Shortest prefix strings containing all subset permutations

AbstractWhat is the length of the shortest string consisting of elements of {1,…n} that contains as subsequences all permutations of any k-element subset? Many authors have considered the special case where k=n. We instead consider an incremental variation on this problem first proposed by Koutas and Hu. For a fixed value of n they ask for a string such that for all values of k⩽n, the prefix containing all permutations of any k-element subset as subsequences is as short as possible. The problem can also be viewed as follows:For k=1 one needs n distinct digits to find each of the n possible permutations. In going from k to k+1, one starts with a string containing all k-element permutations as subsequences, and one adds as few digits as possible to the end of the string so that the new string contains all (k+1)-element permutations.We give a new construction that gives shorter strings than the best previous construction. We then prove a weak form of lower bound for the number of digits added in successive suffixes. The lower bound proof leads to a construction that matches the bound exactly. The length of a shortest prefix string is k(n−2)+[13(k+1)]+3, for k > 2.The lengths for k=1, 2 are n and 2n−1. This proves the natural conjecture that requiring the strings to be prefixes strictly increases the length of the strings required for all but the smallest values of k

On the Complexity of Local Search for Weighted Standard Set Problems

In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in Johnson et al., [JPY88]. We show that for most of these problems, computing a locally optimal solution is already PLS-complete for a simple neighborhood of size one. For the local search versions of weighted SetPacking and SetCover, we derive tight bounds for a simple neighborhood of size two. To the best of our knowledge, these are one of the very few PLS results about local search for weighted standard set problems

Численное моделирование тектонической и термической истории Кындалского грабена Буреинского бассейна (Дальний Восток России)

Because the endocrine disrupting effects of nonylphenol (NP) and octylphenol became evident, the degradation of long-chain alkylphenols (AP) by microorganisms was intensively studied. Most NP-degrading bacteria belong to the sphingomonads and closely related genera, while NP metabolism is not restricted to defined fungal taxa. Growth on NP and its mineralization was demonstrated for bacterial isolates, whereas ultimate degradation by fungi still remains unclear. While both bacterial and fungal degradation of short-chain AP, such as cresols, and the bacterial degradation of long-chain branched AP involves aromatic ring hydroxylation, alkyl chain oxidation and the formation of phenolic polymers seem to be preferential elimination pathways of long-chain branched AP in fungi, whereby both intracellular and extracellular oxidative enzymes may be involved. The degradation of NP by sphingomonads does not proceed via the common degradation mechanisms reported for short-chain AP, rather, via an unusual ipso-substitution mechanism. This fact underlies the peculiarity of long-chain AP such as NP isomers, which possess highly branched alkyl groups mostly containing a quaternary alpha-carbon. In addition to physicochemical parameters influencing degradation rates, this structural characteristic confers to branched isomers of NP a biodegradability different to that of the widely used linear isomer of NP. Potential biotechnological applications for the removal of AP from contaminated media and the difficulties of analysis and application inherent to the hydrophobic NP, in particular, are also discussed. The combination of bacteria and fungi, attacking NP at both the phenolic and alkylic moiety, represents a promising perspective

Dynamic dictionary matching with failure functions

AbstractAmir and Farach (1991) and Amir et al. (to appear) recently initiated the study of the dynamic dictionary pattern matching problem. The dictionary D contains a set of patterns that can change over time by insertion and deletion of individual patterns. The user may also present a text string and ask to search for all occurrences of any patterns in the text. For the static dictionary problem, Aho and Corasick (1975) gave a strategy based on a failure function automaton that takes O(|D|log|Σ|) time to build a dictionary of size |D| and searches a text T in time O(|T|log|Σ|+tocc), where tocc, is the total number of pattern occurrences in the text.Amir et al. (to appear) used an automaton based on suffix trees to solve the dynamic problem. Their method can insert or delete a pattern P in time O(|P|log|D|) and can search a text in time O((|T|+tocc)log|D|).We show that the same bounds can be achieved using a framework based on failure functions. We then show that our approach also allows us to achieve faster search times at the expense of the update times; for constant k, we can achieve linear O(|T|(k+log|Σ|)+k tocc) search time with an update time of O(k|P∥D|1k). This is advantageous if the search texts are much larger than the dictionary or searches are more frequent than updates.Finally, we show how to build the initial dictionary in O(|D|log|Σ|) time, regardless of what combination of search and update times is used

