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At least 307 records · Page 17Linked to original sources
PubMed2000

Hazardous materials transportation: a risk-analysis-based routing methodology.

This paper introduces a new methodology based on risk analysis for the selection of the best route for the transport of a hazardous substance. In order to perform this optimisation, the network is considered as a graph composed by nodes and arcs; each arc is assigned a cost per unit vehicle travelling on it and a vehicle capacity. After short discussion about risk measures suitable for linear risk sources, the arc capacities are introduced by comparison between the societal and individual risk measures of each arc with hazardous materials transportation risk criteria; then arc costs are defined in order to take into account both transportation out-of-pocket expenses and risk-related costs. The optimisation problem can thus be formulated as a 'minimum cost flow problem', which consists of determining for a specific hazardous substance the cheapest flow distribution, honouring the arc capacities, from the origin nodes to the destination nodes. The main features of the optimisation procedure, implemented on the computer code OPTIPATH, are presented. Test results about shipments of ammonia are discussed and finally further research developments are proposed.

Cost-Benefit Analysis↗
PubMed2003

A description of dynamical graphs associated to elementary regulatory circuits.

The biological and dynamical importance of feedback circuits in regulatory graphs has often been emphasized. The work presented here aims at completely describing the dynamics of isolated elementary regulatory circuits. Our analytical approach is based on a discrete formal framework, built upon the logical approach of R. Thomas. Given a regulatory circuit, we show that the structure of synchronous and asynchronous dynamical graphs depends only on the length of the circuit (number of genes) and on its sign (which depends on the parity of the number of negative interactions). This work constitutes a first step towards the analytical characterisation of discrete dynamical graphs for more complex regulatory networks in terms of contributions corresponding to their embedded elementary circuits.

Algorithms↗
PubMed2004

Modeling the evolution of weighted networks.

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a nontrivial time evolution of vertices' properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices' degree.

Journal Article↗
PubMed2005

Mean-field limit of systems with multiplicative noise.

A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise intensity (weak, intermediate, and strong noise) are identified by performing a self-consistent calculation on a fully connected lattice. The most interesting, strong-noise, regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations, as a Ginzburg criterion shows. On the other hand, the self-consistent approach is shown to be valid only in the thermodynamic limit, while for finite systems the critical behavior is found to be different. In this last case, the self-consistent field itself is broadly distributed rather than taking a well defined mean value; its fluctuations, described by an effective zero-dimensional multiplicative noise equation, govern the critical properties. These findings are obtained analytically for a fully connected graph, and verified numerically both on fully connected graphs and on random regular networks. The results presented here shed some doubt on what is the validity and meaning of a standard mean-field approach in systems with multiplicative noise in finite dimensions, where each site does not see an infinite number of neighbors, but a finite one. The implications of all this on the existence of a finite upper critical dimension for multiplicative noise and Kardar-Parisi-Zhang problems are briefly discussed.

Journal Article↗
PubMed2006

Degree-dependent intervertex separation in complex networks.

We study the mean length (l)(k) of the shortest paths between a vertex of degree k and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law correction to a logarithmic dependence, (l)(k) = A ln[N/k((gamma-1)/2)]-Ck(gamma-1)/N+ in a wide range of network sizes. Here N is the number of vertices in the network, gamma is the degree distribution exponent, and the coefficients A and C depend on a network. We compare this law with a corresponding (l)(k) dependence obtained for random scale-free networks growing through the preferential attachment mechanism. In stochastic and deterministic growing trees with an exponential degree distribution, we observe a linear dependence on degree, (l)(k)approximately A ln N-Ck. We compare our findings for growing networks with those for uncorrelated graphs.

Journal Article↗
PubMed2000

Automated assignment of graph-set descriptors for crystallographically symmetric molecules

Algorithms for the automatic assignment of graph-set notation for intermolecular networks have been extended to molecules having internal crystallographic symmetry, for patterns up to the second level. This provides a means of achieving systematic and consistent assignments for networks containing symmetric molecules. These methodologies have been implemented in the program RPLUTO. Examples are given of the application of the method to a number of molecules with hydrogen-bonded and other intermolecular networks, illustrating the diversity of the patterns that occur.

Journal Article↗
PubMed1998

Network thermodynamic model of coupled transport in a multicellular tissue--the islet of Langerhans.

