SEARCH · PubMed Health

Results for “Graph”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20Linked to original sources

PubMed1982

Computer-assisted sequencing, interval graphs, and molecular evolution.

In 1945, Fox developed the strategy for sequencing long proteins by using overlapping fragments. We show how the formal mathematical technique for the construction of interval graphs (Gilmore and Hoffman, 1964) is useful both pedagogically for understanding the underlying logic of sequencing linear molecules and is more amenable to automation because of its algorithmic nature. We also present a computer program, that employs the interval graph algorithm, which can be used to sequence proteins when given digest data. An example is given to illustrate all the steps involved in the algorithmic processing of the data. The need for such developments with respect to molecular evolution is discussed.

Amino Acid Sequence↗

PubMed1995

Use of graph theoretic parameters in risk assessment of chemicals.

In many instances of risk assessment, one has to estimate the potential risk of chemicals using limited experimental data, or no empirical data at all. In such cases, the use of non-empirical parameters, which can be calculated directly from structure, is a viable option for the risk assessor. Graph invariants have been used in predicting properties of congeneric sets of chemicals and determining structural similarity/dissimilarity of molecules. In this paper we have used (a) topological parameters in predicting mutagenicity of a diverse set of 520 chemicals and (b) graph theoretic parameters in quantifying structural similarity for a selection of analogs. The results of these analyses are presented along with a critical discussion of the utility and limitations of these methods.

Data Interpretation, Statistical↗

PubMed2006

Complexity and non-commutativity of learning operations on graphs.

We present results from numerical studies of supervised learning operations in small recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors, which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the sequence of inputs, this structure is generally non-commutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated.

Artificial Intelligence↗

PubMed2005

QSAR of the testosterone binding globulin affinity by means of correlation weighting of local invariants of the graph of atomic orbitals.

Numerical values of the testosterone binding globulin affinity have been modeled as a mathematical function of molecular structure in two versions of molecular structure elucidation: first, by hydrogen-filled molecular graphs (HFG); second, by the so-called graphs of atomic orbitals (GAO). Increased orders of Morgan extended connectivity in the HFG and GAO have been examined as local invariants. Using optimisation of the correlation weights of the above-mentioned invariants, quantitative structure-activity relationships (QSAR) have been obtained. Best statistical characteristics of these QSARs are derived in the case of the Morgan extended connectivity of first order in the GAO. They are as follows: n = 11, r2 = 0.6540, s = 0.824, F = 17 (training set); n = 9, r2 = 0.8791, s = 0.388, F = 51 (test set).

Molecular Structure↗

PubMed2006

QSAR models of quail dietary toxicity based on the graph of atomic orbitals.

Graphs of atomic orbitals (GAOs) have been used to represent molecular structures. We describe rules to convert the labelled hydrogen-filled graphs (LHFGs) into GAOs. The GAO is one possible way of taking account of the structure of atoms (i.e., atomic orbitals, such as 1s(1), 2p(2) and 3d(10)) for QSPR/QSAR analyses. Optimization of correlation weights of local invariants (OCWLI) of the LHFGs and the GAOs was used to obtain a method of quail dietary toxicity modelling. Statistical characteristics of the models based on the OCWLI of GAO are better than those based on the OCWLI of the LHFGs.

Animals↗

PubMed2006

Disturbed functional connectivity in brain tumour patients: evaluation by graph analysis of synchronization matrices.

OBJECTIVE: Cerebral functions are based on the functional interactions between multiple distinct specialized regions of the brain. Functional interactions require anatomical connections as well as the synchronization of brain oscillations. The present work aims at evaluating the impact of brain tumours on spatial patterns of functional connectivity of the brain measured at rest by MEG. METHODS: We analyzed the statistical dependency (by computing the synchronization likelihood (SL, a measure of generalized synchronization)) between MEG signals at rest, in 17 patients with a brain tumour and in 15 healthy controls. Following an approach that derives from graph theory, we also analyzed the architectural properties of the networks by computing two parameters from the SL matrix, the cluster coefficient C and the characteristic path length L. RESULTS: Alterations in synchronization levels were found in the patients and were not focal but involved intra-hemispheric connectivity. Effects were different considering the frequencies sub-bands, predominating in a decrease in high frequencies bands for long-distance connections and an increase in slower bands for local connectivity. In addition, graph analysis reveals changes in the normal "small-world" network architecture in addition to changes in synchronization levels with some differences according to the studied frequency sub-bands. CONCLUSIONS: Brain tumours alter the functional connectivity and the "network" architecture of the brain. These alterations are not focal and effects are different considering the frequencies sub-bands. SIGNIFICANCE: These neurophysiological changes may contribute to the cognitive alterations observed in patients with brain tumours.

