Comparison of optimal allocations of vaccines with target vaccination in uncorrelated scale-free networks.

<p>Optimal allocation (a), (d), and (g) for (left column); optimal allocation (b), (e), and (h) for (center column); target allocation (c), (f), and (i) (right column). At equilibrium, the fractions of infected nodes are (), (), and (target vaccination), respectively. The total costs for the optimal allocation are (), (), ( for target vaccination), and ( for target vaccination). and the maximal vaccination coverage is . The degree distribution is generated with and the network size . The minimal degree is and the maximal degree is . Nodes are grouped into 30 groups.</p

Optimal allocations of vaccines in correlated scale-free networks with different degree correlations for .

<p>(a) and ; (b) and ; (c) and ; (d) and ; (e) and ; (f) and . Other parameters are set to the same values as in Fig. 3. Nodes are grouped into 30 groups.</p

Comparison of optimal allocations of vaccines in networks with different degree correlations .

<p>(a) and ; (b) and ; (c) and ; (d) and . and the maximal vaccination coverage is . Other parameters are set to the same values as in Fig. 3. Nodes are grouped into 30 groups.</p

Cost versus for (from bottom to top) in homogeneous networks.

<p>(The green dotted vertical line) the theoretical solution ; (the blue short dashed line) the cost of vaccination; (the red dashed lines) the cost of treatment; and (the black solid lines) the total cost. Parameters are set as , , and . The basic per capita cost is set as and the vaccine efficacy is .</p

Direct imaging the thermal reversion of wild-type AsLOV2.

<p>(A) Bacterial colonies expressing wild-type AsLOV2 on an agar plate were irradiated with blue light, and fluorescence recovery of its flavin cofactor was visualized with a stereoscopic fluorescence microscope. (B) Time-lapse imaging of the fluorescence recovery of wild-type AsLOV2 after irradiation with blue light. The region boxed with a white square in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082693#pone-0082693-g003" target="_blank">Fig. 3A</a> are magnified. (C) Time course of the fluorescence recovery of three independent bacterial colonies shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082693#pone-0082693-g003" target="_blank">Fig. 3B</a> with white dashed circles. The fluorescence recovery was fit with single exponential curves (solid lines).</p

Fluorescence Imaging-Based High-Throughput Screening of Fast- and Slow-Cycling LOV Proteins

<div><p>Light-oxygen-voltage (LOV) domains function as blue light-inducible molecular switches. The photosensory LOV domains derived from plants and fungi have provided an indispensable tool for optogenetics. Here we develop a high-throughput screening system to efficiently improve switch-off kinetics of LOV domains. The present system is based on fluorescence imaging of thermal reversion of a flavin cofactor bound to LOV domains. We conducted multi site-directed random mutagenesis of seven amino acid residues surrounding the flavin cofactor of the second LOV domain derived from <i>Avena sativa</i> phototropin 1 (AsLOV2). The gene library was introduced into <i>Escherichia coli</i> cells. Then thermal reversion of AsLOV2 variants, respectively expressed in different bacterial colonies on agar plate, was imaged with a stereoscopic fluorescence microscope. Based on the mutagenesis and imaging-based screening, we isolated 12 different variants showing substantially faster thermal reversion kinetics than wild-type AsLOV2. Among them, AsLOV2-V416T exhibited thermal reversion with a time constant of 2.6 s, 21-fold faster than wild-type AsLOV2. With a slight modification of the present approach, we also have efficiently isolated 8 different decelerated variants, represented by AsLOV2-V416L that exhibited thermal reversion with a time constant of 4.3×10³ s (78-fold slower than wild-type AsLOV2). The present approach based on fluorescence imaging of the thermal reversion of the flavin cofactor is generally applicable to a variety of blue light-inducible molecular switches and may provide a new opportunity for the development of molecular tools for emerging optogenetics.</p></div

Representative example of words belonging to clusters obtained by TENMF before and after Japanese earthquake.

