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PubMed2001

Design of graph-based evolutionary algorithms: a case study for chemical process networks.

This paper describes the adaptation of evolutionary algorithms (EAs) to the structural optimization of chemical engineering plants, using rigorous process simulation combined with realistic costing procedures to calculate target function values. To represent chemical engineering plants, a network representation with typed vertices and variable structure will be introduced. For this representation, we introduce a technique on how to create problem specific search operators and apply them in stochastic optimization procedures. The applicability of the approach is demonstrated by a reference example. The design of the algorithms will be oriented at the systematic framework of metric-based evolutionary algorithms (MBEAs). MBEAs are a special class of evolutionary algorithms, fulfilling certain guidelines for the design of search operators, whose benefits have been proven in theory and practice. MBEAs rely upon a suitable definition of a metric on the search space. The definition of a metric for the graph representation will be one of the main issues discussed in this paper. Although this article deals with the problem domain of chemical plant optimization, the algorithmic design can be easily transferred to similar network optimization problems. A useful distance measure for variable dimensionality search spaces is suggested.

Algorithms↗
PubMed2006

Use of social network analysis to characterize the pattern of animal movements in the initial phases of the 2001 foot and mouth disease (FMD) epidemic in the UK.

Aggregated movement data do not take into account the relative position of the units within a higher-level structure. Social network analysis (SNA) and graph theory provide a tool to organise and analyse relational data overcoming the limitations of standard methods where the position of individuals/observations does not affect the result of the analysis. Some recorded movements of cattle and sheep during the initial phase of the 2001 foot and mouth disease (FMD) outbreak in the UK, before the ban on animal movements was imposed, are analysed descriptively using SNA. With the data available, a directed dichotomized network with 653 nodes and 797 arches was analysed. Most of the 10 nodes with the highest betweenness (3 farms, 4 markets and 3 dealers) were identified as key players in the initial spread of the infection. Three groups of nodes with distinctive proportion of k < or = 2 neighbours would result in three different theoretical outbreak dimensions assuming that the infection is only disseminated by the movements included in the network: no spread, spread up to 7% and around 25%. There are three hierarchical clusters with 308, 215 and 130 nodes, respectively. Farms in cluster 1 appear to be more similar in their movement patterns to non-farm holdings than to farms in clusters 2 and 3. Relative betweenness, k-neighbours and structural equivalence using hierarchical clustering were able to identify key actors in the evolution of the initial phases of the FMD outbreak such as markets, dealers and farms with atypical movement patterns. Holdings with high betweenness, large number of k < or = 2 neighbours and with movement pattern as in cluster 1 should be targeted in disease control activities once primary actors like markets, dealers and slaughter houses have been contained.

Animals↗
PubMed2003

A social network analysis of communication about hereditary nonpolyposis colorectal cancer genetic testing and family functioning.

Hereditary cancers are relational diseases. A primary focus of research in the past has been the biological relations that exist within the families and how genes are passed along family lines. However, hereditary cancers are relational in a psychosocial sense, as well. They can impact communication relationships within a family, as well as support relationships among family members. Furthermore, the familial culture can affect an individual's participation in genetic counseling and testing endeavors. Our aims are (a) to describe the composition of familial networks, (b) to characterize the patterns of family functioning within families, (c) to analyze how these patterns relate to communications about genetic counseling and testing among family members, and (d) to identify influential family members. Specifically, we asked how the relationship between mutation status, kinship ties, and family functioning constructs, e.g., communication, cohesion, affective involvement, leadership, and conflict, was associated with discussions about genetic counseling and testing. We used social network analysis and random graph techniques to examine 783 dyadic relationships in 36 members of 5 hereditary nonpolyposis colorectal cancer (HNPCC) families interviewed from 1999-2000. Results suggest that in these five HNPCC families, two family members are more likely to discuss genetic counseling and testing if either one carries the mutation, if either one is a spouse or a first-degree relative of the other, or if the relationship is defined by positive cohesion, leadership, or lack of conflict. Furthermore, the family functioning patterns suggest that mothers tend to be the most influential persons in the family network. Results of this study suggest encouraging family members who act in the mother role to take a "team approach" with the family proband when discussing HNPCC risks and management with family members.

Adult↗
PubMed2005

Inferring meaningful pathways in weighted metabolic networks.