Adult↗

PubMed2004

Protein synthesis profiling in the developing brain: a graph theoretic clustering approach.

Mapping regional brain development in terms of protein synthesis (PS) activity yields insight on specific spatio-temporal ontogenetic patterns. The biosynthetic activity of an individual brain nucleus is represented as a time-series object, and clustering of time-series contributes to the problem of inducing indicative patterns of brain developmental events and forming respective PS chronological maps. Clustering analysis of PS chronological maps, in comparison with epigenetic influences of alpha2 adrenoceptors treatment, reveals relationships between distantly located brain structures. Clustering is performed with a novel graph theoretic clustering approach (GTC). The approach is based on the weighted graph arrangement of the input objects and the iterative partitioning of the corresponding minimum spanning tree. The final result is a hierarchical clustering-tree organization of the input objects. Application of GTC on the PS patterns in developing brain revealed five main clusters that correspond to respective brain development indicative profiles. The induced profiles confirm experimental findings, and provide evidence for further experimental studies.

Animals↗

PubMed2004

A graph theory analysis of renal glomerular microvascular networks.

A graph theory model and its invariants are used to compare previously published renal glomerular networks of six adult rats, one adult uremic rat, and one newborn rat. Invariants calculated include order, size, cycle rank, eccentricity, root distance, planarity, and vertex degree distribution. These invariants enabled the differentiation of six normal adult glomerular microvascular networks from that of the uremic glomerulus and from that of the normal newborn glomerulus. These invariants might then be used to differentiate between normal and pathological vascular networks. Also proposed are graph theory invariants that might be used to develop a quantitative model for angiogenesis.

Animals↗

PubMed2005

Graph kernels for chemical informatics.

Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their covalent bonds, machine learning methods in this domain must be capable of processing graphical structures with variable size. Here, we first briefly review the literature on graph kernels and then introduce three new kernels (Tanimoto, MinMax, Hybrid) based on the idea of molecular fingerprints and counting labeled paths of depth up to d using depth-first search from each possible vertex. The kernels are applied to three classification problems to predict mutagenicity, toxicity, and anti-cancer activity on three publicly available data sets. The kernels achieve performances at least comparable, and most often superior, to those previously reported in the literature reaching accuracies of 91.5% on the Mutag dataset, 65-67% on the PTC (Predictive Toxicology Challenge) dataset, and 72% on the NCI (National Cancer Institute) dataset. Properties and tradeoffs of these kernels, as well as other proposed kernels that leverage 1D or 3D representations of molecules, are briefly discussed.

Anticarcinogenic Agents↗

PubMed2006

Network and graph analyses of folding free energy surfaces.

Protein folding is governed by a complex free energy surface whose entropic contributions are relevant because of the large number of degrees of freedom involved. Such complexity, in particular the conformational heterogeneity of the denatured state, is hidden in projections onto one or two order parameters (e.g. fraction of native contacts and/or radius of gyration), which usually results in relatively smooth surfaces. Recent approaches borrowed from network and graph theory have yielded quantitative unprojected representations of the free energy surfaces of a beta-hairpin and a three-stranded beta-sheet peptide using equilibrium folding-unfolding molecular dynamics simulations. Interestingly, the network and graph analyses of these structured peptides have revealed a very heterogeneous denatured state ensemble. It includes high-enthalpy, high-entropy conformations with fluctuating non-native secondary structure, as well as low-enthalpy, low-entropy traps.

Computational Biology↗

PubMed2005

Integrating genealogy and epidemiology: the ancestral infection and selection graph as a model for reconstructing host virus histories.

