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PubMed2006

Building k-connected neighborhood graphs for isometric data embedding.

Isometric data embedding using geodesic distance requires the construction of a connected neighborhood graph so that the geodesic distance between every pair of data points can be estimated. This paper proposes an approach for constructing k-connected neighborhood graphs. The approach works by applying a greedy algorithm to add each edge, in a nondecreasing order of edge length, to a neighborhood graph if end vertices of the edge are not yet k-connected on the graph. The k-connectedness between vertices is tested using a network flow technique by assigning every vertex a unit flow capacity. This approach is applicable to a wide range of data. Experiments show that it gives better estimation of geodesic distances than other approaches, especially when the data are undersampled or nonuniformly distributed.

Algorithms↗
PubMed1994

Mixed Bayesian networks: a mixture of Gaussian distributions.

Mixed Bayesian networks are probabilistic models associated with a graphical representation, where the graph is directed and the random variables are discrete or continuous. We propose a comprehensive method for estimating the density functions of continuous variables, using a graph structure and a set of samples. The principle of the method is to learn the shape of densities from a sample of continuous variables. The densities are approximated by a mixture of Gaussian distributions. The estimation algorithm is a stochastic version of the Expectation Maximization algorithm (Stochastic EM algorithm). The inference algorithm corresponding to our model is a variant of junction three method, adapted to our specific case. The approach is illustrated by a simulated example from the domain of pharmacokinetics. Tests show that the true distributions seem sufficiently fitted for practical application.

Algorithms↗
PubMed2025

Learning directed acyclic graphs for ligands and receptors based on spatially resolved transcriptomic data of ovarian cancer.

To unravel the mechanism of immune activation and suppression within tumors, a critical step is to identify transcriptional signals governing cell-cell communication between tumor and immune/stromal cells in the tumor microenvironment. Central to this communication are interactions between secreted ligands and cell-surface receptors, creating a highly connected signaling network among cells. Recent advancements in in situ-omics profiling, particularly spatial transcriptomic (ST) technology, provide unique opportunities to directly characterize ligand-receptor signaling networks that power cell-cell communication. In this paper, we propose a novel statistical method, LRnetST, to characterize the ligand-receptor interaction networks between adjacent tumor and immune/stroma cells based on ST data. LRnetST utilizes a directed acyclic graph model with a novel approach to handle the zero-inflated distributions of ST data. It also leverages existing ligand-receptor regulation databases as prior information, and employs a bootstrap aggregation strategy to achieve robust network estimation. Application of LRnetST to ST data of high-grade serous ovarian tumor samples revealed both common and distinct ligand-receptor regulations across different tumors. Some of these interactions were validated through both a MERFISH dataset and a CosMx SMI dataset of independent ovarian tumor samples. These results cast light on biological processes relating to the communication between tumor and immune/stromal cells in ovarian tumors. An open-source R package of LRnetST is available on GitHub at https://github.com/jie108/LRnetST.

Humans↗
PubMed2003

An automated method for finding molecular complexes in large protein interaction networks.

BACKGROUND: Recent advances in proteomics technologies such as two-hybrid, phage display and mass spectrometry have enabled us to create a detailed map of biomolecular interaction networks. Initial mapping efforts have already produced a wealth of data. As the size of the interaction set increases, databases and computational methods will be required to store, visualize and analyze the information in order to effectively aid in knowledge discovery. RESULTS: This paper describes a novel graph theoretic clustering algorithm, "Molecular Complex Detection" (MCODE), that detects densely connected regions in large protein-protein interaction networks that may represent molecular complexes. The method is based on vertex weighting by local neighborhood density and outward traversal from a locally dense seed protein to isolate the dense regions according to given parameters. The algorithm has the advantage over other graph clustering methods of having a directed mode that allows fine-tuning of clusters of interest without considering the rest of the network and allows examination of cluster interconnectivity, which is relevant for protein networks. Protein interaction and complex information from the yeast Saccharomyces cerevisiae was used for evaluation. CONCLUSION: Dense regions of protein interaction networks can be found, based solely on connectivity data, many of which correspond to known protein complexes. The algorithm is not affected by a known high rate of false positives in data from high-throughput interaction techniques. The program is available from ftp://ftp.mshri.on.ca/pub/BIND/Tools/MCODE.