An approach is presented for computing meaningful pathways in the network of small molecule metabolism comprising the chemical reactions characterized in all organisms. The metabolic network is described as a weighted graph in which all the compounds are included, but each compound is assigned a weight equal to the number of reactions in which it participates. Path finding is performed in this graph by searching for one or more paths with lowest weight. Performance is evaluated systematically by computing paths between the first and last reactions in annotated metabolic pathways, and comparing the intermediate reactions in the computed pathways to those in the annotated ones. For the sake of comparison, paths are computed also in the un-weighted raw (all compounds and reactions) and filtered (highly connected pool metabolites removed) metabolic graphs, respectively. The correspondence between the computed and annotated pathways is very poor (<30%) in the raw graph; increasing to approximately 65% in the filtered graph; reaching approximately 85% in the weighted graph. Considering the best-matching path among the five lightest paths increases the correspondence to 92%, on average. We then show that the average distance between pairs of metabolites is significantly larger in the weighted graph than in the raw unfiltered graph, suggesting that the small-world properties previously reported for metabolic networks probably result from irrelevant shortcuts through pool metabolites. In addition, we provide evidence that the length of the shortest path in the weighted graph represents a valid measure of the "metabolic distance" between enzymes. We suggest that the success of our simplistic approach is rooted in the high degree of specificity of the reactions in metabolic pathways, presumably reflecting thermodynamic constraints operating in these pathways. We expect our approach to find useful applications in inferring metabolic pathways in newly sequenced genomes.

Amino Acids↗
PubMed2006

BNArray: an R package for constructing gene regulatory networks from microarray data by using Bayesian network.

UNLABELLED: BNArray is a systemized tool developed in R. It facilitates the construction of gene regulatory networks from DNA microarray data by using Bayesian network. Significant sub-modules of regulatory networks with high confidence are reconstructed by using our extended sub-network mining algorithm of directed graphs. BNArray can handle microarray datasets with missing data. To evaluate the statistical features of generated Bayesian networks, re-sampling procedures are utilized to yield collections of candidate 1st-order network sets for mining dense coherent sub-networks. AVAILABILITY: The R package and the supplementary documentation are available at http://www.cls.zju.edu.cn/binfo/BNArray/.

Algorithms↗
PubMed2001

Random graphs with arbitrary degree distributions and their applications.

Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

Journal Article↗
PubMed2001

Replication and mutation on neutral networks.

Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. The mapping is non-invertible since many sequences fold into the same minimum free energy (secondary) structure or shape. The pre-images of this map, called neutral networks, are uniquely associated with the shapes and vice versa. Random graph theory is used to construct networks in sequence space which are suitable models for neutral networks. The theory of molecular quasispecies has been applied to replication and mutation on single-peak fitness landscapes. This concept is extended by considering evolution on degenerate multi-peak landscapes which originate from neutral networks by assuming that one particular shape is fitter than all the others. On such a single-shape landscape the superior fitness value is assigned to all sequences belonging to the master shape. All other shapes are lumped together and their fitness values are averaged in a way that is reminiscent of mean field theory. Replication and mutation on neutral networks are modeled by phenomenological rate equations as well as by a stochastic birth-and-death model. In analogy to the error threshold in sequence space the phenotypic error threshold separates two scenarios: (i) a stationary (fittest) master shape surrounded by closely related shapes and (ii) populations drifting through shape space by a diffusion-like process. The error classes of the quasispecies model are replaced by distance classes between the master shape and the other structures. Analytical results are derived for single-shape landscapes, in particular, simple expressions are obtained for the mean fraction of master shapes in a population and for phenotypic error thresholds. The analytical results are complemented by data obtained from computer simulation of the underlying stochastic processes. The predictions of the phenomenological approach on the single-shape landscape are very well reproduced by replication and mutation kinetics of tRNA(phe). Simulation of the stochastic process at a resolution of individual distance classes yields data which are in excellent agreement with the results derived from the birth-and-death model.

Base Pairing↗
PubMedDate not supplied

A mathematical approach to the connectivity between the cortical visual areas of the macaque monkey.

The visual cortex of the macaque monkey is divided into many distinct visual information processing areas. In many cases, anatomical and physiological results allow one to determine the presence or the absence of neuronal connections from one area to another. We have approached the topology of this neuronal network within the mathematical framework of graph theory. At first, we studied the unknown part of the network, i.e. the part where anatomical and physiological results are lacking. Relying on a specific topological property of the network established on the known part, we developed an interpolation algorithm for reducing the level of uncertainty concerning the unknown part. From these results, we then constructed a connectional model of the neuronal network for the entire cortical visual system. Subsequently, a topological analysis of this model, with the help of factorial analysis and clustering technics, shows its structural properties and singular vertices. This analysis suggests the existence of two distinct classes of areas, one in the parietal part of the cortex and the other in the temporal part, which are connected to each other via relay areas, especially involving the frontal eye field. These results may help to understand the functional role of particular cortical areas in vision and, more generally, to explore how visual information flows within the visual cortex.

Algorithms↗
PubMed2001

Topological properties of citation and metabolic networks.

