Independent Graph Research Articles

A novel link prediction algorithm for reconstructing protein–protein interaction networks by topological similarity

Recent advances in technology have dramatically increased the availability of protein-protein interaction (PPI) data and stimulated the development of many methods for improving the systems level understanding the cell. However, those efforts have been significantly hindered by the high level of noise, sparseness and highly skewed degree distribution of PPI networks. Here, we present a novel algorithm to reduce the noise present in PPI networks. The key idea of our algorithm is that two proteins sharing some higher-order topological similarities, measured by a novel random walk-based procedure, are likely interacting with each other and may belong to the same protein complex. Applying our algorithm to a yeast PPI network, we found that the edges in the reconstructed network have higher biological relevance than in the original network, assessed by multiple types of information, including gene ontology, gene expression, essentiality, conservation between species and known protein complexes. Comparison with existing methods shows that the network reconstructed by our method has the highest quality. Using two independent graph clustering algorithms, we found that the reconstructed network has resulted in significantly improved prediction accuracy of protein complexes. Furthermore, our method is applicable to PPI networks obtained with different experimental systems, such as affinity purification, yeast two-hybrid (Y2H) and protein-fragment complementation assay (PCA), and evidence shows that the predicted edges are likely bona fide physical interactions. Finally, an application to a human PPI network increased the coverage of the network by at least 100%. www.cs.utsa.edu/∼jruan/RWS/.

Brain network of semantic integration in sentence reading: Insights from independent component analysis and graph theoretical analysis

A set of cortical and sub-cortical brain structures has been linked with sentence-level semantic processes. However, it remains unclear how these brain regions are organized to support the semantic integration of a word into sentential context. To look into this issue, we conducted a functional magnetic resonance imaging (fMRI) study that required participants to silently read sentences with semantically congruent or incongruent endings and analyzed the network properties of the brain with two approaches, independent component analysis (ICA) and graph theoretical analysis (GTA). The GTA suggested that the whole-brain network is topologically stable across conditions. The ICA revealed a network comprising the supplementary motor area (SMA), left inferior frontal gyrus, left middle temporal gyrus, left caudate nucleus, and left angular gyrus, which was modulated by the incongruity of sentence ending. Furthermore, the GTA specified that the connections between the left SMA and left caudate nucleus as well as that between the left caudate nucleus and right thalamus were stronger in response to incongruent vs. congruent endings.

Resting-State fMRI: A Review of Methods and Clinical Applications

Resting-state fMRI measures spontaneous low-frequency fluctuations in the BOLD signal to investigate the functional architecture of the brain. Application of this technique has allowed the identification of various RSNs, or spatially distinct areas of the brain that demonstrate synchronous BOLD fluctuations at rest. Various methods exist for analyzing resting-state data, including seed-based approaches, independent component analysis, graph methods, clustering algorithms, neural networks, and pattern classifiers. Clinical applications of resting-state fMRI are at an early stage of development. However, its use in presurgical planning for patients with brain tumor and epilepsy demonstrates early promise, and the technique may have a future role in providing diagnostic and prognostic information for neurologic and psychiatric diseases.

An Algebraic Exploration of Dominating Sets and Vizing's Conjecture

Systems of polynomial equations are commonly used to model combinatorial problems such as independent set, graph coloring, Hamiltonian path, and others. We formulate the dominating set problem as a system of polynomial equations in two different ways: first, as a single, high-degree polynomial, and second as a collection of polynomials based on the complements of domination-critical graphs. We then provide a sufficient criterion for demonstrating that a particular ideal representation is already the universal Grobner bases of an ideal, and show that the second representation of the dominating set ideal in terms of domination-critical graphs is the universal Grobner basis for that ideal. We also present the first algebraic formulation of Vizing's conjecture, and discuss the theoretical and computational ramifications to this conjecture when using either of the two dominating set representations described above.