Algorithms↗
PubMed2003

Computational complexity arising from degree correlations in networks.

We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the nondeterministic polynomial time hard optimization problem of finding minimal vertex covers on these graphs, we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks. This results in a higher complexity of the network in a computational sense: Simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case, whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization.

Journal Article↗
PubMed2003

On the structure of protein-protein interaction networks.

We present a simple model for the underlying structure of protein-protein pairwise interaction graphs that is based on the way in which proteins attach to each other in experiments such as yeast two-hybrid assays. We show that data on the interactions of human proteins lend support to this model. The frequency of the number of connections per protein under this model does not follow a power law, in contrast to the reported behaviour of data from large-scale yeast two-hybrid screens of yeast protein-protein interactions. Sampling sub-graphs from the underlying graphs generated with our model, in a way analogous to the sampling performed in large-scale yeast two-hybrid searches, gives degree distributions that differ subtly from the power law and that fit the observed data better than the power law itself. Our results show that the observation of approximate power law behaviour in a sampled sub-graph does not imply that the underlying graph follows a power law.

Models, Theoretical↗
PubMed2006

Language models based on Hebbian cell assemblies.

This paper demonstrates how associative neural networks as standard models for Hebbian cell assemblies can be extended to implement language processes in large-scale brain simulations. To this end the classical auto- and hetero-associative paradigms of attractor nets and synfire chains (SFCs) are combined and complemented by conditioned associations as a third principle which allows for the implementation of complex graph-like transition structures between assemblies. We show example simulations of a multiple area network for object-naming, which categorises objects in a visual hierarchy and generates different specific syntactic motor sequences ("words") in response. The formation of cell assemblies due to ongoing plasticity in a multiple area network for word learning is studied afterwards. Simulations show how assemblies can form by means of percolating activity across auditory and motor-related language areas, a process supported by rhythmic, synchronized propagating waves through the network. Simulations further reproduce differences in own EEG&MEG experiments between responses to word- versus non-word stimuli in human subjects.

Animals↗
PubMed2004

TopNet: a tool for comparing biological sub-networks, correlating protein properties with topological statistics.

Biological networks are a topic of great current interest, particularly with the publication of a number of large genome-wide interaction datasets. They are globally characterized by a variety of graph-theoretic statistics, such as the degree distribution, clustering coefficient, characteristic path length and diameter. Moreover, real protein networks are quite complex and can often be divided into many sub-networks through systematic selection of different nodes and edges. For instance, proteins can be sub-divided by expression level, length, amino-acid composition, solubility, secondary structure and function. A challenging research question is to compare the topologies of sub- networks, looking for global differences associated with different types of proteins. TopNet is an automated web tool designed to address this question, calculating and comparing topological characteristics for different sub-networks derived from any given protein network. It provides reasonable solutions to the calculation of network statistics for sub-networks embedded within a larger network and gives simplified views of a sub-network of interest, allowing one to navigate through it. After constructing TopNet, we applied it to the interaction networks and protein classes currently available for yeast. We were able to find a number of potential biological correlations. In particular, we found that soluble proteins had more interactions than membrane proteins. Moreover, amongst soluble proteins, those that were highly expressed, had many polar amino acids, and had many alpha helices, tended to have the most interaction partners. Interestingly, TopNet also turned up some systematic biases in the current yeast interaction network: on average, proteins with a known functional classification had many more interaction partners than those without. This phenomenon may reflect the incompleteness of the experimentally determined yeast interaction network.

Algorithms↗
PubMed2006

Using the topology of metabolic networks to predict viability of mutant strains.

