Random Graph Coloring - a Statistical Physics Approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the 2-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges.Comment: 17 pages, 9 figure

Ploidy Reductions in Murine Fusion-Derived Hepatocytes

We previously showed that fusion between hepatocytes lacking a crucial liver enzyme, fumarylacetoacetate hydrolase (FAH), and wild-type blood cells resulted in hepatocyte reprogramming. FAH expression was restored in hybrid hepatocytes and, upon in vivo expansion, ameliorated the effects of FAH deficiency. Here, we show that fusion-derived polyploid hepatocytes can undergo ploidy reductions to generate daughter cells with one-half chromosomal content. Fusion hybrids are, by definition, at least tetraploid. We demonstrate reduction to diploid chromosome content by multiple methods. First, cytogenetic analysis of fusion-derived hepatocytes reveals a population of diploid cells. Secondly, we demonstrate marker segregation using ß-galactosidase and the Y-chromosome. Approximately 2–5% of fusion-derived FAH-positive nodules were negative for one or more markers, as expected during ploidy reduction. Next, using a reporter system in which ß-galactosidase is expressed exclusively in fusion-derived hepatocytes, we identify a subpopulation of diploid cells expressing ß-galactosidase and FAH. Finally, we track marker segregation specifically in fusion-derived hepatocytes with diploid DNA content. Hemizygous markers were lost by ≥50% of Fah-positive cells. Since fusion-derived hepatocytes are minimally tetraploid, the existence of diploid hepatocytes demonstrates that fusion-derived cells can undergo ploidy reduction. Moreover, the high degree of marker loss in diploid daughter cells suggests that chromosomes/markers are lost in a non-random fashion. Thus, we propose that ploidy reductions lead to the generation of genetically diverse daughter cells with about 50% reduction in nuclear content. The generation of such daughter cells increases liver diversity, which may increase the likelihood of oncogenesis

Network conduciveness with application to the graph-coloring and independent-set optimization transitions

We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another. We exemplify its use through an application to the two problems in combinatorial optimization that, given an undirected graph, ask that its so-called chromatic and independence numbers be found. Though NP-hard, when solved on sequences of expanding random graphs there appear marked transitions at which optimal solutions can be obtained substantially more easily than right before them. We demonstrate that these phenomena can be understood by resorting to the network that represents the solution space of the problems for each graph and examining its conduciveness between the non-optimal solutions and the optimal ones. At the said transitions, this network becomes strikingly more conducive in the direction of the optimal solutions than it was just before them, while at the same time becoming less conducive in the opposite direction. We believe that, besides becoming useful also in other areas in which network theory has a role to play, network conduciveness may become instrumental in helping clarify further issues related to NP-hardness that remain poorly understood

Iterative focused screening with biological fingerprints identifies selective Asc-1 inhibitors distinct from traditional high throughput screening

N-methyl-d-aspartate receptors (NMDARs) mediate glutamatergic signaling that is critical to cognitive processes in the central nervous system, and NMDAR hypofunction is thought to contribute to cognitive impairment observed in both schizophrenia and Alzheimer’s disease. One approach to enhance the function of NMDAR is to increase the concentration of an NMDAR coagonist, such as glycine or d-serine, in the synaptic cleft. Inhibition of alanine–serine–cysteine transporter-1 (Asc-1), the primary transporter of d-serine, is attractive because the transporter is localized to neurons in brain regions critical to cognitive function, including the hippocampus and cortical layers III and IV, and is colocalized with d-serine and NMDARs. To identify novel Asc-1 inhibitors, two different screening approaches were performed with whole-cell amino acid uptake in heterologous cells stably expressing human Asc-1: (1) a high-throughput screen (HTS) of 3 M compounds measuring 35S l-cysteine uptake into cells attached to scintillation proximity assay beads in a 1536 well format and (2) an iterative focused screen (IFS) of a 45 000 compound diversity set using a 3H d-serine uptake assay with a liquid scintillation plate reader in a 384 well format. Critically important for both screening approaches was the implementation of counter screens to remove nonspecific inhibitors of radioactive amino acid uptake. Furthermore, a 15 000 compound expansion step incorporating both on- and off-target data into chemical and biological fingerprint-based models for selection of additional hits enabled the identification of novel Asc-1-selective chemical matter from the IFS that was not identified in the full-collection HTS