Maximal independent sets in caterpillar graphs

A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is # P — c o m p l e t e . We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (intersection graph of mis) and the clique graph (intersection graph of cliques) of complete caterpillar graphs.

On Achieving Local View Capacity Via Maximal Independent Graph Scheduling

"If we know more, we can achieve more." This adage also applies to communication networks, where more information about the network state translates into higher sumrates. In this paper, we formalize this increase of sum-rate with increased knowledge of the network state. The knowledge of network state is measured in terms of the number of hops, h, of information available to each transmitter and is labeled as h-local view. To understand how much capacity is lost due to limited information, we propose to use the metric of normalized sum-capacity, which is the h-local view sum-capacity divided by global-view sum capacity. For the cases of one and two-local view, we characterize the normalized sum-capacity for many classes of deterministic and Gaussian interference networks. In many cases, a scheduling scheme called maximal independent graph scheduling is shown to achieve normalized sum-capacity. We also show that its generalization for 1-local view, labeled coded set scheduling, achieves normalized sum-capacity in some cases where its uncoded counterpart fails to do so.

Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large , and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.

Maximal independent set graph partitions for representations of body-centered cubic lattices

A maximal independent set graph data structure for a body-centered cubic lattice is presented. Refinement and coarsening operations are defined in terms of set-operations resulting in robust and easy implementation compared to a quad-tree-based implementation. The graph only stores information corresponding to the leaves of a quad-tree thus has a smaller memory foot-print. The adjacency information in the graph relieves one from going up and down the quad-tree when searching for neighbors. This results in constant time complexities for refinement and coarsening operations.

The non-solvability by radicals of generic 3-connected planar Laman graphs

We show that planar embeddable 3-connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity. Formally, a Laman graph is a maximally independent graph, that is, one that satisfies the vertex-edge count 2v - 3 = e together with a corresponding inequality for each subgraph. The following main theorem of the paper resolves a conjecture of Owen (1991) in the planar case. Let G be a maximally independent 3-connected planar graph, with more than 3 vertices, together with a realisable assignment of generic distances for the edges which includes a normalised unit length (base) edge. Then, for any solution configuration for these distances on a plane, with the base edge vertices placed at rational points, not all coordinates of the vertices lie in a radical extension of the distance field.

Asynchronous NoC Router Design

The Quality of Service Network on Chip (QNoC) is the most perferment solution that provides low latency transfers and power efficient System on Chip (SoC) interconnect. This study presents an asynchronous NoC router, for use in 2-D mesh-connected networks. It comprises multiple interconnected input and output ports and dynamic arbitration mechanisms that resolve any output port conflicts based on the messages priorities. The proposed router protocol and its asynchronous modeling are based on the Speed Independent State Transition Graph (STG) model. The generated STG are transformed into VHDL data flow descriptions and the low level implementation is based onto a parameterized library. This library integrates the popular asynchronous SI modules such as C-element, Q-element, fairly arbiter, etc. The device is implemented in 0.35 µm CMOS technology and its performance is compared with a synchronous router of the same functionality. The asynchronous router enables a higher data rate and a comparable silicon area.

Assessing the joint effects of chlorinated dioxins, some pesticides and polychlorinated biphenyls on thyroid hormone status in Japanese breast‐fed infants

AbstractJoint effects of dioxin related chemicals (DXNs), hexachlorocyclohexanes (HCHs), DDT, dieldrin, heptachlor‐epoxide (HCE), chlordane and polychlorinated biphenyls (PCB) on the levels of triirodothyronine (T3), thyroxine (T4), thyroid stimulating hormones (TSH) and thyroid binding globulin (TBG) in the peripheral blood of 101 breast‐fed infants are studied. The statistical issue involved is how to estimate the effects based on data from volunteer subjects with possible measurement errors. A chain independent graph is applied for modeling the associations among factors, and dicotomizations of selected factors are performed for estimating the effects. Use of nonparametric methods with careful consideration of over‐adjustment is suggested. It is shown that the estimated odds ratios of DXNs∪DDT, the first principal component of DXNs and DDT, relative to TSH are 3.02 (p‐value=0.03) and 7.15 (p‐value=0.02), respectively, when PCB is not adjusted and adjusted for, respectively. Copyright © 2003 John Wiley & Sons, Ltd.

