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Figure S1-2

Additional file 2: Supplementary Figure S1. Geographic location of the 17 freshwater lakes sampled in this study. Trophic state of each lake is marked by a different color. Supplementary Figure S2. Randomized Axelerated Maximum Likelihood (RAxML) tree of 16S rRNA genes of different classes of Patescibacteria. The tree was split in two subtrees with collapsed branches for better visibility. The 16S rRNA gene sequences recovered from MAGs generated in this study are shown in bold. Targets for eight newly designed oligonucleotide probes for CARD-FISH are indicated with different colors. Bootstrap values (100 bootstraps) are indicated as differently sized circles, the tree scale is given on top. Asterisks indicate sequences not targeted by probes pgri-99 and ABY1b-1343, # indicate one outgroup hit of probe adl2-134. Supplementary Figure S3. Abundance (%) of 16S rRNA gene sequences affiliated to different classes in CPR. Samples that had < 1% of total abundance in any CPR class were not added to the plot. Supplementary Figure S4. Epifluorescence microscopy images of ABY1 class members using the ABY1a-193 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S5. Epifluorescence microscopy images of ABY1 class members using the ABY1b-1343 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S6. Epifluorescence microscopy images of Paceibacteria class members using the Adl1-132 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S7A. Epifluorescence microscopy images of Paceibacteria class members using the Adl1-134 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S7B. Epifluorescence microscopy images of Paceibacteria class members using the Adl1-134 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S8. Epifluorescence microscopy images of Gracilibacteria class members using the Pgri-99 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S9. Epifluorescence microscopy images of Gracilibacteria class members using the Pgri-124 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S10. Epifluorescence microscopy images of Saccharimonadia class members using the SacA-77 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S11. Epifluorescence microscopy images of Paceibacteria class members using the ZE-1429 probe. Panels labeled with a. are the overlap of the probe (green), DAPI (blue) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S12. Positive control for the Saccharibacteria class members performed using the SacA-77 and EUB I-III probes. Panels labeled with a. are the overlap of DAPI (blue), the Sac-77 probe (green), the EUB I-III probe (orange) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S13. Positive control for the Gracilibacteria class members performed using the Pgri-124 and EUB I-III probes. Panels labeled with a. are the overlap of DAPI (blue), the Pgri-124 probe (green), the EUB I-III probe (orange) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S14a. Negative controls for filters used for FISH from different lakes. Panels labeled with a. are the overlap of DAPI (blue), the NON338 probe (green) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S14b. Negative controls for filters used for FISH from different lakes. Panels labeled with a. are the overlap of DAPI (blue), the NON338 probe (green) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S15a. Negative controls for filters used for FISH from different lakes. Panels labeled with a. are the overlap of DAPI (blue), CARD amplification (green) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S15b. Negative controls for filters used for FISH from different lakes. Panels labeled with a. are the overlap of DAPI (blue), CARD amplification (green) and autofluorescence (red) signal. The rest of the panels represent individual signals. Supplementary Figure S16. Boxplots for the length and width of individual CPR cells observed with the 8 FISH probed designed and tested in this study. L – Length, W – Width. Supplementary Figure S17. Percentage of genes in each KEGG module encoded by CPRs, free-living freshwater bacteria and symbionts. All representative CPR genomes from GTDB (>40% completeness

A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for ordered trees with n vertices such that each ordered tree is derived from the preceding ordered tree by removing a leaf then appending a leaf elsewhere. Thus the change is just remove-and-append a leaf, which is the minimum., Comment: 14 pages

Additional file 1. Identification of phage defense mechanisms in CPRs.

