Asymptotically Optimal Encodings of Range Data Structures for Selection and Top-k Queries

Given an array A[1, n] of elements with a total order, we consider the problem of building a data structure that solves two queries: (a) selection queries receive a range [i, j] and an integer k and return the position of the kth largest element in A[i, j]; (b) top-k queries receive [i, j] and k and return the positions of the k largest elements in A[i, j]. These problems can be solved in optimal time, O(1 + lg k/ lg lg n) and O(k), respectively, using linear-space data structures. We provide the first study of the encoding data structures for the above problems, where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A, and their positions, rather their actual values, and thus we do not need to keep A at query time. In those cases, encodings save storage space: we first show that any encoding answering such queries requires n lg k − O(n + k lg k) bits of space; then, we design encodings using O(n lg k) bits, that is, asymptotically optimal up to constant factors, while preserving optimal query time.Peer-reviewedPost-prin

Fraction of probe sets with large LOD scores for each group of selected probe sets

<p><b>Copyright information:</b></p><p>Taken from "Mapping of -acting regulatory factors from microarray data"</p><p>http://www.biomedcentral.com/1753-6561/1/S1/S155</p><p>BMC Proceedings 2007;1(Suppl 1):S155-S155.</p><p>Published online 18 Dec 2007</p><p>PMCID:PMC2367593.</p><p></p

Iron(III)-Modified Tungstophosphoric Acid Supported on Titania Catalyst: Synthesis, Characterization, and Friedel–Craft Acylation of <i>m</i>‑Xylene

The Friedel–Craft acylation of <i>m</i>-xylene with benzoyl chloride over iron-modified tungstophosphoric acid supported on titania was investigated. It was found that FeTPA/TiO₂ catalyst displayed excellent catalytic performance for this reaction. Furthermore, a series of catalysts were prepared and characterized by FT-IR, XRD, BET, NH₃-TPD, and Py-IR. The results indicated that both the Lewis acidity and the textural properties presented significant influences on their catalytic performance. Moreover, the influence of catalyst calcination temperature to the above reaction was also studied. The reaction parameters, including reaction temperature, catalyst dose, and molar ratio of <i>m</i>-xylene to benzoyl chloride, were optimized, and a 95.1% yield of 2,4-dimethylbenzophenone was obtained under optimal conditions. Finally, the kinetics of the benzoylation of <i>m</i>-xylene over 30% FeTPA/TiO₂ was established

A Naphthalimide-Based Glyoxal Hydrazone for Selective Fluorescence Turn-On Sensing of Cys and Hcy

A fluorescent turn-on probe for Cys/Hcy based on inhibiting the CN isomerization quenching process by an intramolecular hydrogen bond was reported. The probe exhibited higher selectivity toward Cys/Hcy over other amino acids as well as thiol-containing compounds

Additional file 8: Table S2. of System modeling reveals the molecular mechanisms of HSC cell cycle alteration mediated by Maff and Egr3 under leukemia

Model parameters. Symbols, definitions, values, units and references for all model parameters are listed in the table here. (XLS 28 kb

Additional file 5: Figure S5. of System modeling reveals the molecular mechanisms of HSC cell cycle alteration mediated by Maff and Egr3 under leukemia

Binding motif of Maff is also discovered within 2 kb upstream of Pf4 gene. The Maff binding motif for transcriptional activation occurs at a location <1 kb upstream the transcription start site (TSS) of Pf4, which is potentially within the promoter region of the gene. The observation indicated that Maff might positively regulate Pf4, which is a regulator of platelet formation. (PDF 5 kb

Circulating miRNAs visually differentiate patients into different groups.

<p>Patients are numbered (left side of Fig 3) according to convention established, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141279#pone.0141279.g002" target="_blank">Fig 2</a>. Patients grouped visually based on clustering (red numbers = group 1, green numbers = group 2, and blue numbers = group 3). The clustering was based on similarity between the changes in miRNA concentrations between baseline (dC_{T baseline}) and after chemotherapy treatment (dC_{T treatment}). Blue = decreased concentrations after chemotherapy, Red = increased concentrations after treatment.</p

Additional file 7: Table S1. of System modeling reveals the molecular mechanisms of HSC cell cycle alteration mediated by Maff and Egr3 under leukemia

Table for the combinatorial numerical tests. Qualitative results of the numerical tests on combinations of possible regulatory relations are documented here, with all 81 combinations exhausted. The first four columns represent the regulatory code, “1” – inhibitory, “2” – none, and “3” – activatory effects, respectively. Molecular actions are indicated by the column headers. The last two columns show the agreement or discrepancy with input experimental data, “0” qualitative discrepancy, “1” qualitative agreement. The input experimental data for model training are the cell-cycle status after transduction of Maff/Egr3 and qRT-PCR results for cell-cycle genes. (XLSX 13 kb

Additional file 4: Figure S4. of System modeling reveals the molecular mechanisms of HSC cell cycle alteration mediated by Maff and Egr3 under leukemia

Outcomes produced by other regulatory sturctures. Apparently false dynamics resulted by other hypotheses of regulations. Basically, all the other network structures than the one in Fig. 5/Additional file 1: Figure S1 produce qualitatively false results on (at least) one of Cdk4/6:CyclinD, Cdk2:CyclinE, and E2F. Here we show the most typically false results, combinations of regulatory relations are randomly assigned. Upper panel: unrealistic dynamic levels of Cdk2:CyclinE and E2F with respect to Maff transcription under low Egr3 expression, which is dictated by a randomly assigned network structure (regulatory code 1212); middle panel: results of Cdk2:CyclinE and E2F dictated by another network structure (regulatory code 2133); results of Cdk4/6:CyclinD and E2F dictated by a third different network structure (regulatory code 3321). Refer to Additional file 7: Table S1 for depiction of the regulatory codes. (PNG 52 kb

Additional file 2: Figure S2. of System modeling reveals the molecular mechanisms of HSC cell cycle alteration mediated by Maff and Egr3 under leukemia

Simulation results with additional regulation “Maff → Cdk2 (:Cyclin E)” with respect to Maff. Dynamics with respect to the transcription rate of Maff at high (upper), medium (middle), and low (lower) Egr3 expression-levels. In each panel, steady-state molecular quantities of Cyclin D-Cdk4/6 (left), Cyclin E-Cdk2 (middle) and E2F (right) are shown. The correct bistability with respect to Maff is qualitatively reproduced with the additional molecular action. (PNG 73 kb