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PubMed2006

Perfect quantum state transfer with spinor bosons on weighted graphs.

A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in polynomial time, even as the number of nodes increases exponentially. The one-dimensional "quantum wire" and the hypercube are special cases in this construction, where the number of spin degrees of freedom is equal to one and the number of particles, respectively. An implementation of a near-perfect quantum state transfer across a weighted parallelepiped with ultracold atoms in optical lattices is discussed.

Journal Article↗

PubMed2002

Analysis of voids in crystal structures: the methods of 'dual' crystal chemistry.

The theoretical basics of the analysis of voids in crystal structures by means of Voronoi-Dirichlet polyhedra (VDP) and of the graph theory are stated. Topological relations are considered between VDPs and atomic domains in a crystal field. These relations allow the separation of two non-intersecting topological subspaces in a crystal structure, whose connectednesses are defined by two finite 'reduced' graphs. The first, 'direct', subspace includes the atoms (VDP centres) and the network of interatomic bonds (VDP faces), the second, 'dual', one comprises the void centres (VDP vertices) and the system of channels (VDP edges) between them. Computer methods of geometrical-topological analysis of the 'dual' subspace are developed and implemented within the program package TOPOS. They are designed for automatically restoring the system of channels, visualizing and sizing voids and void conglomerates, dimensional analysis of continuous void systems, and comparative topological analysis of 'dual' subspaces for various substances. The methods of analysis of 'dual' and 'direct' subspaces are noted to differ from each other only in some details that allows the term 'dual' crystal chemistry to be introduced. The efficiency of the methods is shown with the analysis of compounds of different chemical nature: simple substances, ionic structures, superionic conductors, zeolites, clathrates, organic supramolecular complexes.

Journal Article↗

PubMed2005

The use of edge-betweenness clustering to investigate biological function in protein interaction networks.

BACKGROUND: This paper describes an automated method for finding clusters of interconnected proteins in protein interaction networks and retrieving protein annotations associated with these clusters. RESULTS: Protein interaction graphs were separated into subgraphs of interconnected proteins, using the JUNG implementation of Girvan and Newman's Edge-Betweenness algorithm. Functions were sought for these subgraphs by detecting significant correlations with the distribution of Gene Ontology terms which had been used to annotate the proteins within each cluster. The method was implemented using freely available software (JUNG and the R statistical package). Protein clusters with significant correlations to functional annotations could be identified and included groups of proteins know to cooperate in cell metabolism. The method appears to be resilient against the presence of false positive interactions. CONCLUSION: This method provides a useful tool for rapid screening of small to medium size protein interaction datasets.

Algorithms↗

PubMed2001

The risk environment for HIV transmission: results from the Atlanta and Flagstaff network studies.

The purpose of this study was to investigate the hypothesis that human immunodeficiency virus (HIV) transmission may be facilitated or obstructed by network structure, incorporating a measure of risk that combines true risk and surrogates. Persons at presumed high risk for HIV were enrolled in long-term follow-up studies of urban and rural networks in Atlanta, Georgia, and Flagstaff, Arizona. We focused on respondents who were also contacts to evaluate information on both sides of the observed dyads and constructed a Risk Indicator, based on a four-digit binary number, that permitted assessment and visualization of the overall risk environment. We constructed graphs that provided visualization of the level of risk, the types of relationships, and the actual network. Although some of the findings conform to the hypotheses relating network structure to transmission, there were several anomalies. In Atlanta, HIV prevalence was most strongly related to men with a male sexual orientation, despite the widespread use of injectable drugs. In Flagstaff, an area of very low prevalence and no transmission, the risk environment appeared more intense, and the frequency of microstructures was as great or greater than representative areas in Atlanta. The network hypothesis is not yet sufficiently developed to account for empirical observations that demonstrate the presence of intense, interactive networks in the absence of transmission of HIV.

Adult↗

PubMed2005

Fitting of random tessellation models to keratin filament networks.

The role of specific structural patterns in keratin filament networks for regulating biophysical properties of epithelial cells is poorly understood. This is at least partially due to a lack of methods for the analysis of filament network morphology. We have previously developed a statistical approach to the analysis of keratin filament networks imaged by scanning electron microscopy. The segmentation of images in this study resulted in graph structures, i.e. tessellations, whose structural characteristics are now further investigated by iteratively fitting geometrical statistical models. An optimal model as well as corresponding optimal parameters are detected from a given set of possible random tessellation models, i.e. Poisson-Line tessellations (PLT), Poisson-Voronoi tessellations (PVT) and Poisson-Delaunay tessellations (PDT). Using this method, we investigated the remodeling of keratin filament networks in pancreatic cancer cells in response to transforming growth factor alpha (TGFalpha), which is involved in pancreatic cancer progression. The results indicate that the fitting of random tessellation models represents a suitable method for the description of complex filament networks.