Microcystis aeruginosa was quantitatively surveyed in 88 freshwater environments across Japan within 3‍ ‍weeks in 2011. In order to clarify the distribution pattern of M. aeruginosa at the intra-species level, three major genotypes, which were defined by 16S-23S rRNA inter-transcribed-spacer (ITS) regions, were selectively detected using quantitative real-time PCR assays. Of the 68 sites at which the Microcystis intergenic-spacer region of the phycocyanin (IGS-PC) gene was detected, the M. aeruginosa morphotype-related genotype (MG1) dominated in 41 sites, followed by the non-toxic M. wesenbergii-related genotype (MG3). A correlation analysis showed that total nitrogen and phosphate positively correlated with the abundance of IGS-PC, which positively correlated with microcystin synthetase gene abundance. A redundancy analysis of genotype compositions showed that pH positively correlated with the dominance of MG3 and negatively correlated with MG1, i.e., both toxic and non-toxic genotypes. Our survey of Microcystis populations over a wide area revealed that MG1 is a dominant genotype in Japan.

グラフの描画方法には大きな任意性があり, さまざまな観点から見やすいグラフの描画方法が研究されている. 本稿では, パスを見つけやすいグラフの描画として提案されている強単調性描画に若目し, それを精密化した概念として, a-強単調性描画を提案する. 木, 極大平面的グラフ, 平面的3—木, 2-連結外平面的グラフについて, 既存研究で強単調性描画可能であることがわかっているが, 本稿では, それらについてa—強単調性描画可能なaの値の評価を行い, それらの結果の精密化を行う.

Given a set P of n elements, and a function d that assigns a non-negative real number d(p, q) for each pair of elements p,q∈P, we want to find a subset S⊆P with |S|=k such that cost(S)=min{d(p,q)∣p,q∈S} is maximized. This is the max-min k-dispersion problem. In this paper, exact algorithms for the max-min k-dispersion problem are studied. We first show the max-min k-dispersion problem can be solved in O(n^/^3logn) time. Then, we show two special cases in which we can solve the problem quickly., Frontiers in Algorithmics,12th International Workshop, FAW 2018, Guangzhou, China, May 8-10, 2018, Proceedings

We study the k-center problem in a kinetic setting: given a set of continuously moving points P in the plane, determine a set of k (moving) disks that cover P at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move smoothly over time. Existing results on this problem require the disks to move with a bounded speed, but this model allows positive results only for k 3 . Hence, the results are limited and offer little theoretical insight. Instead, we study the topological stability of k-centers. Topological stability was recently introduced and simply requires the solution to change continuously, but may do so arbitrarily fast. We prove upper and lower bounds on the ratio between the radii of an optimal but unstable solution and the radii of a topologically stable solution—the topological stability ratio—considering various metrics and various optimization criteria. For k = 2 we provide tight bounds, and for small k > 2 we can obtain nontrivial lower and upper bounds. Finally, we provide an algorithm to compute the topological stability ratio in polynomial time for constant k.

In the present study, we perform the first direct analysis on how the composition of the prokaryotic soil community differs depending on whether high-throughput sequencing or fluorescent in situ hybridization (FISH) coupled with catalyzed reporter deposition (CARD) is used. Soil samples were collected along short (

The grazing and lysis mortalities of planktonic bacteria were estimated using the modified dilution method and respiratory quinone (RQ) analysis in mesotrophic Lake Biwa, Japan. The planktonic bacterial assemblages in the lake consisted of various RQ subgroups with different growth and mortality rates. The sum of total bacterial mortalities due to protistan grazing and viral lysis accounted for 96.6 % (range 89.0–107.2 %) of daily total bacterial production. This is the first report that successfully demonstrates a balanced relationship between bacterial production and losses using the modified dilution method in a lake. The growth rates of ubiquinone (UQ)-containing bacteria were faster than those of menaquinone-containing bacteria. Especially the dominant and fastest growing bacterial groups in the present study were the bacterial groups containing UQ-8 or UQ-10. The sum of their production and loss accounted for 60 % of carbon fluxes within the microbial loop. Thus, a large portion of the carbon cycling through the bacterial community in Lake Biwa can be explained by the carbon fluxes through dominant bacterial groups., Published online: 18 April 2014

A ladder lottery, known as the “Amidakuji” in Japan, is a network with n vertical lines and many horizontal lines each of which connects two consecutive vertical lines. Each ladder lottery corresponds to a permutation. Ladder lotteries are frequently used as natural models in many areas. Given a permutation π, an algorithm to enumerate all ladder lotteries of π with the minimum number of horizontal lines is known. In this paper, given a permutation π and an integer k, we design an algorithm to enumerate all ladder lotteries of π with exactly k horizontal lines.