<p>To conduct the experiment, we collect tweets from 4th to 16th March 2011: the period for the huge earthquakes in Japan. Clusters represent some characteristics of user groups. We list the words with high scores that might represent the characteristics of each cluster. Italic words here are originally in Japanese shown in parentheses, and translated into English by the authors. If further parentheses are attached, the words are explained. Cluster 1 can be interpreted as ‘English speaking’ users or ‘symbols’ everyone uses. Cluster 2 can represent ‘businesspeople’. Cluster 3 can represent ‘Internet addicted’ users. Cluster 4 can represent ‘news sources’.</p><p>Representative example of words belonging to clusters obtained by TENMF before and after Japanese earthquake.</p

Dataset from Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation

This dataset contains tweets ID posted before and after one week Tohoku Earthquake and iPhone 4 announcement. We collected 11,418,600 tweets posted in the interval of 301 from 4th March 2011 to 16th March and 2,319,874 tweets posted in the interval of from 1st June 2010 to 17th June 2010 by 438,464 users, which are mainly Japanese tweets, to know the dynamics in Twitter when Japan had huge earthquakes in 11th March 2011 and iPhone announcement in 7th June 2010

Comparison of Time Evolution Nonnegative Matrix Factorisation and simple Nonnegative Matrix Factorisation.

<p>(a) Snapshots of the original synthetic data for time-sequential matrices <i>V</i>^{(<i>t</i>_<i>k</i>)}. Time evolves from left to right, and from top to bottom. The vertical and horizontal axes correspond to rows and columns of the matrices, and the values of the elements are represented by colour. We generate matrices such that the four equally sized blocks are filled with numbers that follow a Poisson distribution. (b), (c) Snapshots of the matrices <i>W</i>^{(<i>t</i>_<i>k</i>)} decomposed by (b) NMF and (c) TENMF with <i>r</i> = 4. Both NMF and TENMF decompose the original matrices properly, in the sense that each column of <i>W</i>^{(<i>t</i>_<i>k</i>)}s corresponds to one block in the original matrices. On the other hand, each column of <i>W</i>^{(<i>t</i>_<i>k</i>)}s decomposed by TENMF does not change the corresponding cluster. Moreover, the elements in one column evolve as the block evolves, which means each column in <i>W</i>^{(<i>t</i>_<i>k</i>)} can track the growth of the corresponding blocks in the original. (d) Iteration times required for decomposing <i>W</i>^{(<i>t</i>_<i>k</i>)} by NMF and TENMF. The number of iterations are counted for 200 runs, and the mean value and standard deviation are shown with error bars for each <i>k</i>. We can see that NMF requires more iteration time than TENMF. Moreover, NMF has larger variance than TENMF. This result shows that TENMF exploits the solution at time <i>t</i>_<i>k</i> as a good initial guess for the nearest locally optimal solution at time <i>t</i>_<i>k</i>+1. This also means that TENMF respects the temporal similarity between the solutions at time <i>t</i>_<i>k</i> and <i>t</i>_<i>k</i>+1.</p

A LOV domain and its photocycle.

<p>(A) The second light-oxygen-voltage (LOV) domain derived from <i>Avena sativa</i> phototropin 1 (AsLOV2) binds a flavin cofactor (FMN) to sense blue light. In the dark state, the C-terminal Jα helix of AsLOV2 is tightly bound to its core domain (switch-off, left panel). Upon irradiation with blue light, the Jα helix is released from the core domain of AsLOV2 (switch-on, right panel). When the blue light is turned off, the open conformation of AsLOV2 in the light state is returned back to its closed conformation in the dark state (right to left). The blue light-dependent conformational change of AsLOV2 switches the activity of an effector domain, such as a protein with enzymatic activity and a peptide, connected at the C-terminus of AsLOV2. (B) A photochemical reaction, known as a photocycle, occurring between a LOV domain and a flavin cofactor. Blue light irradiation induces the formation of a covalent bond between the thiol group of a cysteine within a LOV domain and the C4a position of the isoalloxazine ring of flavin (left to right). The photoadduct spontaneously breaks when the LOV domain is returned back to the dark condition (right to left). The photoadduct formation and its break lead to loss of fluorescence from the flavin cofactor and its recovery, respectively.</p