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PubMed2002

Global organization of the Wordnet lexicon.

The lexicon consists of a set of word meanings and their semantic relationships. A systematic representation of the English lexicon based in psycholinguistic considerations has been put together in the database Wordnet in a long-term collaborative effort. We present here a quantitative study of the graph structure of Wordnet to understand the global organization of the lexicon. Semantic links follow power-law, scale-invariant behaviors typical of self-organizing networks. Polysemy (the ambiguity of an individual word) is one of the links in the semantic network, relating the different meanings of a common word. Polysemous links have a profound impact in the organization of the semantic graph, conforming it as a small world network, with clusters of high traffic (hubs) representing abstract concepts such as line, head, or circle. Our results show that: (i) Wordnet has global properties common to many self-organized systems, and (ii) polysemy organizes the semantic graph in a compact and categorical representation, in a way that may explain the ubiquity of polysemy across languages.

Cluster Analysis↗
PubMed2005

Circuit topology and the evolution of robustness in two-gene circadian oscillators.

Many parameters driving the behavior of biochemical circuits vary extensively and are thus not fine-tuned. Therefore, the topology of such circuits (the who-interacts-with-whom) is key to understanding their central properties. I here explore several hundred different topologies of a simple biochemical model of circadian oscillations to ask two questions: Do different circuits differ dramatically in their robustness to parameter change? If so, can a process of gradual molecular evolution find highly robust topologies when starting from less robust topologies? I find that the distribution of robustness among different circuit topologies is highly skewed: Most show low robustness, whereas very few topologies are highly robust. To address the second evolutionary question, I define a topology graph, each of whose nodes corresponds to one circuit topology that shows circadian oscillations. Two nodes in this graph are connected if they differ by only one regulatory interaction within the circuit. For the circadian oscillator I study, most topologies are connected in this graph, making evolutionary transitions from low to high robustness easy. A similar approach has been used to study the evolution of robustness in biological macromolecules, with similar results. This suggests that the same principles govern the evolution of robustness on different levels of biological organization. The regulatory interlocking of several oscillating gene products in biological circadian oscillators may exist because it provides robustness.

Biological Clocks↗
PubMed2005

Subnets of scale-free networks are not scale-free: sampling properties of networks.

Most studies of networks have only looked at small subsets of the true network. Here, we discuss the sampling properties of a network's degree distribution under the most parsimonious sampling scheme. Only if the degree distributions of the network and randomly sampled subnets belong to the same family of probability distributions is it possible to extrapolate from subnet data to properties of the global network. We show that this condition is indeed satisfied for some important classes of networks, notably classical random graphs and exponential random graphs. For scale-free degree distributions, however, this is not the case. Thus, inferences about the scale-free nature of a network may have to be treated with some caution. The work presented here has important implications for the analysis of molecular networks as well as for graph theory and the theory of networks in general.

Journal Article↗
PubMed2006

Evolutionary dynamics of social dilemmas in structured heterogeneous populations.

Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.

Biological Evolution↗
PubMed1977

Food webs and the dimensionality of trophic niche space.

If the trophic niche of a kind of organism is a connected region in niche space, then it is possible for trophic niche overlaps to be described in a one-dimensional niche space if and only if the trophic niche overlap graph is an interval graph. An analysis of 30 food webs, using the combinatorial theory of interval graphs, suggests that a niche space of dimension 1 suffices, with unexpectedly high frequency and perhaps always, to describe the trophic niche overlaps implied by real food webs in single habitats. Consequently, real food webs fall in a small subset of the set of mathematically possible food webs. That real food webs are compatible with one-dimensional trophic niche spaces, more often than can be explained by chance alone, has not been noticed previously.

Journal Article↗
PubMed1987

Conformational analysis of the deoxyribofuranose ring in DNA by means of sums of proton-proton coupling constants: a graphical method.