Understanding the relationships between the structure (topology) and function of biological networks is a central question of systems biology. The idea that topology is a major determinant of systems function has become an attractive and highly disputed hypothesis. Although structural analysis of interaction networks demonstrates a correlation between the topological properties of a node (protein, gene) in the network and its functional essentiality, the analysis of metabolic networks fails to find such correlations. In contrast, approaches utilizing both the topology and biochemical parameters of metabolic networks, e.g., flux balance analysis, are more successful in predicting phenotypes of knockout strains. We reconcile these seemingly conflicting results by showing that the topology of the metabolic networks of both Escherichia coli and Saccharomyces cerevisiae are, in fact, sufficient to predict the viability of knockout strains with accuracy comparable to flux balance analysis on large, unbiased mutant data sets. This surprising result is obtained by introducing a novel topology-based measure of network transport: synthetic accessibility. We also show that other popular topology-based characteristics such as node degree, graph diameter, and node usage (betweenness) fail to predict the viability of E. coli mutant strains. The success of synthetic accessibility demonstrates its ability to capture the essential properties of the metabolic network, such as the branching of chemical reactions and the directed transport of material from inputs to outputs. Our results strongly support a link between the topology and function of biological networks and, in agreement with recent genetic studies, emphasize the minimal role of flux rerouting in providing robustness of mutant strains.

Algorithms↗
PubMed2000

FPNA: interaction between FPGA and neural computation.

Neural networks are usually considered as naturally parallel computing models. But the number of operators and the complex connection graph of standard neural models can not be directly handled by digital hardware devices. More particularly, several works show that programmable digital hardware is a real opportunity for flexible hardware implementations of neural networks. And yet many area and topology problems arise when standard neural models are implemented onto programmable circuits such as FPGAs, so that the fast FPGA technology improvements can not be fully exploited. Therefore neural network hardware implementations need to reconcile simple hardware topologies with complex neural architectures. The theoretical and practical framework developed, allows this combination thanks to some principles of configurable hardware that are applied to neural computation: Field Programmable Neural Arrays (FPNA) lead to powerful neural architectures that are easy to map onto FPGAs, thanks to a simplified topology and an original data exchange scheme. This paper shows how FPGAs have led to the definition of the FPNA computation paradigm. Then it shows how FPNAs contribute to current and future FPGA-based neural implementations by solving the general problems that are raised by the implementation of complex neural networks onto FPGAs.

Computers↗
PubMed1995

Neuronal growth via hybrid system of self-growing and diffusion based grammar rules: I.

The formation of neuronal networks requires axonal growth towards target neurons. A simple set of grammar rules is introduced to describe axonal growth towards target cells situated both at short and long distances from the growing neuron. Growth for short distances is described by growth following the highest gradient of a chemical compound (which is spread by diffusion from the targets). This approach fails to describe long-distance growth, which is addressed by adopting a graph grammar theory for growing trees. With these rules a flexible tool to draw network of neurons by computer can be developed.

Animals↗
PubMed2003

Improving HIV/AIDS services through a network-based health information system.

RW CAREWare is a free Microsoft Accessâ-based application developed and distributed by the HIV/AIDS Bureau (HAB) in the Health Resources and Services Administration of the US Dept. of Health and Human Services. This presentation will demonstrate the main screens and functions of CAREWare, including the ability to generate a number of service and clinical outcome reports; produce lists of clients requiring specific follow-up for care and treatment; create custom fields; and produce longitudinal graphs of laboratory tests and medication regimens. The security features, data-sharing arrangements among network members, and flexibility of the.NET version will also be emphasized.

Acquired Immunodeficiency Syndrome↗
PubMed2005

Finding local community structure in networks.

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(k2d) for general graphs when d is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time consuming, the running time is linear, O(k). We show that on computer-generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge. As an application, we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer.

Journal Article↗
PubMed2005

Bayesian networks and probabilistic reasoning about scientific evidence when there is a lack of data.