Algorithms↗

PubMed2003

Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network.

We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. Selecting the optimal graph, which gives the best representation of the system among genes, is still a problem to be solved. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes.

Bayes Theorem↗

PubMed2005

Random graph model with power-law distributed triangle subgraphs.

Clustering is well known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance of small subgraphs is important. Here, we study the arrangement of triangles in a model for scale-free random graphs and determine the asymptotic behavior of the clustering coefficient, the average number of triangles, as well as the number of triangles attached to the vertex of maximum degree. We prove that triangles are power-law distributed among vertices and characterized by both vertex and edge coagulation when the degree exponent satisfies 2< beta <2.5; furthermore, a finite density of triangles appears as beta = 2 + 1/3.

Journal Article↗

PubMed2004

Perturbing general uncorrelated networks.

This paper is a direct continuation of an earlier work, where we studied Erdös-Rényi random graphs perturbed by an interaction Hamiltonian favoring the formation of short cycles. Here, we generalize these results. We keep the same interaction Hamiltonian but let it act on general graphs with uncorrelated nodes and an arbitrary given degree distribution. It is shown that the results obtained for Erdös-Rényi graphs are generic, at the qualitative level. However, scale-free graphs are an exception to this general rule and exhibit a singular behavior, studied thoroughly in this paper, both analytically and numerically.

Journal Article↗

PubMed2003

Topological structure analysis of the protein-protein interaction network in budding yeast.

Interaction detection methods have led to the discovery of thousands of interactions between proteins, and discerning relevance within large-scale data sets is important to present-day biology. Here, a spectral method derived from graph theory was introduced to uncover hidden topological structures (i.e. quasi-cliques and quasi-bipartites) of complicated protein-protein interaction networks. Our analyses suggest that these hidden topological structures consist of biologically relevant functional groups. This result motivates a new method to predict the function of uncharacterized proteins based on the classification of known proteins within topological structures. Using this spectral analysis method, 48 quasi-cliques and six quasi-bipartites were isolated from a network involving 11,855 interactions among 2617 proteins in budding yeast, and 76 uncharacterized proteins were assigned functions.

Algorithms↗

PubMed2025

Interrogating functional connectivity of in vitro neural glia tissue model modulated through integrative control of matrix stiffness and a neurotrophic factor.

Brain function emerges from intricate cellular communication within neural networks. Both In silico neuronal models and primary neuron cells have revealed that the branching architecture of individual neurons determines the bioelectrical signal propagation pattern and dynamics. However, whether stem cell-differentiated neurons can build functional connectivity regulated by neuronal morphology has yet to be determined. Here, we hypothesized that neurite length, branching, or both factors would regulate the functional connectivity of the stem cell-differentiated neural network. We examined this hypothesis by differentiating mouse cortical neural stem cells (NSCs) on Matrigel substrates with varying storage moduli, both with and without basic fibroblast growth factor (bFGF). Interestingly, with bFGF, Matrigel with a storage modulus (G') of 100 Pa drives NSCs to differentiate into neurons with more dendritic branches, while the gel with G' of 50 Pa led to the development of longer neurites with fewer branches. Notably, branch-rich neural networks exhibited an increased frequency of calcium transients. Using a MATLAB-based analysis pipeline incorporating graph theory, we constructed spatial and temporal calcium activity maps, revealing that branching complexity, more than neurite length, correlates with the density and strength of functional neural circuits. Overall, this study demonstrates that the dendritic branching of neurons, modulated with matrix stiffness and neurotrophic factors, is a key element in enhancing the electrophysiological functionality of the stem cell-differentiated neural network. This finding will have a significant impact on efforts to reconstruct functional neural tissue models, advancing both regenerative therapies and unexplored applications, including biological computing.

Animals↗

PubMed2002

Synchronization in small-world systems.

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.

Models, Theoretical↗

PubMed2002

Ising model on networks with an arbitrary distribution of connections.

We find the exact critical temperature T(c) of the nearest-neighbor ferromagnetic Ising model on an "equilibrium" random graph with an arbitrary degree distribution P(k). We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when P(k) is fat tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, T(c) approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.

Journal Article↗

PubMed1979

A graph theoretic approach to the development of minimal phylogenetic trees.

The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the lenghtof any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.

Mathematics↗

PubMed1989

BIOLAB--a computerized on-line system for physiological measurements in experimental animals.

An on-line system for the acquisition and analysis of physiological signals measured in experimental animals is described. The modular design makes it flexible and easily adaptable to various kinds of physiological measurements. Currently, the system includes support for hemodynamic and cardiac electrophysiological studies. The system is designed for intermittent recordings initiated either manually by the operator or automatically. The distributed computer system consists of three parts: the data acquisition subsystem, the on-line analysis subsystem, and the final data processing subsystem. The communication between the subsystem utilizes an Ethernet local area network, and the analysis and plot programs include support for RS/1 tables and graphs.