A graphical method is presented for the conformational analysis of the sugar ring in DNA fragments by means of proton-proton couplings. The coupling data required for this analysis consist of sums of couplings, which are referred to as sigma 1' (= J1'2' + J1'2''), sigma 2' (= J1'2' + J2'3' + J2'2''), sigma 2'' (= J1'2'' + J2''3' + J2'2'') and sigma 3' (= J2'3' + J2''3' + J3'4'). These sums of couplings correspond to the distance between the outer peaks of the H1', H2', H2'' and H3' [31P] resonances, respectively, (except for sigma 2' and sigma 2'' in the case of a small chemical shift difference between the H2' and H2'' resonances) and can often be obtained from 1H-NMR spectra via first-order measurement, obviating the necessity of a computer-assisted simulation of the fine structure of these resonances. Two different types of graphs for the interpretation of the coupling data are discussed: the first type of graph serves to probe as to whether or not the sugar ring occurs as a single conformer, and if so to analyze the coupling data in terms of the geometry of this sugar ring. In cases where the sugar ring does not occur as a single conformer, but as a blend of N- and S-type sugar puckers, the second type of graph is used to analyze the coupling data in terms of the geometry and population of the most abundant form. It is shown that the latter type of analysis can be carried out on the basis of experimental values for merely sigma 1',sigma 2' and sigma 2'', without any assumptions or restrictions concerning a relation between the geometry of the N- and S-type conformer. In addition, the question is discussed as to how insight can be gained into the conformational purity of the sugar ring from the observed fine structure of the H1' resonance. Finally, a comparison is made between experimental coupling data reported for single-stranded and duplex DNA fragments and covalent RNA-DNA hybrids on the one hand and the predicted couplings and sums of couplings presented in this paper on the other hand.

Computer Graphics↗
PubMed1995

Prediction of traffic noise: a screening technique.

Traffic noise is ubiquitous in many communities and is an important environmental concern, especially for persons located near major roadways. Several different methods are available to estimate noise levels resulting from roadway traffic. These include computational, graphical, and computer modeling techniques. The prediction methodology presented here is a simplified technique that can be used for estimating noise resulting from traffic and for screening traffic noise impacts. This Traffic Noise Screening (TNS) approach consists of a series of traffic noise level prediction graphs developed for different roadway configurations. The graphs are based on the results from using the Federal Highway Administration (FHWA) STAMINA2.0 computerized noise prediction model for various scenarios. Data inputs to the TNS approach include roadway genometries, traffic volumes, vehicle travel speed, and centerline distance to the receptors. The TNS graphs allow easy estimation of traffic noise levels for use in predicting traffic-related noise impacts. This TNS approach is not intended as a substitute for detailed modeling, such as with STAMINA2.0, but as a screening tool to aid in determining when detailed modeling may be necessary. If screening results indicate that noise estimates are significant, or if the scenario is rather complex, then additional, more detailed modeling can be performed.

Automobiles↗
PubMed1998

Comparison of benzodiazepine-like compounds using topological analysis and genetic algorithms.

Four compounds within a set of ligands for the benzodiazepine receptors are characterized by their electron density maps at different resolution levels and reconstructed from calculated structure factors. The resulting complex three-dimensional density maps are first simplified into connected graphs using topological analysis. Then, an original genetic algorithm method, GAGS (Genetic Algorithm for Graph Similarity search), is developed and implemented in order to compare the connected graphs. Finally, the analysis of the best solutions of the algorithm are expressed in terms of functional group superimpositions. The GAGS analysis is applied to different resolution levels of the electron density maps and the resulting models are compared in order to assess the influence of the resolution on the resulting pharmacophore models.

Algorithms↗
PubMed2006

The influence of graphic format on breast cancer risk communication.

Graphic displays can enhance quantitative risk communication. However, empiric data regarding the effect of graphic format on risk perception is lacking. We evaluate the effect of graphic format elements on perceptions of risk magnitude and perceived truth of data. Preferences for format also were assessed. Participants (254 female primary care patients) viewed a series of hypothetical risk communications regarding the lifetime risk of breast cancer. Identical numeric risk information was presented using different graphic formats. Risk was perceived to be of lower magnitude when communicated with a bar graph as compared with a pictorial display (p < 0.0001), or with consecutively versus randomly highlighted symbols in a pictorial display (p = 0.0001). Data were perceived to be more true when presented with random versus consecutive highlights in a pictorial display (p < 0.01). A pictorial display was preferred to a bar graph format for the presentation of breast cancer risk estimates alone (p = 0.001). When considering breast cancer risk in comparison to heart disease, stroke, and osteoporosis, however, bar graphs were preferred pictorial displays (p < 0.001). In conclusion, elements of graphic format used to convey quantitative risk information effects key domains of risk perception. One must be cognizant of these effects when designing risk communication strategies.

Adult↗
PubMed1998

Measures of operator performance in complex, dynamic microworlds: advancing the state of the art.