Lasing on a narrow transition in a cold thermal strontium ensemble

Highly stable laser sources based on narrow atomic transitions provide a promising platform for direct generation of stable and accurate optical frequencies. Here we investigate a simple system operating in the high-temperature regime of cold atoms. The interaction between a thermal ensemble of $^{88}$Sr at mK temperatures and a medium-finesse cavity produces strong collective coupling and facilitates high atomic coherence which causes lasing on the dipole forbidden $^1$S$_0 \leftrightarrow ^3$P$_1$ transition. We experimentally and theoretically characterize the lasing threshold and evolution of such a system, and investigate decoherence effects in an unconfined ensemble. We model the system using a Tavis-Cummings model, and characterize velocity-dependent dynamics of the atoms as well as the dependency on the cavity-detuning.Comment: 9 pages, 7 figure

Bovine Fasciolose in bayerischen `Bio-Milchkuhbetrieben`: Prävalenz und Risikofaktoren

This study about fasciolosis in Bavarian dairy farms is part of the project “Tackling the parasitological challenges in organic ruminant farming systems (ProPara)” (Core Organic Plus).The first aim of this project was to analyse the prevalence of Fasciola hepatica in Bavarian organic dairy farms in comparison to conventional farms. For this purpose, 366 bulk tank milk (BTM) samples of Bavarian organic cattle herds and 366 BTM samples of Bavarian conventional farms were collected in October 2015. Seroprevalence of each BTM sample was estimated using the `IDEXX Fasciola hepatica Antibody Test Kit`. The second aim of this project was to identify risk factors for the transmission of F. hepatica, which are important especially for organic cattle farming. In order to exclude pasturing as a risk factor, only herds with grazing were included in the study. A questionnaire, including 37 questions, was discussed with each participating farmer by telephone. BTM or fecal samples of every herd was examined to assess the infectionstatus. Thus, the herds were divided into 4 groups: - organic Fasciola-negative, - organic Fasciola-positive, - conventional Fasciola-negative, - conventional Fasciola-positive. As risk factors in all herds breed, the collective grazing of different production groups (e. g. dairy and dry cows), grazing depending on the weather, and the percentage of pastures with wetlands

Chiral logic computing with twisted antiferromagnetic magnon modes

Antiferromagnetic (AFM) materials offer an exciting platform for ultrafast information handling with low cross-talks and compatibility with existing technology. Particularly interesting for low-energy cost computing is the spin wave-based realization of logic gates, which has been demonstrated experimentally for ferromagnetic waveguides. Here, we predict chiral magnonic eigenmodes with a finite intrinsic, magnonic orbital angular momentum ℓ in AFM waveguides. ℓ is an unbounded integer determined by the spatial topology of the mode. We show how these chiral modes can serve for multiplex AFM magnonic computing by demonstrating the operation of several symmetry- and topology-protected logic gates. A Dzyaloshinskii–Moriya interaction may arise at the waveguide boundaries, allowing coupling to external electric fields and resulting in a Faraday effect. The uncovered aspects highlight the potential of AFM spintronics for swift data communication and handling with high fidelity and at a low-energy cost

Effect of sludge treatment on the bioaccumulation of nonylphenol in grass grown on sludge-amended soil

We studied the accumulation of p353-nonylphenol residues in the biomass of grass grown in soil amended with sewage sludge submitted to various conditioning/dewatering treatments. Incubation experiments were conducted growing Poa pratensis in sludge-amended soils and applying one 14C-labelled isomer of nonylphenol in the different systems. More metabolites than parent compounds were recovered in both roots and leaves of the grass. The type of sludge conditioning and dewatering treatment had a slight effect on the bioaccumulation of nonylphenol and its metabolites. When the grass was cultivated in soils amended with dewatered sludge without conditioning pretreatment, an increased accumulation was observed in the roots, while the final biomass of the grass was lowe