Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks

We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the network. The heterogeneous-$k$-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds $k_i$ are $1$ with probability $f$ or $k \geq 3$ with probability $(1-f)$, the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-$k$-core process: the giant heterogeneous-$k$-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-$k$-core and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-$k$-core appearing immediately at a finite value for any $f > 0$ when the degree distribution tends to a power law $P(q) \sim q^{-\gamma}$ with $\gamma < 3$.Comment: 10 pages, 4 figure

The entropy of randomized network ensembles

Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same degree-correlations or the same community structure of any given real network. We characterize these randomized network ensembles by their entropy, i.e. the normalized logarithm of the total number of networks which are part of these ensembles. We estimate the entropy of randomized ensembles starting from a large set of real directed and undirected networks. We propose entropy as an indicator to assess the role of each structural feature in a given real network.We observe that the ensembles with fixed scale-free degree distribution have smaller entropy than the ensembles with homogeneous degree distribution indicating a higher level of order in scale-free networks.Comment: (6 pages,1 figure,2 tables

A CpG island hypermethylation profile of primary colorectal carcinomas and colon cancer cell lines

BACKGROUND: Tumor cell lines are commonly used as experimental tools in cancer research, but their relevance for the in vivo situation is debated. In a series of 11 microsatellite stable (MSS) and 9 microsatellite unstable (MSI) colon cancer cell lines and primary colon carcinomas (25 MSS and 28 MSI) with known ploidy stem line and APC, KRAS, and TP53 mutation status, we analyzed the promoter methylation of the following genes: hMLH1, MGMT, p16(INK4a )(CDKN2A α-transcript), p14(ARF )(CDKN2A β-transcript), APC, and E-cadherin (CDH1). We compared the DNA methylation profiles of the cell lines with those of the primary tumors. Finally, we examined if the epigenetic changes were associated with known genetic markers and/or clinicopathological variables. RESULTS: The cell lines and primary tumors generally showed similar overall distribution and frequencies of gene methylation. Among the cell lines, 15%, 50%, 75%, 65%, 20% and 15% showed promoter methylation for hMLH1, MGMT, p16(INK4a), p14(ARF), APC, and E-cadherin, respectively, whereas 21%, 40%, 32%, 38%, 32%, and 40% of the primary tumors were methylated for the same genes. hMLH1 and p14(ARF )were significantly more often methylated in MSI than in MSS primary tumors, whereas the remaining four genes showed similar methylation frequencies in the two groups. Methylation of p14(ARF), which indirectly inactivates TP53, was seen more frequently in tumors with normal TP53 than in mutated samples, but the difference was not statistically significant. Methylation of p14(ARF )and p16(INK4a )was often present in the same primary tumors, but association to diploidy, MSI, right-sided location and female gender was only significant for p14(ARF). E-cadherin was methylated in 14/34 tumors with altered APC further stimulating WNT signaling. CONCLUSIONS: The present study shows that colon cancer cell lines are in general relevant in vitro models, comparable with the in vivo situation, as the cell lines display many of the same molecular alterations as do the primary carcinomas. The combined pattern of epigenetic and genetic aberrations in the primary carcinomas reveals associations between them as well as to clinicopathological variables, and may aid in the future molecular assisted classification of clinically distinct stages

Rhythmogenic neuronal networks, pacemakers, and k-cores

Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the breathing rhythm of mammals through periodic firing bursts. We show that the properties of a such a randomly connected network of identical excitatory neurons are fundamentally different from those of uniformly connected neuronal networks as described by mean-field theory. We show that (i) the connectivity properties of the networks determines the location of emergent pacemakers that trigger the firing bursts and (ii) that the collective desensitization that terminates the firing bursts is determined again by the network connectivity, through k-core clusters of neurons.Comment: 4+ pages, 4 figures, submitted to Phys. Rev. Let

Organization of modular networks

We examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts--``communities'' or modules. We develop an analytical approach allowing us to obtain the statistics of connected components and an intervertex distance distribution in these modular networks, and to describe their global organization and structure. In particular, we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks. We demonstrate that even a relatively small number of shortcuts unite the networks into one. In more precise terms, if the number of the interlinks is any finite fraction of the total number of connections, then the intervertex distance distribution approaches a delta-function peaked form, and so the network is united.Comment: 9 pages, 3 figure

Critical phenomena in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende

Identification of chlamydomonas central core centriolar proteins reveals a role for human WDR90 in ciliogenesis