Microworld research provides a useful complement to field studies and highly controlled laboratory studies, aiming to strike a balance between representativeness and experimental control. Yet microworld research has associated methodological difficulties, particularly the problem of performance measurement. Researchers generally adopt a variety of measures to provide converging evidence concerning questions of interest. To confront problems with existing measures, this paper examines a series of objective measures used to characterize the performance of human operators in process control. These measures include novel, quantitative extensions to existing graphical analyses and new graphical representations. The measures are applied in the context of a 6-month longitudinal study using an interactive, thermal-hydraulic process control microworld (DURESS II). The following measures are discussed: steady-state time, action transition graph complexity, the path length in state space diagrams, the area under distance-to-goals graphs, divergence from the temperature goal line in mass inventory versus energy inventory graphs, and the proportion of control actions near the beginning of the trials represented by timelines. Two case studies emphasize the performance and strategy differences of individual operators across the battery of measures.

Adult↗
PubMed2001

A linear-time algorithm for computing inversion distance between signed permutations with an experimental study.

Hannenhalli and Pevzner gave the first polynomial-time algorithm for computing the inversion distance between two signed permutations, as part of the larger task of determining the shortest sequence of inversions needed to transform one permutation into the other. Their algorithm (restricted to distance calculation) proceeds in two stages: in the first stage, the overlap graph induced by the permutation is decomposed into connected components; then, in the second stage, certain graph structures (hurdles and others) are identified. Berman and Hannenhalli avoided the explicit computation of the overlap graph and gave an O(nalpha(n)) algorithm, based on a Union-Find structure, to find its connected components, where alpha is the inverse Ackerman function. Since for all practical purposes alpha(n) is a constant no larger than four, this algorithm has been the fastest practical algorithm to date. In this paper, we present a new linear-time algorithm for computing the connected components, which is more efficient than that of Berman and Hannenhalli in both theory and practice. Our algorithm uses only a stack and is very easy to implement. We give the results of computational experiments over a large range of permutation pairs produced through simulated evolution; our experiments show a speed-up by a factor of 2 to 5 in the computation of the connected components and by a factor of 1.3 to 2 in the overall distance computation.

Algorithms↗
PubMed2003

Stochastic roadmap simulation: an efficient representation and algorithm for analyzing molecular motion.

Classic molecular motion simulation techniques, such as Monte Carlo (MC) simulation, generate motion pathways one at a time and spend most of their time in the local minima of the energy landscape defined over a molecular conformation space. Their high computational cost prevents them from being used to compute ensemble properties (properties requiring the analysis of many pathways). This paper introduces stochastic roadmap simulation (SRS) as a new computational approach for exploring the kinetics of molecular motion by simultaneously examining multiple pathways. These pathways are compactly encoded in a graph, which is constructed by sampling a molecular conformation space at random. This computation, which does not trace any particular pathway explicitly, circumvents the local-minima problem. Each edge in the graph represents a potential transition of the molecule and is associated with a probability indicating the likelihood of this transition. By viewing the graph as a Markov chain, ensemble properties can be efficiently computed over the entire molecular energy landscape. Furthermore, SRS converges to the same distribution as MC simulation. SRS is applied to two biological problems: computing the probability of folding, an important order parameter that measures the "kinetic distance" of a protein's conformation from its native state; and estimating the expected time to escape from a ligand-protein binding site. Comparison with MC simulations on protein folding shows that SRS produces arguably more accurate results, while reducing computation time by several orders of magnitude. Computational studies on ligand-protein binding also demonstrate SRS as a promising approach to study ligand-protein interactions.

Algorithms↗
PubMed2004

Efficient extraction of mapping rules of atoms from enzymatic reaction data.

Many computational problems and methods have been proposed for analysis of biological pathways. Among them, this paper focuses on extraction of mapping rules of atoms from enzymatic reaction data, which is useful for drug design, simulation of tracer experiments, and consistency checking of pathway databases. Most of existing methods for this problem are based on maximal common subgraph algorithms. In this paper, we propose a novel approach based on graph partition and graph isomorphism. We show that this problem is NP-hard in general, but can be solved in polynomial time for wide classes of enzymatic reactions. We also present an O(n(1.5)) time algorithm for a special but fundamental class of reactions, where n is the maximum size of compounds appearing in a reaction. We develop practical polynomial-time algorithms in which the Morgan algorithm is used for computing the normal form of a graph, where it is known that the Morgan algorithm works correctly for most chemical structures. Computational experiments are performed for these practical algorithms using the chemical reaction data stored in the KEGG/LIGAND database. The results of computational experiments suggest that practical algorithms are useful in many cases.

Algorithms↗
PubMed1995

Toward simplifying and accurately formulating fragment assembly.

