat of nitride formation is significantly smaller than that of iron nitride. Importantly, it was observed that N self-diffusion plays only a trivial role, as compared to Fe self-diffusion, in affecting the thermal stability of iron nitride thin films. Based on the obtained results effect of dopants on self-diffusion process is discussed.Comment: 10 pages, 9 fig

The effect of dietary n-3 HUFA levels and DHA/EPA ratios on growth, survival and osmotic stress tolerance of Chinese mitten crab <i>Eriocheir sinensis</i> larvae

The effect of varying levels of dietary n-3 highly unsaturated fatty acid (HUFA) and docosahexaenoic acid/eicosapentaenoic acid (DHA/EPA) ratios on growth, survival and osmotic stress tolerance of Eriocheir sinensis zoea larvae was studied in two separate experiments. In experiment I, larvae were fed rotifers and Artemia enriched with ICES emulsions with 0, 30 and 50% total n-3 HUFA levels but with the same DHA/EPA ratio of 0.6. In experiment II, larvae were fed different combinations of enriched rotifers and Artemia, in which, rotifers were enriched with emulsions containing 30% total n-3 HUFA, but different DHA/EPA ratio of 0.6, 2 and 4; while Artemia were enriched with the same emulsions, but DHA/EPA ratio of 0.6 and 4. In both experiments, un-enriched rotifers cultured on baker's yeast and newly-hatched Artemia nauplii were used as control diets. Larvae were fed rotifers at zoea 1 and zoea 2 stages; upon reaching zoea 3 stage, Artemia was introduced.Experiment I revealed no significant effect of prey enrichment on the survival of megalopa among treatments, but higher total n-3 HUFA levels significantly enhanced larval development (larval stage index, LSI) and resulted in higher individual dry body weight of megalopa. Furthermore higher dietary n-3 HUFA levels also resulted in better tolerance to salinity stress. Experiment II indicated that at the same total n-3 HUFA level, larvae continuously receiving a low dietary DHA/EPA ratio had significantly lower survival at the megalopa stage and inferior individual body weight at the megalopa stage, but no negative effect was observed on larval development (LSI). The ability to endure salinity stress of zoea 3, zoea 5 and megalopa fed diets with higher DHA/EPA ratio was also improved

Insights from 125Te and 57Fe nuclear resonance vibrational spectroscopy: a [4Fe-4Te] cluster from two points of view.

Iron-sulfur clusters are common building blocks for electron transport and active sites of metalloproteins. Their comprehensive investigation is crucial for understanding these enzymes, which play important roles in modern biomimetic catalysis and biotechnology applications. We address this issue by utilizing (Et4N)3[Fe4Te4(SPh)4], a tellurium modified version of a conventional reduced [4Fe-4S]+ cluster, and performed both 57Fe- and 125Te-NRVS to reveal its characteristic vibrational features. Our analysis exposed major differences in the resulting 57Fe spectrum profile as compared to that of the respective [4Fe-4S] cluster, and between the 57Fe and 125Te profiles. DFT calculations are applied to rationalize structural, electronic, vibrational, and redox-dependent properties of the [4Fe-4Te]+ core. We herein highlight the potential of sulfur/tellurium exchange as a method to isolate the iron-only motion in enzymatic systems

Clones in Graphs

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.Comment: 11 pages, 2 figures, 1 tabl

Influence of highly unsaturated fatty acids in live food on larviculture of mud crab <i>Scylla paramamosain</i> (Estampador 1949)

Two experiments were carried out to investigate the effects of docosahexaenoic acid (DHA), eicosapentaenoic acid (EPA) and arachidonic acid (ARA) levels in rotifers (Brachionus plicatilis) and Artemia on the survival, development and metamorphosis of mud crab Scylla paramamosain larvae. Five different lipid emulsions, varying in the level of total n-3 and n-6 highly unsaturated fatty acids (HUFA), DHA, EPA and ARA were used to manipulate the fatty acid profile of the live food. Fatty acid profiles of the live food and crab larvae at zoea one, three and five stages were analysed to study the HUFA uptake by the larvae. The fatty acid content of the live food affected the fatty acid profiles of the crab larvae. In both experiments, the survival rate in the zoeal stages was not statistically different among treatments. However, larval development rate and metamorphosis success were affected by the dietary treatments. In this respect, the DHA/EPA ratio in the live food seems to be a key factor. Enrichment emulsions with a very high (50%) total HUFA content but a low DHA/EPA ratio (0.6), or zero total HUFA content caused developmental retardation and/or metamorphosis failure. An emulsion with a moderate total HUFA (30%) and a high DHA/EPA ratio (4) was the best in terms of larval development during the zoeal stages and resulted in improved metamorphosis. Dietary ARA seemed to improve first metamorphosis, but its exact role needs further clarification. For the larval rearing of S. paramamosain, an enrichment medium containing about 30% total n-3 HUFA with a minimum DHA/EPA ratio of 1 is recommended. Further investigation is needed on the total HUFA and optimum DHA/EPA ratio requirements for each crab larval stage