Centrioles are evolutionarily conserved macromolecular structures that are fundamental to form cilia, flagella, and centrosomes. Centrioles are 9-fold symmetrical microtubule-based cylindrical barrels comprising three regions that can be clearly distinguished in the Chlamydomonas reinhardtii organelle: an ∼100-nm-long proximal region harboring a cartwheel; an ∼250-nm-long central core region containing a Y-shaped linker; and an ∼150-nm-long distal region ending at the transitional plate. Despite the discovery of many centriolar components, no protein has been localized specifically to the central core region in Chlamydomonas thus far. Here, combining relative quantitative mass spectrometry and super-resolution microscopy on purified Chlamydomonas centrioles, we identified POB15 and POC16 as two proteins of the central core region, the distribution of which correlates with that of tubulin glutamylation. We demonstrated that POB15 is an inner barrel protein within this region. Moreover, we developed an assay to uncover temporal relationships between centriolar proteins during organelle assembly and thus established that POB15 is recruited after the cartwheel protein CrSAS-6 and before tubulin glutamylation takes place. Furthermore, we discovered that two poc16 mutants exhibit flagellar defects, indicating that POC16 is important for flagellum biogenesis. In addition, we discovered that WDR90, the human homolog of POC16, localizes to a region of human centrioles that we propose is analogous to the central core of Chlamydomonas centrioles. Moreover, we demonstrate that WDR90 is required for ciliogenesis, echoing the findings in Chlamydomonas. Overall, our work provides novel insights into the identity and function of centriolar central core components

Finding needles in haystacks: linking scientific names, reference specimens and molecular data for Fungi

DNA phylogenetic comparisons have shown that morphology-based species recognition often underestimates fungal diversity. Therefore, the need for accurate DNA sequence data, tied to both correct taxonomic names and clearly annotated specimen data, has never been greater. Furthermore, the growing number of molecular ecology and microbiome projects using high-throughput sequencing require fast and effective methods for en masse species assignments. In this article, we focus on selecting and re-annotating a set of marker reference sequences that represent each currently accepted order of Fungi. The particular focus is on sequences from the internal transcribed spacer region in the nuclear ribosomal cistron, derived from type specimens and/or ex-type cultures. Re-annotated and verified sequences were deposited in a curated public database at the National Center for Biotechnology Information (NCBI), namely the RefSeq Targeted Loci (RTL) database, and will be visible during routine sequence similarity searches with NR_prefixed accession numbers. A set of standards and protocols is proposed to improve the data quality of new sequences, and we suggest how type and other reference sequences can be used to improve identification of Fungi

Louisville Seamount Trail: implications for geodynamic mantle flow models and the geochemical evolution of primary hotspots