The fragment assembly problem is that of reconstructing a DNA sequence from a collection of randomly sampled fragments. Traditionally, the objective of this problem has been to produce the shortest string that contains all the fragments as substrings, but in the case of repetitive target sequences this objective produces answers that are overcompressed. In this paper, the problem is reformulated as one of finding a maximum-likelihood reconstruction with respect to the two-sided Kolmogorov-Smirnov statistic, and it is argued that this is a better formulation of the problem. Next the fragment assembly problem is recast in graph-theoretic terms as one of finding a noncyclic subgraph with certain properties and the objectives of being shortest or maximally likely are also recast in this framework. Finally, a series of graph reduction transformations are given that dramatically reduce the size of the graph to be explored in practical instances of the problem. This reduction is very important as the underlying problems are NP-hard. In practice, the transformed problems are so small that simple branch-and-bound algorithms successfully solve them, thus permitting auxiliary experimental information to be taken into account in the form of overlap, orientation, and distance constraints.

Base Sequence↗
PubMed1996

An algorithm for finding maximal common subtopologies in a set of protein structures.

For the comparison and analysis of protein structures, it is of interest to find maximal common substructures in a given set of proteins. This question is also relevant for motif definition and structure classification. In this paper we describe first a new suitable representation of the secondary structure topology of a protein by an undirected labeled graph. Based on this representation we developed a new fast algorithm that finds all common subtopologies in a set of protein structures. Our method is based on the algorithm by Bron and Kerbosch (1973), which enumerates all maximal cliques in a graph. The main improvement of our algorithm is to restrict the search process to cliques that represent connected substructures. This restriction reduces the number of cliques to be considered during the search process and the size of the search tree drastically. Thus we are able to handle large proteins. Experiments show the efficiency and superiority of our algorithm in comparison with other existing algorithms basing on graph-theoretical methods.

Algorithms↗
PubMed2004

Clustering binary fingerprint vectors with missing values for DNA array data analysis.

Oligonucleotide fingerprinting is a powerful DNA array-based method to characterize cDNA and ribosomal RNA gene (rDNA) libraries and has many applications including gene expression profiling and DNA clone classification. We are especially interested in the latter application. A key step in the method is the cluster analysis of fingerprint data obtained from DNA array hybridization experiments. Most of the existing approaches to clustering use (normalized) real intensity values and thus do not treat positive and negative hybridization signals equally (positive signals are much more emphasized). In this paper, we consider a discrete approach. Fingerprint data are first normalized and binarized using control DNA clones. Because there may exist unresolved (or missing) values in this binarization process, we formulate the clustering of (binary) oligonucleotide fingerprints as a combinatorial optimization problem that attempts to identify clusters and resolve the missing values in the fingerprints simultaneously. We study the computational complexity of this clustering problem and a natural parameterized version and present an efficient greedy algorithm based on MINIMUM CLIQUE PARTITION on graphs. The algorithm takes advantage of some unique properties of the graphs considered here, which allow us to efficiently find the maximum cliques as well as some special maximal cliques. Our preliminary experimental results on simulated and real data demonstrate that the algorithm runs faster and performs better than some popular hierarchical and graph-based clustering methods. The results on real data from DNA clone classification also suggest that this discrete approach is more accurate than clustering methods based on real intensity values in terms of separating clones that have different characteristics with respect to the given oligonucleotide probes.

Algorithms↗
PubMed2006

Hypothesis generation in signaling networks.

Biological signaling networks comprise the chemical processes by which cells detect and respond to changes in their environment. Such networks have been implicated in the regulation of important cellular activities, including cellular reproduction, mobility, and death. Though technological and scientific advances have facilitated the rapid accumulation of information about signaling networks, utilizing these massive information resources has become infeasible except through computational methods and computer-based tools. To date, visualization and simulation tools have received significant emphasis. In this paper, we present a graph-theoretic formalization of biological signaling network models that are in wide but informal use, and formulate two problems on the graph: the Constrained Downstream and Minimum Knockout Problems. Solutions to these problems yield qualitative tools for generating hypotheses about the networks, which can then be experimentally tested in a laboratory setting. Using established graph algorithms, we provide a solution to the Constrained Downstream Problem. We also show that the Minimum Knockout Problem is NP-Hard, propose a heuristic, and assess its performance. In tests on the Epidermal Growth Factor Receptor (EGFR) network, we find that our heuristic reports the correct solution to the problem in seconds. Source code for the implementations of both solutions is available from the authors upon request.

Algorithms↗
PubMed2006

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.

Algorithms↗