The size and composition of soil microbial communities have important influences on terrestrial ecosystem processes such as soil decomposition. However, compared with studies of aboveground plant communities, there are relatively few studies on belowground microbial communities and their interactions with aboveground vegetations in the arctic region. In this study, we conducted the first investigation of the abundance and composition of prokaryotic communities along small-scale vegetation gradients (ca. 1–3 m) in a dry arctic tundra ecosystem in Northern Sweden using fluorescent in situ hybridization (FISH) coupled with catalyzed reporter deposition (CARD). The number of prokaryotic cells increased with increasing vegetation cover along vegetation gradients, mainly as a function of increased amounts of soil carbon and moisture. Eubacteria and Archaea constituted approximately 59.7% and 33.4% of DAPI-positive cells, respectively. Among the analyzed bacterial phyla and sub-phyla, Acidobacteria and α-proteobacteria were the most dominant groups, constituting approximately 13.5% and 10.7% of DAPI-positive cells, respectively. Interestingly, the soil prokaryotic community composition was relatively unaffected by the dramatic changes in the aboveground vegetation community. Multivariate analyses suggested that the prokaryotic community composition depended on soil pH rather than on aboveground vegetation. Surface plants are weak predictors of the composition of the soil microbial community in the studied soil system and the size of the community is constrained by carbon and water availability. In addition, our study demonstrated that CARD-FISH, which is still a rarely-used technique in soil ecology, is effective for quantifying soil microbes.

Microcystis aeruginosa is one of the bloom-forming harmful algae in freshwater ecosystems. We genetically characterized Microcystis populations during bloom-forming periods in various reservoirs, lakes, and ponds in Japan during 2009. Using phylogenetic analysis, we evaluated the relationship between current genotype expansions and geographic location within western Japan and intraspecific variation. Microcystis aeruginosa colonies were isolated at 15 sites and were analyzed by sequencing the 16S-23S internal transcribed spacer (ITS) region of the ribosomal operon, and the potential to produce toxins was assessed by PCR-based detection of the microcystin synthetase gene mcyG. In total, 171 colonies were separated into 41 genotypes. The highest genotypic composition was detected in the south basin of Lake Biwa and the lowest in Lagoon Iba. Cluster analysis indicated no obvious association between genotypic composition and geographic distance. Thus, clear genetic differentiation accompanied by geographic origins was not found in western Japan. The resulting neighbor-joining tree revealed 3 clusters, 2 of which contained strains that showed both nonamplification and amplification of the mcyG gene.

Uncultured bacteria affiliated with the CL500-11 cluster (phylum Chloroflexi) were first reported from the oxygenated hypolimnion of Crater Lake (USA) as a predominant bacterioplankton, although this dominance has not been reported in other environments. In this study, we showed that CL500-11 is also dominant in the oxygenated hypolimnion of Lake Biwa (Japan) and followed its spatiotemporal succession using fluorescent in situ hybridization. CL500-11 cells were almost absent [< 1% of 4', 6-diamidino-2-phenylindole (DAPI)-stained cells] at the beginning of the stratification period, dominated (> 10% of DAPI-stained cells; maximum = 16.5%) in the hypolimnion during the stratification period, and decreased to below the detection limit with the collapse of the thermocline. This pattern was observed over two annual cycles. A longitudinal assessment also showed that CL500-11 was the dominant bacterium in the hypolimnion over the whole lake, but was generally undetectable in the stratified epilimnion. These data suggest that CL500-11 is acclimated to the oxygenated hypolimnion and is a potentially important component of the pelagic biogeochemical cycling of the lake. A comparative analysis of 16S rRNA gene sequences revealed that almost all CL500-11 sequences previously deposited in the database were detected from hypolimnion or holomictic water in deep oxic freshwater lakes, suggesting that the bacteria may form one of the common lineages residing in an aerobic hypolimnetic niche.