Tutorial on Surrogate Constraint Approaches for Optimization in Graphs

Surrogate constraint methods have been embedded in a variety of mathematical programming applications over the past thirty years, yet their potential uses and underlying principles remain incompletely understood by a large segment of the optimization community. In a number of significant domains of combinatorial optimization, researchers have produced solution strategies without recognizing that they can be derived as special instances of surrogate constraint methods. Once the connection to surrogate constraint ideas is exposed, additional ways to exploit this framework become visible, frequently offering opportunities for improvement. We provide a tutorial on surrogate constraint approaches for optimization in graphs, illustrating the key ideas by reference to independent set and graph coloring problems, including constructions for weighted independent sets which have applications to associated covering and weighted maximum clique problems. In these settings, the surrogate constraints can be generated relative to well-known packing and covering formulations that are convenient for exposing key notions. The surrogate constraint approaches yield widely used heuristics for identifying independent sets as simple special cases, and also afford previously unidentified heuristics that have greater power in these settings. Our tutorial also shows how the use of surrogate constraints can be placed within the context of vocabulary building strategies for independent set and coloring problems, providing a framework for applying surrogate constraints that can be used in other applications. At a higher level, we show how to make use of surrogate constraint information, together with specialized algorithms for solving associated sub-problems, to obtain stronger objective function bounds and improved choice rules for heuristic or exact methods. The theorems that support these developments yield further strategies for exploiting surrogate constraint relaxations, both in graph optimization and integer programming generally.

Forest Harvesting and Minimum Cuts: A New Approach to Handling Spatial Constraints

Abstract In this paper we discuss two forest harvesting optimization problems that arise in forest management. We consider one-stage decision problems in which the forest to be managed is partitioned into cells and the decision is to be made as to which cells to harvest. There are competing concerns to consider in assessing the value of a particular harvesting decision: the first has to do with the value of the timber harvested, and the second has to do with assessing the relative values of the resulting spatial layout from a wildlife habitat point of view. The two problems that we consider are similar, but they assess the relative merits of resulting spatial layouts somewhat differently and therefore have different objective functions to be optimized. The first problem we consider assigns benefits for harvesting cells and penalties for harvesting adjacent cells; the second problem considered assigns benefits for harvesting cells as well as benefits for creating borders that separate harvested and unharvested cells. We show that both forest harvesting problems can be interpreted as instances of the Generalized Independent Set graph optimization problem, which we introduce in this article. Generalized Independent Set is a generalization of the well-known Independent Set graph optimization problem (a set of nodes in a graph is said to be independent if no two nodes in the set are adjacent). When the underlying graph is bipartite, we derive an efficient solution method for Generalized Independent Set via network flow methods. If the cell structure is grid-like in the forest harvesting problems, then an instance of either forestry problem can be reduced to an instance of Generalized Independent Set on a bipartite graph. For such instances we developed efficient algorithms for determining an optimal harvesting strategy. The running time is O(n² log n), where n is the number of cells in the land area to be spatially managed. For. Sci. 43(4):544-554.

Linear time algorithms for NP-hard problems restricted to partial k-trees

We present and illustrate by a sequence of examples an algorithm paradigm for solving NP- hard problems on graphs restricted to partial graphs of k-trees and given with an embedding in a k-tree. Such algorithms, linear in the size of the graph but exponential or superexponential in k, exist for most NP-hard problems that have linear time algorithms for trees. The examples used are optimization problems involving independent sets, dominating sets, graph coloring, Hamiltonian circuits, network reliability and minimum vertex deletion forbidden subgraphs. The results generalize previous results for series-parallel graphs, bandwidth-constrained graphs, and non- serial dynamic programming.