Succinct Partial Sums and Fenwick Trees

We consider the well-studied partial sums problem in succint space where one is to maintain an array of n k-bit integers subject to updates such that partial sums queries can be efficiently answered. We present two succint versions of the Fenwick Tree - which is known for its simplicity and practicality. Our results hold in the encoding model where one is allowed to reuse the space from the input data. Our main result is the first that only requires nk + o(n) bits of space while still supporting sum/update in O(log_b n) / O(b log_b n) time where 2 <= b <= log^O(1) n. The second result shows how optimal time for sum/update can be achieved while only slightly increasing the space usage to nk + o(nk) bits. Beyond Fenwick Trees, the results are primarily based on bit-packing and sampling - making them very practical - and they also allow for simple optimal parallelization

Syntactic View of Sigma-Tau Generation of Permutations

We give a syntactic view of the Sawada-Williams $(\sigma,\tau)$-generation of permutations. The corresponding sequence of $\sigma-\tau$-operations, of length $n!-1$ is shown to be highly compressible: it has $O(n^2\log n)$ bit description. Using this compact description we design fast algorithms for ranking and unranking permutations.Comment: accepted on LATA201

Mechanical Strength of 17 134 Model Proteins and Cysteine Slipknots

A new theoretical survey of proteins' resistance to constant speed stretching is performed for a set of 17 134 proteins as described by a structure-based model. The proteins selected have no gaps in their structure determination and consist of no more than 250 amino acids. Our previous studies have dealt with 7510 proteins of no more than 150 amino acids. The proteins are ranked according to the strength of the resistance. Most of the predicted top-strength proteins have not yet been studied experimentally. Architectures and folds which are likely to yield large forces are identified. New types of potent force clamps are discovered. They involve disulphide bridges and, in particular, cysteine slipknots. An effective energy parameter of the model is estimated by comparing the theoretical data on characteristic forces to the corresponding experimental values combined with an extrapolation of the theoretical data to the experimental pulling speeds. These studies provide guidance for future experiments on single molecule manipulation and should lead to selection of proteins for applications. A new class of proteins, involving cystein slipknots, is identified as one that is expected to lead to the strongest force clamps known. This class is characterized through molecular dynamics simulations.Comment: 40 pages, 13 PostScript figure

Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization

We employ the exponential parametrization of the metric and a \u201cphysical\u201d gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. \ua9 2016, The Author(s)

Ambient temperature does not affect fuelling rate in absence of digestive constraints in long-distance migrant shorebird fuelling up in captivity

Pre-flight fuelling rates in free-living red knots Calidris canutus, a specialized long-distance migrating shorebird species, are positively correlated with latitude and negatively with temperature. The single published hypothesis to explain these relationships is the heat load hypothesis that states that in warm climates red knots may overheat during fuelling. To limit endogenous heat production (measurable as basal metabolic rate BMR), birds would minimize the growth of digestive organs at a time they need. This hypothesis makes the implicit assumption that BMR is mainly driven by digestive organ size variation during pre-flight fuelling. To test the validity of this assumption, we fed captive knots with trout pellet food, a diet previously shown to quickly lead to atrophied digestive organs, during a fuelling episode. Birds were exposed to two thermal treatments (6 and 24°C) previously shown to generate different fuelling rates in knots. We made two predictions. First, easily digested trout pellet food rather than hard-shelled prey removes the heat contribution of the gut and would therefore eliminate an ambient temperature effect on fuelling rate. Second, if digestive organs were the main contributors to variations in BMR but did not change in size during fuelling, we would expect no or little change in BMR in birds fed ad libitum with trout pellets. We show that cold-acclimated birds maintained higher body mass and food intake (8 and 51%) than warm-acclimated birds. Air temperature had no effect on fuelling rate, timing of fuelling, timing of peak body mass or BMR. During fuelling, average body mass increased by 32% while average BMR increased by 15% at peak of mass and 26% by the end of the experiment. Our results show that the small digestive organs characteristic of a trout pellet diet did not prevent BMR from increasing during premigratory fuelling. Our results are not consistent with the heat load hypothesis as currently formulated