We examined the growth of testate amoebae preying on Microcystis whose physiological states were different in laboratory experiments and a hypertrophic pond. We prepared three experimental systems using water samples dominated by Microcystis aeruginosa: light incubation (control), dark incubation (dark), and light incubation with addition of nitrogen and phosphorus (+NP). In all the systems, the colony density of M. aeruginosa decreased slightly during incubation. Physiological activity of phytoplankton as determined by chlorophyll fluorescence was high and almost constant in the control and +NP systems, whereas it decreased in the dark system. Cell densities of testate amoebae increased in the control and +NP systems, whereas in the dark system they remained low. Thus, growth of the amoebae was low in the systems where physiological activity of Microcystis was low. In a hypertrophic pond, cell density of testate amoebae increased and remained high when M. aeruginosa predominated. Cell density of testate amoebae increased remarkably, simultaneously with the increases in M. aeruginosa colony density and phytoplankton physiological activity. We also found a significant correlation between densities of M. aeruginosa colonies and testate amoebae. We suggested that the physiological activity of Microcystis is one important factor affecting the growth of testate amoebae grazing on Microcystis.

The airlines in the real world form small-world network. This implies that they are constructed with an ad hoc strategy. The small-world network is not so bad from the viewpoints of customers and managers. The customers can fly to any destination through a few airline hubs, and the number of airlines is not so many comparing to the number of airports. However, clearly, it is not the best solution in either viewpoint since there is a trade off. In this paper, one of the extreme cases, which is the standpoint of the manager, is considered; we assume that customers are silent and they never complain even if they are required to transit many times. This assumption is appropriate for some transportation service and packet communication. Under this assumption, the airline problem is to construct the least cost connected network for given distribution of the populations of cities with no a priori connection. First, we show an efficient algorithm that produces a good network which is minimized the number of vacant seats. The resultant network contains at most n connections (or edges), where n is the number of cities. Next we aim to minimize not only the number of vacant seats, but also the number of airline connections. The connected network with the least number of edges is a tree which has exactly n−1 connections. However, the problem to construct a tree airline network with the minimum number of vacant seats is NP-complete. We also propose efficient approximation algorithms to construct a tree airline network with the minimum number of vacant seats.

In this paper we give an algorithm to generate all rooted trees with at most n vertices. The algorithm generates each tree in constant time on average. Furthermore the algorithm is simple, and clarifies a simple relation among the trees, that is a family tree of trees, and outputs trees based on the relation.

A plane drawing of a graph is called a floorplan if every face (including the outer face) is a rectangle. A based floorplan is a floorplan with a designated base line segment on the outer face. In this paper we give a simple algorithm to generate all based floorplans with at most n faces. The algorithm uses O(n) space and generates such floorplans in O(1) time per floorplan without duplications. The algorithm does not output entire floorplans but the difference from the previous floorplan. By modifying the algorithm we can generate without duplications all based floorplans having exactly n faces in O(1) time per floorplan, and all (non-based) floorplans having exactly n faces in O(n) time per floorplan. Also, given three integers n, k1 and k2, we can generate all based floorplans with exactly n faces containing at least k1 and at most k2 inner rooms in O(1) time per floorplan, where an inner room means a face which does not contain a line segment of the contour of the outer face.

Article, 信州大学理学部附属諏訪臨湖実験所報告 9: 53-60(1995)

The edge-coloring problem is one of the fundamental problems on graphs, which often appears in various scheduling problems like the file transfer problem on computer networks. In this paper, we survey old and new results on the classical edge-coloring problem as well as the generalized edge-coloring problems, called the f?-coloring and f g?-coloring problems. In particular we especially review various upper bounds on the minimum number of colors required to edge-color graphs, and present efficient algorithms to edge-color graphs with a number of colors not exceeding the upper bounds.