We model the genealogies of coupled haploid host-virus populations. Hosts reproduce and replace other hosts as in the Moran model. The virus can be transmitted between individuals of the same and succeeding generations. The epidemic model allows a selective advantage for susceptible over infected hosts. The coupled host-virus ancestry of a sample of hosts is embedded in a branching and coalescing structure that we call the Ancestral Infection and Selection Graph, a direct analogue to the Ancestral Selection Graph of Krone and Neuhauser [1997. Theoret. Population Biol. 51, 210-237]. We prove this and discuss various special cases. We show that the inter-host viral genealogy is a scaled coalescent. Using simulations, we compare the viral genealogy under this model to earlier published models and investigate the estimatability of the selection and infectious contact rates. We use simulations to compare the persistence of the disease with the time to the ultimate ancestor.

Computer Simulation↗

PubMed1998

Evaluating the statistical conclusion validity of weighted mean results in meta-analysis by analysing funnel graph diagrams.

The validity of weighted mean results estimated in meta-analysis has been criticized. This paper presents a set of simple statistical and graphical techniques that can be used in meta-analysis to evaluate common points of criticism. The graphical techniques are based on funnel graph diagrams. Problems and techniques for dealing with them that are discussed include: (1) the so-called 'apples and oranges' problem, stating that mean results in meta-analysis tend to gloss over important differences that should be highlighted. A test of the homogeneity of results is described for testing the presence of this problem. If results are highly heterogeneous, a random effects model of meta-analysis is more appropriate than the fixed effects model of analysis. (2) The possible presence of skewness in a sample of results. This can be tested by comparing the mode, median and mean of the results in the sample. (3) The possible presence of more than one mode in a sample of results. This can be tested by forming a frequency distribution of the results and examining the shape of this distribution. (4) The sensitivity of the mean to the possible presence of atypical results (outliers) can be tested by comparing the overall mean to the mean of all results except the one suspected of being atypical. (5) The possible presence of publication bias can be tested by visual inspection of funnel graph diagrams in which data points have been sorted according to statistical significance and direction of effect. (6) The possibility of underestimating the standard error of the mean in meta-analyses by using multiple, correlated results from the same study as the unit of analysis can be addressed by using the jack-knife technique for estimating the uncertainty of the mean. Brief examples, taken from road safety research, are given of all these techniques.

Accidents, Traffic↗

PubMed1998

Categorization of interictal epileptiform potentials using a graph-theoretic method.

OBJECTIVES: In patients with epileptic seizures, localization of the source of interictal epileptiform activity is of interest. For correct source localization, a favorable signal to noise ratio is important, and to achieve this, averaging of several epileptiform potentials is often necessary. Before averaging, a careful categorization of epileptiform potentials with different potential distributions is crucial. The aim of this study was to investigate whether a a hierarchic, graph-theoretic algorithm could be used for this categorization. METHODS: In 4 patients, 50-100 sharp waves with different surface distributions were categorized independently with the algorithm, and by visual inspection of the traces. As an independent evaluation of the algorithm, a dipole reconstruction was performed for each sharp wave, and the dipole results for the sharp waves from the different automatically obtained categories were compared. RESULTS: All patients showed a high degree of correspondence between the results of the automatic analysis and the visual estimation. There were clear differences in dipole results between the sharp waves of the different categories obtained from the automatic categorization. CONCLUSION: The results indicate that the graph-theoretic categorization algorithm provides a reliable clustering of interictal epileptiform potentials, and that the method may become a useful tool in the pre-averaging categorization of interictal epileptiform potentials prior to source localization.

Action Potentials↗

PubMed2002

Fusion of qualitative bond graph and genetic algorithms: a fault diagnosis application.

In this paper, the problem of fault diagnosis via integration of genetic algorithms (GA's) and qualitative bond graphs (QBG's) is addressed. We suggest that GA's can be used to search for possible fault components among a system of qualitative equations. The QBG is adopted as the modeling scheme to generate a set of qualitative equations. The qualitative bond graph provides a unified approach for modeling engineering systems, in particular, mechatronic systems. In order to demonstrate the performance of the proposed algorithm, we have tested the proposed algorithm on an in-house designed and built floating disc experimental setup. Results from fault diagnosis in the floating disc system are presented and discussed. Additional measurements will be required to localize the fault when more than one fault candidate is inferred. Fault diagnosis is activated by a fault detection mechanism when a discrepancy between measured abnormal behavior and predicted system behavior is observed. The fault detection mechanism is not presented here.