The Louisville Seamount Trail is a 4300 km long volcanic chain that has been built in the past 80 m.y. as the Pacific plate moved over a persistent mantle melting anomaly or hotspot. Because of its linear morphology and its long-lived age-progressive volcanism, Louisville is the South Pacific counterpart of the much better studied Hawaiian-Emperor Seamount Trail. Together, Louisville and Hawaii are textbook examples of two primary hotspots that have been keystones in deciphering the motion of the Pacific plate relative to a set of "fixed" deep-mantle plumes. However, drilling during Ocean Drilling Program (ODP) Leg 197 in the Emperor Seamounts documented a large ~15° southward motion of the Hawaiian hotspot prior to 50 Ma. Is it possible that the Hawaiian and Louisville hotspots moved in concert and thus constitute a moving reference frame for modeling plate motion in the Pacific? Alternatively, could they have moved independently, as predicted by mantle flow models that reproduce the observed latitudinal motion for Hawaii but that predict a largely longitudinal shift for the Louisville hotspot? These two end-member geodynamic models were tested during Integrated Ocean Drilling Program (IODP) Expedition 330 to the Louisville Seamount Trail. In addition, existing data from dredged lavas suggest that the mantle plume source of the Louisville hotspot has been remarkably homogeneous for as long as 80 m.y. These lavas are predominantly alkali basalts and likely represent a mostly alkalic shield-building stage, which is in sharp contrast to the massive tholeiitic shield-building stage of Hawaiian volcanoes. Geochemical and isotopic data for the recovered lavas during Expedition 330 will provide insights into the magmatic evolution and melting processes of individual Louisville volcanoes, their progression from shield-building to postshield and (maybe) posterosional stages, the temperature and depth of partial melting of their mantle plume source, and the enigmatic long-lived and apparent geochemical homogeneity of the Louisville mantle source. Collectively, this will enable us to characterize the Louisville Seamount Trail as a product of one of the few global primary hotspots, to better constrain its plume-lithosphere interactions, and to further test the hypothesis that the Ontong Java Plateau formed from the plume head of the Louisville mantle plume around 120 Ma. During Expedition 330 we replicated the drilling strategy of Leg 197, the first expedition to provide compelling evidence for the motion of the Hawaiian mantle plume between 80 and 50 Ma. For that reason we targeted Louisville seamounts that have ages similar to Detroit, Suiko, Nintoku, and Koko Seamounts in the Emperor Seamount Trail. In total, five seamounts were drilled in the Louisville Seamount Trail: Canopus, Rigil, Burton, Achernar, and Hadar Guyots (old to young). By analyzing a large number of time-independent in situ lava flows (and other volcanic eruptive products) from these seamounts using modern paleomagnetic, 40Ar/39Ar geochronological, and geochemical techniques, we will be able to directly compare the paleolatitude estimates and geochemical signatures between the two longest-lived hotspot systems in the Pacific Ocean. We drilled into the summits of the five Louisville guyots and reached volcanic basement at four of these drilling targets. In two cases we targeted larger seamount structures and drilled near the flanks of these ancient volcanoes, and in the other three cases we selected smaller edifices that we drilled closer to their centers. Drilling and logging plans for each of these sites were similar, with coring reaching 522.0 meters below seafloor (mbsf) for Site U1374 and 232.9, 65.7, 11.5, 182.8, and 53.3 mbsf for Sites U1372, U1373, U1375, U1376, and U1377, respectively. Some Expedition 330 drill sites were capped with only a thin layer of pelagic ooze between 6.6 and 13.5 m thick, and, if present, these were cored by using a low-rotation gravity-push technique with the rotary core barrel to maximize recovery. However, at Sites U1373 and U1376 no pelagic ooze was present, and the holes needed to be started directly into cobble-rich hardgrounds. In all cases, the bulk of the seamount sediment cover comprised sequences of volcanic sandstones and various kinds of basalt breccia or basalt conglomerate, which often were interspersed with basaltic lava flows, the spatter/tephra products of submarine eruptions, or other volcanic products, including auto-brecciated flows or peperites. Also several intervals of carbonate were cored, with the special occurrence of a ~15 m thick algal limestone reef at Site U1376 on Burton Guyot. In addition, some condensed pelagic limestone units were recovered on three of the other seamounts, but these did not exceed 30 cm in thickness. Despite their limited presence in the drilled sediment, these limestones provide valuable insights for the paleoclimate record at high ~50° southern latitudes since Mesozoic times. Several Louisville sites progressed from subaerial conditions in the top of volcanic basement into submarine eruptive environments, or drilling of the igneous basement immediately started in submarine volcanic sequences, as was the case for Sites U1376 and U1377 on Burton and Hadar Guyots. At three sites we cored >100 m into the igneous basement: 187.3 m at Site U1372, 505.3 m at Site U1374, and 140.9 m at Site U1376. At the other sites we did not core into basement (Site U1375) or we cored only 38.2 m (Site U1377) because of unstable hole conditions. Even so, drilling during Expedition 330 resulted in a large number of in situ lava flows, pillow basalts, or other types of volcanic products such as auto-brecciated lava flows, intrusive sheets or dikes, and peperites. In particular, the three holes on Canopus and Rigil Guyots (the two oldest seamounts drilled in the Louisville Seamount Trail), resulted in adequate numbers of in situ lava flows to average out paleosecular variation, with probable eruption ages estimated at ~78 and 73 Ma, respectively. Remarkably, at all drill sites large quantities of hyaloclastites, volcanic sandstones, and basaltic breccias were also recovered, which in many cases show consistent paleomagnetic inclinations compared to the lava flows bracketing these units. For Site U1374 on Rigil Guyot we also observed a magnetic polarity reversal in the cored sequence. Overall, this is very promising for determining a reliable paleolatitude record for the Louisville Seamounts following detailed postcruise examinations. The deeper penetrations of several hundred meters required bit changes and reentries using free-fall funnels. Basement penetration rates were 1.8–2.5 m/h depending on drill depth. In total, 1114 m of sediment and igneous basement at five seamounts was drilled, and 806 m was recovered (average recovery = 72.4%). At Site U1374 on Rigil Guyot, a total of 522 m was drilled, with a record-breaking 87.8% recovery. Most outstandingly, nearly all Expedition 330 core material is characterized by low degrees of alteration, providing us with a large quantity of samples of mostly well-preserved basalt, containing, for example, pristine olivine crystals with melt inclusions, fresh volcanic glass, unaltered plagioclase, carbonate, zeolite and celadonite alteration minerals, various micro- and macrofossils, and, in one case, mantle xenoliths and xenocrysts. The large quantity and excellent quality of the recovered sample material allow us to address all the scientific objectives of this expedition and beyond

High methylmercury in Arctic and subarctic ponds is related to nutrient levels in the warming eastern Canadian Arctic

Permafrost thaw ponds are ubiquitous in the eastern Canadian Arctic, yet little information exists on their potential as sources of methylmercury (MeHg) to freshwaters. They are microbially active and conducive to methylation of inorganic mercury, and are also affected by Arctic warming. This multiyear study investigated thaw ponds in a discontinuous permafrost region in the Subarctic taiga (Kuujjuarapik-Whapmagoostui, QC) and a continuous permafrost region in the Arctic tundra (Bylot Island, NU). MeHg concentrations in thaw ponds were well above levels measured in most freshwater ecosystems in the Canadian Arctic (>0.1 ng L−1). On Bylot, ice-wedge trough ponds showed significantly higher MeHg (0.3−2.2 ng L−1) than polygonal ponds (0.1−0.3 ng L−1) or lakes (<0.1 ng L−1). High MeHg was measured in the bottom waters of Subarctic thaw ponds near Kuujjuarapik (0.1−3.1 ng L−1). High water MeHg concentrations in thaw ponds were strongly correlated with variables associated with high inputs of organic matter (DOC, a320, Fe), nutrients (TP, TN), and microbial activity (dissolved CO2 and CH4). Thawing permafrost due to Arctic warming will continue to release nutrients and organic carbon into these systems and increase ponding in some regions, likely stimulating higher water concentrations of MeHg. Greater hydrological connectivity from permafrost thawing may potentially increase transport of MeHg from thaw ponds to neighboring aquatic ecosystems