Bayesian networks (BNs) are a kind of graphical model that formally combines elements of graph and probability theory. BNs are a mathematically and statistically rigorous technique allowing their user to define a pictorial representation of assumed dependencies and influences among a set of variables deemed to be relevant for a particular inferential problem. The formalism allows one to process newly acquired evidence according to the rules of probability calculus. Applications of BNs have been reported in various forensic disciplines. However, there seems to be some reluctance to consider BNs as a more general framework for representing and evaluating sources of uncertainties associated with scientific evidence. Notably, BNs are widely thought of as an essentially numerical method, requiring "exact" numbers with a high "accuracy". The present paper aims to draw the reader's attention to the point that the availability of hard numerical data is not a necessary requirement for using BNs in forensic science. An abstraction of quantitative BNs, known as qualitative probabilistic networks (QPNs), and sensitivity analyses are presented and their potential applications discussed. As a main difference to their quantitative counterpart, QPNs contain qualitative probabilistic relationships instead of numerical relations. Sensitivity analyses consist of varying the probabilities assigned to one or more variables and evaluating the effect on one or more other variables of interest. Both QPNs and sensitivity analyses appear to be useful concepts that permit one to work in contexts with acute lack of numerical data and where reasoning consistent with the laws of probability should nevertheless be performed.

Journal Article↗
PubMed2005

The evolution of domain arrangements in proteins and interaction networks.

Proteins are composed of domains, which are conserved evolutionary units that often also correspond to functional units and can frequently be detected with reasonable reliability using computational methods. Most proteins consist of two or more domains, giving rise to a variety of combinations of domains. Another level of complexity arises because proteins themselves can form complexes with small molecules, nucleic acids and other proteins. The networks of both domain combinations and protein interactions can be conceptualised as graphs, and these graphs can be analysed conveniently by computational methods. In this review we summarise facts and hypotheses about the evolution of domains in multi-domain proteins and protein complexes, and the tools and data resources available to study them.

Amino Acid Sequence↗
PubMed2004

Qualitative simulation of genetic regulatory networks using piecewise-linear models.

In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarse-grained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.

Computer Simulation↗
PubMed2005

An incremental regression method for graph structured data.

In this paper, we consider learning problems defined on graph-structured data. We propose an incremental supervised learning algorithm for network-based estimators using diffusion kernels. Diffusion kernel nodes are iteratively added in the training process. For each new node added, the kernel function center and the output connection weight are decided according to an empirical risk driven rule based on an extended chained version of the Nadaraja-Watson estimator. Then the diffusion parameters are determined by a genetic-like optimization technique.

Algorithms↗
PubMed2003

Protein complexes and functional modules in molecular networks.

Proteins, nucleic acids, and small molecules form a dense network of molecular interactions in a cell. Molecules are nodes of this network, and the interactions between them are edges. The architecture of molecular networks can reveal important principles of cellular organization and function, similarly to the way that protein structure tells us about the function and organization of a protein. Computational analysis of molecular networks has been primarily concerned with node degree [Wagner, A. & Fell, D. A. (2001) Proc. R. Soc. London Ser. B 268, 1803-1810; Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N. & Barabasi, A. L. (2000) Nature 407, 651-654] or degree correlation [Maslov, S. & Sneppen, K. (2002) Science 296, 910-913], and hence focused on single/two-body properties of these networks. Here, by analyzing the multibody structure of the network of protein-protein interactions, we discovered molecular modules that are densely connected within themselves but sparsely connected with the rest of the network. Comparison with experimental data and functional annotation of genes showed two types of modules: (i) protein complexes (splicing machinery, transcription factors, etc.) and (ii) dynamic functional units (signaling cascades, cell-cycle regulation, etc.). Discovered modules are highly statistically significant, as is evident from comparison with random graphs, and are robust to noise in the data. Our results provide strong support for the network modularity principle introduced by Hartwell et al. [Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. (1999) Nature 402, C47-C52], suggesting that found modules constitute the "building blocks" of molecular networks.

Biophysical Phenomena↗