Network thermodynamic modeling via bond graphs was used to describe the water and cryoprotectant additive (CPA) transport in a multicellular tissue. The model is presented as a tool to understand the osmotic behavior of the islets of Langerhans when exposed to ternary aqueous solutions containing an electrolyte and a CPA. It accounts for the effects of the location of cells within the tissue and an interstitial matrix, plus differential permeabilities to water and CPA. The interstitial matrix was assumed to be a porous medium able to store the chemical species being transported. Controlled osmotic stress experiments were conducted on isolated rat pancreas islets to measure the transient volumetric response to step-wise changes in dimethyl sulfoxide, Me2SO, concentration. The model provides a tool for predicting the transient volumetric response of peripheral and interior cells and of interstitial tissue, as well as the build up of solute concentration, during addition and removal of CPAs and freezing and thawing protocols. Inverse solution methods were applied to determine values for standard cell membrane permeability parameters Lp, omega and sigma as well as for the interstitial flow conductivities Kw and Kp'.

Animals↗
PubMed2002

Analysis and visualization of functional relationships between RNA expression and clinical annotation using PathlinX.

We have analyzed a publicly available dataset consisting of gene-expression measurements from 105 lung carcinomas joined with clinical parameters describing the age, smoking history, and survival statistics for the patients that the tumors originated in. Our aim was to demonstrate how the unsupervised analysis technique embodied in PathlinX allows researchers to quickly gain an intuition for the most significant relationships between heterogeneous data elements. A variety of metrics were evaluated empirically by their ability to distinguish biological signal in the data from random noise; this was accomplished by random permutation of the data rows followed by comprehensive pair-wise comparison of all experimental elements. Thresholds of significance were established based on the metric scores for the permuted data. Sub-threshold associations were then removed. The remaining associations were then grouped by a transitive closure process to generate undirected graphs of associations called PathlinX networks. We discuss the various features of each generated PathlinX network and demonstrate the ability of the technique to highlight biological features in large heterogeneous datasets.

Algorithms↗
PubMed2001

Giant strongly connected component of directed networks.

We describe how to calculate the sizes of all giant connected components of a directed graph, including the strongly connected one. In particular, the World Wide Web is a directed network. The results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out-degree distribution P(k(i),k(o)). We show that if P(k(i),k(o)) does not factorize, the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in- and out-components. The calculations of the relative sizes of all the giant components are demonstrated using the simplest examples. We explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one.

Journal Article↗
PubMed2006

Protein interaction networks in plants.

Protein-protein interactions are fundamental to virtually every aspect of cellular functions. With the development of high-throughput technologies of both the yeast two-hybrid system and tandem mass spectrometry, genome-wide protein-linkage mapping has become a major objective in post-genomic research. While at least partial "interactome" networks of several model organisms are already available, in the plant field, progress in this respect is slow. However, even with comprehensive protein interaction data still missing, substantial recent advance in the graph-theoretical functional interpretation of complex network architectures might pave the way for novel approaches in plant research. This article reviews current progress and discussions in network biology. Emphasis is put on the question of what can be learned about protein functions and cellular processes by studying the topology of complex protein interaction networks and the evolutionary mechanisms underlying their development. Particularly the intermediate and local levels of network organization--the modules, motifs and cliques--are increasingly recognized as the operational units of biological functions. As demonstrated by some recent results from systematic analyses of plant protein families, protein interaction networks promise to be a valuable tool for a molecular understanding of functional specificities and for identifying novel regulatory components and pathways.

Biological Evolution↗
PubMed2002

Crashes, recoveries, and "core shifts" in a model of evolving networks.

A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self- organizes into an autocatalytic structure, which consists of an irreducible "core" surrounded by a parasitic "periphery." Crashes typically occur when the existing autocatalytic set becomes fragile and suffers a "core shift," defined graph theoretically. The nature of the recovery after a crash, in particular, the time of recovery, depends upon the organizational structure that survives the crash. The largest eigenvalue of the adjacency matrix of the graph is an important signal of network fragility or robustness.

Journal Article↗
PubMed2002

Pseudofractal scale-free web.

We find that scale-free random networks are excellently modeled by simple deterministic graphs. Our graph has a discrete degree distribution (degree is the number of connections of a vertex), which is characterized by a power law with exponent gamma=1+ln 3/ln 2. Properties of this compact structure are surprisingly close to those of growing random scale-free networks with gamma in the most interesting region, between 2 and 3. We succeed to find exactly and numerically with high precision all main characteristics of the graph. In particular, we obtain the exact shortest-path-length distribution. For a large network (ln N>>1) the distribution tends to a Gaussian of width approximately sqrt[ln N] centered at (-)l approximately ln N. We show that the eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail with exponent 2+gamma.

Journal Article↗
PubMed2005

Mining coherent dense subgraphs across massive biological networks for functional discovery.