Recognizing Treelike k-Dissimilarities

A k-dissimilarity D on a finite set X, |X| >= k, is a map from the set of size k subsets of X to the real numbers. Such maps naturally arise from edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y) is defined to be the total length of the smallest subtree of T with leaf-set Y . In case k = 2, it is well-known that 2-dissimilarities arising in this way can be characterized by the so-called "4-point condition". However, in case k > 2 Pachter and Speyer recently posed the following question: Given an arbitrary k-dissimilarity, how do we test whether this map comes from a tree? In this paper, we provide an answer to this question, showing that for k >= 3 a k-dissimilarity on a set X arises from a tree if and only if its restriction to every 2k-element subset of X arises from some tree, and that 2k is the least possible subset size to ensure that this is the case. As a corollary, we show that there exists a polynomial-time algorithm to determine when a k-dissimilarity arises from a tree. We also give a 6-point condition for determining when a 3-dissimilarity arises from a tree, that is similar to the aforementioned 4-point condition.Comment: 18 pages, 4 figure

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Causal Set Dynamics: A Toy Model

We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any analogue in classical percolation. Most notably, instead of the single phase transition of classical percolation, the quantum model displays two distinct crossover points. Between these two points, spacetime questions such as "does the network percolate" have no definite or probabilistic answer.Comment: 28 pages incl. 5 figure

Evidence of Weak Habitat Specialisation in Microscopic Animals

Macroecology and biogeography of microscopic organisms (any living organism smaller than 2 mm) are quickly developing into fruitful research areas. Microscopic organisms also offer the potential for testing predictions and models derived from observations on larger organisms due to the feasibility of performing lab and mesocosm experiments. However, more empirical knowledge on the similarities and differences between micro- and macro-organisms is needed to ascertain how much of the results obtained from the former can be generalised to the latter. One potential misconception, based mostly on anedoctal evidence rather than explicit tests, is that microscopic organisms may have wider ecological tolerance and a lower degree of habitat specialisation than large organisms. Here we explicitly test this hypothesis within the framework of metacommunity theory, by studying host specificify in the assemblages of bdelloid rotifers (animals about 350 µm in body length) living in different species of lichens in Sweden. Using several regression-based and ANOVA analyses and controlling for both spatial structure and the kind of substrate the lichen grow over (bark vs rock), we found evidence of significant but weak species-specific associations between bdelloids and lichens, a wide overlap in species composition between lichens, and wide ecological tolerance for most bdelloid species. This confirms that microscopic organisms such as bdelloids have a lower degree of habitat specialisation than larger organisms, although this happens in a complex scenario of ecological processes, where source-sink dynamics and geographic distances seem to have no effect on species composition at the analysed scale

Nutrients, oxygen and inferred new production in the Northeast Water Polynya 1992

Nutrient and oxygen distributions were measured during a hydrographic survey of the Northeast Water Polynya off the northeast coast of Greenland (77–81°N, 6–17°W) during July–August 1992 and were interpreted in the context of satellite imagery of the region. Satellite imagery revealed a convoluted plume of cold water flowing along isobaths from underneath fast ice in the southwestern portion of the polynya toward the northeast. This plume carried relatively high nutrient and low oxygen inventories. Nitrate to phosphate ratios were low in the polar water, consistent with an ultimate source of this water mass in the Pacific sector of the Arctic Ocean. It is hypothesized that the low N:P Arctic outflow might be the cause of nitrate limitation along the east coast of America as far as Cape Hatteras. Gradients of both nutrients and oxygen inventories in the euphotic zone were observed along and across the axis of mean flow within the polynya and are shown to be due to net production of organic matter. On the basis of these spatial gradients of nitrate and oxygen, an assumed along-axis current velocity of 10 cm s−1, and the observed relationships of biologically removed inorganic carbon with nitrate and oxygen, the net organic matter production was estimated to be 40–60 mmol(C) m−2 d−1. This represents the organic carbon available for export from the polynya euphotic zone. Nutrient-deficient and oxygen-rich waters were observed merging with the southward flowing East Greenland Current, suggestive of possible export, however, the ultimate fate of organic carbon produced within the polynya requires further study