The k-Disjoint Paths problem, which takes as input a graph G and k pairs of specified vertices (s i ,t i ), asks whether G contains k mutually vertex-disjoint paths P i such that P i connects s i and t i , for i = 1,…,k. We study a natural variant of this problem, where the vertices of P i must belong to a specified vertex subset U i for i = 1,…,k. In contrast to the original problem, which is polynomial-time solvable for any fixed integer k, we show that this variant is NP-complete even for k = 2. On the positive side, we prove that the problem becomes polynomial-time solvable for any fixed integer k if the input graph is chordal. We use this result to show that, for any fixed graph H, the problems H-Contractibility and H-Induced Minor can be solved in polynomial time on chordal graphs. These problems are to decide whether an input graph G contains H as a contraction or as an induced minor, respectively.

In this paper, we review our data mining algorithms for discovering frequent substructures in a large collection of semi-structured data, where both of the patterns and the data are modeled by labeled trees. These algorithms, namely FREQT for mining frequent ordered trees and UNOT for mining frequent unordered trees, efficiently enumerate all frequent tree patterns without duplicates using reverse search, which is a general scheme for designing efficient algorithms for hard enumeration problems, and incrementally compute of the occurrences of a pattern. We also discuss classes of trees to which reverse search is applicable, such as itemsets, sequential episodes, path trees, and graphs.

In this paper, we study a data mining problem of discovering frequent substructures in a large collection of semi-structured data, where both of the patterns and the data are modeled by labeled unordered trees. An unordered tree is a directed acyclic graph with a specified node called the root, and all nodes but the root have at most one parent. Each node is labeled by a symbol drawn from an alphabet. Such unordered trees can be seen as either a generalization of itemsets in relational databases or an efficient specialization of attributed graphs in graph mining. They are also useful in various applications such as analysis of chemical compounds and mining hyperlink structures in Web. Introducing novel definitions of the support and the canonical form for unordered trees, we present an efficient algorithm called Unot that computes all labeled unordered trees appearing in a collection of data trees with frequency above a user-specified threshold. We prove that the algorithm enumerates each frequent pattern T in $ O(kb^2n) $ per pattern, where $ k $ is the size of $ T $, $ b $ is the branching factor of the data tree, and $ n $ is the total number of occurrences of $ T $ in the data trees. The keys of the algorithm are efficient enumerating all unordered trees in canonical form and incrementally computation of the occurrences based on a powerful design technique known as the reverse search.

Article, 信州大学山地水環境教育研究センター研究報告 6: 11-12(2010)

資料番号: NALSP0012009, レポート番号: NAL SP-12

We show that for all integers t ≥ 8 and arbitrarily small ε > 0, there exists a graph property Π (which depends on ε) such that ε-testing Π has non-adaptive query complexity Q=Θ~(q^(2−2/t)), where q=Θ~(ϵ⁻¹) is the adaptive query complexity. This resolves the question of how beneficial adaptivity is, in the context of proximity-dependent properties. This also gives evidence that the canonical transformation of Goldreich and Trevisan is essentially optimal when converting an adaptive property tester to a non-adaptive property tester. To do so, we provide optimal adaptive and non-adaptive testers for the combined property of having maximum degree O(εN) and being a blow-up collection of an arbitrary base graph H.

A random geometric graph (RGG) is defined by placing n points uniformly at random in [0,n 1/d ] d , and joining two points by an edge whenever their Euclidean distance is at most some fixed r. We assume that r is larger than the critical value for the emergence of a connected component with Ω(n) nodes. We show that, with high probability (w.h.p.), for any two connected nodes with a Euclidean distance of $\omega (\frac{\log n}{r^{d-1}} )$ , their graph distance is only a constant factor larger than their Euclidean distance. This implies that the diameter of the largest connected component is Θ(n 1/d /r) w.h.p. We also prove that the condition on the Euclidean distance above is essentially tight. We also analyze the following randomized broadcast algorithm on RGGs. At the beginning, only one node from the largest connected component of the RGG is informed. Then, in each round, each informed node chooses a neighbor independently and uniformly at random and informs it. We prove that w.h.p. this algorithm informs every node in the largest connected component of an RGG within Θ(n 1/d /r+logn) rounds.