Longest Common Extensions in Trees

The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In this paper we generalize the LCE problem to trees and suggest a few applications of LCE in trees to tries and XML databases. Given a labeled and rooted tree $T$ of size $n$, the goal is to preprocess $T$ into a compact data structure that support the following LCE queries between subpaths and subtrees in $T$. Let $v_1$, $v_2$, $w_1$, and $w_2$ be nodes of $T$ such that $w_1$ and $w_2$ are descendants of $v_1$ and $v_2$ respectively. \begin{itemize} \item \LCEPP(v_1, w_1, v_2, w_2): (path-path \LCE) return the longest common prefix of the paths $v_1 \leadsto w_1$ and $v_2 \leadsto w_2$. \item \LCEPT(v_1, w_1, v_2): (path-tree \LCE) return maximal path-path LCE of the path $v_1 \leadsto w_1$ and any path from $v_2$ to a descendant leaf. \item \LCETT(v_1, v_2): (tree-tree \LCE) return a maximal path-path LCE of any pair of paths from $v_1$ and $v_2$ to descendant leaves. \end{itemize} We present the first non-trivial bounds for supporting these queries. For \LCEPP queries, we present a linear-space solution with $O(\log^{*} n)$ query time. For \LCEPT queries, we present a linear-space solution with $O((\log\log n)^{2})$ query time, and complement this with a lower bound showing that any path-tree LCE structure of size O(n \polylog(n)) must necessarily use $\Omega(\log\log n)$ time to answer queries. For \LCETT queries, we present a time-space trade-off, that given any parameter $\tau$, $1 \leq \tau \leq n$, leads to an $O(n\tau)$ space and $O(n/\tau)$ query-time solution. This is complemented with a reduction to the the set intersection problem implying that a fast linear space solution is not likely to exist

Rapid methods to detect organic mercury and total selenium in biological samples

<p>Abstract</p> <p>Background</p> <p>Organic mercury (Hg) is a global pollutant of concern and selenium is believed to afford protection against mercury risk though few approaches exist to rapidly assess both chemicals in biological samples. Here, micro-scale and rapid methods to detect organic mercury (< 1.5 ml total sample volume, < 1.5 hour) and total selenium (Se; < 3.0 ml total volume, < 3 hour) from a range of biological samples (10-50 mg) are described.</p> <p>Results</p> <p>For organic Hg, samples are digested using Tris-HCl buffer (with sequential additions of protease, NaOH, cysteine, CuSO₄, acidic NaBr) followed by extraction with toluene and Na₂S₂O₃. The final product is analyzed via commercially available direct/total mercury analyzers. For Se, a fluorometric assay has been developed for microplate readers that involves digestion (HNO₃-HClO₄and HCl), conjugation (2,3-diaminonaphthalene), and cyclohexane extraction. Recovery of organic Hg (86-107%) and Se (85-121%) were determined through use of Standard Reference Materials and lemon shark kidney tissues.</p> <p>Conclusions</p> <p>The approaches outlined provide an easy, rapid, reproducible, and cost-effective platform for monitoring organic Hg and total Se in biological samples. Owing to the importance of organic Hg and Se in the pathophysiology of Hg, integration of such methods into established research monitoring efforts (that largely focus on screening total Hg only) will help increase understanding of Hg's true risks.</p

Search of scaling solutions in scalar-tensor gravity

We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the difficulties that were previously present. In three dimensions these equations admit, at least for sufficiently small fields, a solution that may be interpreted as a gravitationally dressed Wilson-Fisher fixed point. We also find for any dimension d>2 two analytic scaling solutions which we study for d=3 and d=4. One of them corresponds to the fixed point of the Einstein-Hilbert truncation, the others involve a nonvanishing minimal coupling