MOTIVATION: The rapid accumulation of biological network data translates into an urgent need for computational methods for graph pattern mining. One important problem is to identify recurrent patterns across multiple networks to discover biological modules. However, existing algorithms for frequent pattern mining become very costly in time and space as the pattern sizes and network numbers increase. Currently, no efficient algorithm is available for mining recurrent patterns across large collections of genome-wide networks. RESULTS: We developed a novel algorithm, CODENSE, to efficiently mine frequent coherent dense subgraphs across large numbers of massive graphs. Compared with previous methods, our approach is scalable in the number and size of the input graphs and adjustable in terms of exact or approximate pattern mining. Applying CODENSE to 39 co-expression networks derived from microarray datasets, we discovered a large number of functionally homogeneous clusters and made functional predictions for 169 uncharacterized yeast genes. AVAILABILITY: http://zhoulab.usc.edu/CODENSE/

Algorithms↗
PubMed2006

Detecting conserved interaction patterns in biological networks.

Molecular interaction data plays an important role in understanding biological processes at a modular level by providing a framework for understanding cellular organization, functional hierarchy, and evolutionary conservation. As the quality and quantity of network and interaction data increases rapidly, the problem of effectively analyzing this data becomes significant. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation to subgraph isomorphism. This paper presents an innovative new algorithm, MULE, for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique based on ortholog contraction, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable and scalable to large numbers of networks. We show, experimentally, that our algorithm can extract frequently occurring patterns in metabolic pathways and protein interaction networks from the KEGG, DIP, and BIND databases within seconds. When compared to existing approaches, our graph simplification technique can be viewed either as a pruning heuristic, or a closely related, but computationally simpler task. When used as a pruning heuristic, we show that our technique reduces effective graph sizes significantly, accelerating existing techniques by several orders of magnitude! Indeed, for most of the test cases, existing techniques could not even be applied without our pruning step. When used as a stand-alone analysis technique, MULE is shown to convey significant biological insights at near-interactive rates. The software, sample input graphs, and detailed results for comprehensive analysis of nine eukaryotic PPI networks are available at www.cs.purdue.edu/homes/koyuturk/mule.

Algorithms↗
PubMed2003

Uncorrelated random networks.

We define a statistical ensemble of nondegenerate graphs, i.e., graphs without multiple-connections and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier publication [Phys. Rev. 64, 046118 (2001)] where trees and degenerate graphs were considered. An efficient algorithm generating nondegenerate graphs is constructed. The corresponding computer code is available on request. Finite-size effects in scale-free graphs, i.e., those where the tail of the degree distribution falls like n(-beta), are carefully studied. We find that in the absence of dynamical internode correlations the degree distribution is cut at a degree value scaling like N(gamma), with gamma=min[1/2,1/(beta-1)], where N is the total number of nodes. The consequence is that, independently of any specific model, the internode correlations seem to be a necessary ingredient of the physics of scale-free networks observed in nature.

Journal Article↗
PubMedDate not supplied

A graph-based toy model of chemistry.

Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known in detail. A computational model for generating them is therefore required. Here we present a Toy Model that provides a consistent framework in which generic properties of extensive chemical reaction networks can be explored in detail and that at the same time preserves the "look-and-feel" of chemistry: Molecules are represented as labeled graphs, i.e., by their structural formulas; their basic properties are derived by a caricature version of the Extended Hückel MO theory that operates directly on the graphs; chemical reaction mechanisms are implemented as graph rewriting rules acting on the structural formulas; reactivities and selectivities are modeled by a variant of the Frontier Molecular Orbital Theory based on the Extended Hückel scheme. The approach is illustrated for two types of reaction networks: Diels-Alder reactions and the formose reaction implicated in prebiotic sugar synthesis.

Journal Article↗
PubMed2005

Sampling properties of random graphs: the degree distribution.

We discuss two sampling schemes for selecting random subnets from a network, random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distributions of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find that this condition is satisfied by classical random graphs; for the vast majority of networks this condition will, however, not be met. We furthermore discuss the case where the probability of sampling a node depends on the degree of a node and we find that even classical random graphs are no longer closed under this sampling regime. We conclude by relating the results to real Eschericia coli protein interaction network data.

Journal Article↗
PubMed2006

A new route to the evolution of cooperation.

The Prisoner's Dilemma (PD) constitutes a widely used metaphor to investigate problems related to the evolution of cooperation. Whenever evolution takes place in well-mixed populations engaged in single rounds of the PD, cooperators cannot resist invasion by defectors, a feature, which is somewhat alleviated whenever populations are spatially distributed. In both cases the populations are characterized by a homogeneous pattern of connectivity, in which every individual is equivalent, sharing the same number of neighbours. Recently, compelling evidence has been accumulated on the strong heterogeneous nature of the network of contacts between individuals in populations. Here we describe the networks of contacts in terms of graphs and show that heterogeneity provides a new mechanism for cooperation to survive. Specifically, we show that cooperators are capable of exploring the heterogeneity of the population structure to become evolutionary competitive. As a result, cooperation becomes the dominating trait in scale-free networks of contacts in which the few highly connected individuals are directly inter-connected, in this way contributing to self-sustain cooperation.

Computer Simulation↗