Animals↗

PubMed2026

VirBinn improves viral genome binning from metagenomic Hi-C through graph diffusion.

MOTIVATION: Metagenomic Hi-C provides in situ proximity signals that can improve genome binning and enable virus-host-association analysis. However, viral genome recovery remains difficult because virus-virus Hi-C contact matrices are extremely sparse. Viral genomes are small, often low-abundance, and frequently assemble into short contigs, leaving many true within-genome links unobserved and causing viral bins to fragment. RESULTS: We present VirBinn, a graph-diffusion framework for viral binning from metagenomic Hi-C. VirBinn enhances virus-virus connectivity through two complementary mechanisms: random-walk-with-restart enhancement on the sparse virus-virus contact graph and host-guided diffusion that propagates viral seeds through the host network to infer indirect virus-virus associations. The enhanced views are integrated and clustered using Leiden community detection to produce viral metagenome-assembled genomes (vMAGs). On dataset-specific simulation benchmarks with ground truth, VirBinn consistently recovers more high-quality vMAGs than Hi-C-based and shotgun-based baselines and substantially increases the number of near-complete genomes. On four real metagenomic Hi-C datasets spanning human gut, pig gut, sheep gut (long-read assembly), and wastewater, VirBinn yields more high-completeness vMAGs under CheckV and produces bins with strong within-cluster contact support. Finally, host linkage analysis using reconstructed host MAGs reveals habitat-specific host-association patterns and plausible host taxonomic profiles. AVAILABILITY AND IMPLEMENTATION: VirBinn is available at https://github.com/dyxstat/VirBinn. The scripts to reproduce the results and figures in this article are available at https://github.com/dyxstat/Reproduce_VirBinn.

Genome, Viral↗

PubMed2006

Polynomial growth in branching processes with diverging reproductive number.

We study the spreading dynamics on graphs with a power law degree distribution pk approximately k-gamma, with 2<gamma<3, as an example of a branching process with a diverging reproductive number. We provide evidence that the divergence of the second moment of the degree distribution carries as a consequence a qualitative change in the growth pattern, deviating from the standard exponential growth. First, the population growth is extensive, meaning that the average number of vertices reached by the spreading process becomes of the order of the graph size in a time scale that vanishes in the large graph size limit. Second, the temporal evolution is governed by a polynomial growth, with a degree determined by the characteristic distance between vertices in the graph. These results open a path to further investigation on the dynamics on networks.

Animals↗

PubMed2003

2-(2-Naphthyloxy)acetate derivatives. I. A new class of antiamnesic agents.

The title compounds 1-(2-naphthyloxymethylcarbonyl)piperidine, C(17)H(19)NO(2), (I), and 3-methyl-1-(2-naphthyloxymethylcarbonyl)piperidine, C(18)H(21)NO(2), (II), are potential antiamnesics. In (II), the methyl-substituted piperidine ring is disordered over two conformations. The piperidine ring has a chair conformation in both compounds. In (I), the molecules are linked by weak intermolecular C-H.O interactions to give networks represented by C(4), C(6) and R(4)(4)(18) graph-set motifs, while in (II), weak intermolecular C-H.O interactions generate R(1)(2)(5), C(4) and C(7) graph-set motifs. The dihedral angle between the naphthalene moiety and the piperidine ring is 33.83 (7) degrees in (I), while it is 31.78 (11) and 19.38 (19) degrees for the major and minor conformations, respectively, in (II).

Journal Article↗

PubMed2004

Detection of functional modules from protein interaction networks.

Complex cellular processes are modular and are accomplished by the concerted action of functional modules (Ravasz et al., Science 2002;297:1551-1555; Hartwell et al., Nature 1999;402:C47-52). These modules encompass groups of genes or proteins involved in common elementary biological functions. One important and largely unsolved goal of functional genomics is the identification of functional modules from genomewide information, such as transcription profiles or protein interactions. To cope with the ever-increasing volume and complexity of protein interaction data (Bader et al., Nucleic Acids Res 2001;29:242-245; Xenarios et al., Nucleic Acids Res 2002;30:303-305), new automated approaches for pattern discovery in these densely connected interaction networks are required (Ravasz et al., Science 2002;297:1551-1555; Bader and Hogue, Nat Biotechnol 2002;20:991-997; Snel et al., Proc Natl Acad Sci USA 2002;99:5890-5895). In this study, we successfully isolate 1046 functional modules from the known protein interaction network of Saccharomyces cerevisiae involving 8046 individual pair-wise interactions by using an entirely automated and unsupervised graph clustering algorithm. This systems biology approach is able to detect many well-known protein complexes or biological processes, without reference to any additional information. We use an extensive statistical validation procedure to establish the biological significance of the detected modules and explore this complex, hierarchical network of modular interactions from which pathways can be inferred.

Algorithms↗