Topological properties of "scale-free" networks are investigated by determining their spectral dimensions d(S), which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model [A.-L. Barabasi and R. Albert, Science 286, 509 (1999)] are probed. For completeness and comparisons lattice, random and small-world models are also investigated. We find that d(S) is around 3 for citation and metabolic networks, which is significantly different from the growing network model, for which d(S) is approximately 7.5. This signals a substantial difference in network topology despite the observed similarities in vertex-order distributions. In addition, the diffusion analysis indicates that the citation networks are treelike in structure, whereas the metabolic networks contain many loops.

Animals↗
PubMed1983

A graph-theoretical analysis of metabolic regulation.

A graph theoretical method is proposed for modeling metabolic networks including enzymic cascades and synergistic binding of ligands to enzymes. Formal operations on the graph of a given network leads to the identification of feedback metabolites and the enzymes which regulate the feedback. These systemic properties are thus isolated from the purely local regulation of individual enzymes. The method was applied to a model of glycogen metabolism. At low cyclic AMP and insulin levels feedback control of the system is predicted to be largely with the glycogen branching and debranching enzymes, which set the amount of glycogen in the metabolically available outer branches.

Cyclic AMP↗
PubMed1997

Three-dimensional modeling of renal glomerular capillary networks.

OBJECTIVE: To quantitatively characterize three-dimensional (3D) vascular patterns based on the path length distribution in networks. STUDY DESIGN: Volume data were stacks of confocal fluorescence images of renal glomeruli, obtained using a confocal laser scanning microscope and spanning 60-130 microns in the z axis. After manual editing to remove nonglomerular components, transverse sections of glomerular capillary lumens were segmented automatically using two-dimensional morphologic filters. The center points and the overlap (between adjacent sections) of lumens segmented in the x vs. y plane were used to derive a graph (i.e., a multiply connected network) for each glomerulus. The average degree and the distance between connected nodes were used to derive the number of graph edges and the overall length of the capillary network. RESULTS: Renderings of the 3D reconstructions demonstrated well the lobular structure of the glomerular tufts. Mean capillary length ranged from 53 to 180 microns in 10 glomeruli. Total capillary length ranged from 3,500 to 9,500 microns (mean 5,833). CONCLUSION: Structural measurements based on confocal data require less effort than do measurements based on serial sections and make detailed study of diseased glomerular populations practical.

Animals↗
PubMed2026

Accurately Deciphering Tissue Heterogeneity From Spatial Multi-Modal and Multi-Omics With STransformer.

Advances in spatially resolved technologies enable the simultaneous acquisition of diverse data modalities within a tissue slice while preserving critical spatial context, which presents unprecedented opportunities to decipher intricate tissue heterogeneity. However, existing computational approaches lack the intrinsic flexibility to universally process both spatial multi-modal and multi-omics data. Here, we introduce STransformer, a unified deep learning framework designed to seamlessly accommodate a comprehensive landscape of spatial data. By simultaneously capturing short-range cellular interactions and tissue-wide semantic patterns, it extracts robust representations to accurately dissect complex tissue heterogeneity. Systematic evaluations across diverse species, tissue types, and data modalities highlight its profound versatility. For spatial multi-modal data, STransformer delineates intricate anatomical structures in the human cortex, uncovers pathological mechanisms in Alzheimer's disease, and characterizes dynamic spatiotemporal developmental trajectories during chicken cardiogenesis. Scaling to spatial multi-omics data, STransformer synergizes spatial transcriptomic and proteomic profiles to decipher intricate immune microenvironments within the human tonsil, and jointly analyzes spatial epigenomic and transcriptomic data to infer regulatory mechanisms in the mouse embryonic brain. Consequently, STransformer serves as a highly versatile and robust analytical framework for advancing our understanding of tissue heterogeneity and disease&#xa0;pathogenesis.

Multiomics↗
PubMedDate not supplied

The signature molecular descriptor. 4. Canonizing molecules using extended valence sequences.

We present a new algorithm to canonize molecular graphs using the signature molecular descriptor introduced in the previous papers of this series. While developed specifically for molecular structures, the algorithm can be used for any graph and is not limited to acyclic graphs, planar graphs, bounded valence, or bounded genus graphs, for which polynomial time algorithms exist. The algorithm is tested with benzenoid hydrocarbons and a database of 126,705 organic compounds. The algorithm's performances are compared against Brendan Mc Kay's Nauty algorithm, which is believed to be the fastest graph canonization algorithm for general graphs, with five series of graphs each comprising up to 30,000 vertices: 2D meshes (pericondensed benzenoids), 3D cages (fullerenes and nanotubes), 3D meshes (crystal lattices), 4D cages, and power law graphs (protein and gene networks). The algorithm can be downloaded as an open source code at http://www.cs.sandia.gov/ approximately jfaulon/QSAR.

Journal Article↗
PubMed2002

Topological determinants of protein folding.

The folding of many small proteins is kinetically a two-state process that represents overcoming the major free-energy barrier. A kinetic characteristic of a conformation, its probability to descend to the native state domain in the amount of time that represents a small fraction of total folding time, has been introduced to determine to which side of the free-energy barrier a conformation belongs. However, which features make a protein conformation on the folding pathway become committed to rapidly descending to the native state has been a mystery. Using two small, well characterized proteins, CI2 and C-Src SH3, we show how topological properties of protein conformations determine their kinetic ability to fold. We use a macroscopic measure of the protein contact network topology, the average graph connectivity, by constructing graphs that are based on the geometry of protein conformations. We find that the average connectivity is higher for conformations with a high folding probability than for those with a high probability to unfold. Other macroscopic measures of protein structural and energetic properties such as radius of gyration, rms distance, solvent-accessible surface area, contact order, and potential energy fail to serve as predictors of the probability of a given conformation to fold.

Kinetics↗
PubMed2004

An architecture for biological information extraction and representation.

MOTIVATIONS: Technological advances in biomedical research are generating a plethora of heterogeneous data at a high rate. There is a critical need for extraction, integration and management tools for information discovery and synthesis from these heterogeneous data. RESULTS: In this paper, we present a general architecture, called ALFA, for information extraction and representation from diverse biological data. The ALFA architecture consists of: (i) a networked, hierarchical, hyper-graph object model for representing information from heterogeneous data sources in a standardized, structured format; and (ii) a suite of integrated, interactive software tools for information extraction and representation from diverse biological data sources. As part of our research efforts to explore this space, we have currently prototyped the ALFA object model and a set of interactive software tools for searching, filtering, and extracting information from scientific text. In particular, we describe BioFerret, a meta-search tool for searching and filtering relevant information from the web, and ALFA Text Viewer, an interactive tool for user-guided extraction, disambiguation, and representation of information from scientific text. We further demonstrate the potential of our tools in integrating the extracted information with experimental data and diagrammatic biological models via the common underlying ALFA representation. CONTACT: aditya_vailaya@agilent.com.

Abstracting and Indexing↗
PubMed2001

Target problem on small-world networks.

In this work we focus on reactions on small-world networks (SWN's), disordered graphs of much recent interest. We study the target problem, since it allows an exact solution on regular lattices. On SWN's we find that the decay of the targets (for which we extend the formalism to disordered lattices) is again related to S(n), the mean number of distinct sites visited in n steps, although the S(n) vs n dependence changes here drastically in going from regular linear chains to their SWN.

Journal Article↗
PubMed2001

Trapping of random walks on small-world networks.

We investigate the trapping of random walkers on small-world networks (SWN's), irregular graphs. We derive bounds for the survival probability Phi(SWN)(n) and display its analysis through cumulant expansions. Computer simulations are performed for large SWNs. We show that in the limit of infinite sizes, trapping on SWNs is equivalent to trapping on a certain class of random trees, which are grown during the random walk.

Journal Article↗
PubMed2005

Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings.

We study the approach to jamming in hard-sphere packings and, in particular, the pair correlation function g(2) (r) around contact, both theoretically and computationally. Our computational data unambiguously separate the narrowing delta -function contribution to g(2) due to emerging interparticle contacts from the background contribution due to near contacts. The data also show with unprecedented accuracy that disordered hard-sphere packings are strictly isostatic: i.e., the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom, once rattlers are removed. For such isostatic packings, we derive a theoretical connection between the probability distribution of interparticle forces P(f) (f) , which we measure computationally, and the contact contribution to g(2) . We verify this relation for computationally generated isostatic packings that are representative of the maximally random jammed state. We clearly observe a maximum in P(f) and a nonzero probability of zero force, shedding light on long-standing questions in the granular-media literature. We computationally observe an unusual power-law divergence in the near-contact contribution to g(2) , persistent even in the jamming limit, with exponent -0.4 clearly distinguishable from previously proposed inverse-square-root divergence. Additionally, we present high-quality numerical data on the two discontinuities in the split-second peak of g(2) and use a shared-neighbor analysis of the graph representing the contact network to study the local particle clusters responsible for the peculiar features. Finally, we present the computational data on the contact contribution to g(2) for vacancy-diluted fcc crystal packings and also investigate partially crystallized packings along the transition from maximally disordered to fully ordered packings. We find that the contact network remains isostatic even when ordering is present. Unlike previous studies, we find that ordering has a significant impact on the shape of P(f) for small forces.

Journal Article↗