Air Movements↗

PubMed1991

Identification of regulatory properties of metabolic networks by graph theoretical modeling.

An earlier graph theoretical model of metabolic and gene-expression networks has been modified and extended to include the effect of electrical potentials on binding constants, representation of uncatalyzed processes, and treatment of parallel reactions catalyzed by a single enzyme. Formal operations on the graph, which are facilitated by a set of standardized guidelines, identify the feedback signals in the network and rank them according to their influence. The technique was applied to a model of glycolysis in ascites tumor cells in the absence and presence of 12.5 mM exogenous glucose. Feedback regulation was widely distributed and mostly due to binding of adenine nucleotide cofactors to the enzymes of the network. The major changes in feedback regulation on adding glucose is the relief of inhibition of hexokinase and phosphofructokinase and the activation of pyruvate kinase. We conclude that regulation of tumor cell glycolysis is not restricted to hexokinase or to (Na+,K+)-ATPase as was previously suggested by others.

Animals↗

PubMed2001

Calculating sequence-dependent melting stability of duplex DNA oligomers and multiplex sequence analysis by graphs.

The analytical methods for characterizing DNA sequence-dependent thermodynamic stability have been reviewed. A set of n-n sequence stability parameters is presented. Examples in which these values are used to calculate the thermodynamic stability of short duplex DNA oligomers are presented. The problem of determining sets of isothermal sequences is addressed by representing DNA sequences as graphs. Representing DNA sequences by a graph descriptor with special mathematical properties minimizes the computational difficulty of determining the number of DNA sequences with identical predicted thermodynamic stability. This is achieved by replacement of a whole set of sequences by a single representative. Applications of this concept were demonstrated for sequences assembled from individual bases and sequences assembled from oligomeric blocks.

Base Sequence↗

PubMed2002

A graph-theoretic method to identify candidate mechanisms for deriving the rate law of a catalytic reaction.

Stoichiometrically, exact candidate pathways or mechanisms for deriving the rate law of a catalytic or complex reaction can be determined through the synthesis of networks of plausible elementary reactions constituting such pathways. A rigorous algorithmic method is proposed for executing this synthesis, which is exceedingly convoluted due to its combinatorial complexity. Such a method for synthesizing networks of reaction pathways follows the general framework of a highly exacting combinatorial method established by us for process-network synthesis. It is based on the unique graph-representation in terms of P-graphs, a set of axioms, and a group of combinatorial algorithms. In the method, the inclusion or exclusion of a step of each elementary reaction in the mechanism of concern hinges on the general combinatorial properties of feasible reaction networks. The decisions are facilitated by solving linear programming problems comprising a set of mass-balance constraints to determine the existence or absence of any feasible solution. The search is accelerated further by exploiting the inferences of preceding decisions, thereby eliminating redundancy. As a result, all feasible independent reaction networks, i.e. pathways, are generated only once; the pathways violating any first principle of either stoichiometry or thermodynamics are eliminated. The method is also capable of generating those combinations of independent pathways directly, which are not microscopically reversible. The efficiency and efficacy of the method are demonstrated with the identification of the feasible mechanisms of ammonia synthesis involving as many as 14 known elementary reactions.

Journal Article↗

PubMed2000

A computer-based approach to describe the 13C NMR chemical shifts of alkanes by the generalized spectral moments of iterated line graphs

A recently introduced strategy to quantitative structure-property relationship studies is used to model the sum of 13C NMR chemical shifts of alkanes. This graph theoretical approach is based on the spectral moments of the iterated line graph sequence (ILGS). The statistical quality of the model developed by using the present approach is compared to those obtained by using spectral moments of the bond matrix or the embedding frequencies of alkanes as independent variables. The embedding frequencies were computed on the basis of the spectral moments of the ILGS. The emphasis of this work is on the structural interpretation of the results. Consequently, the contributions of the different structural fragments of alkanes to the 13C NMR chemical shift sum are computed by the three theoretical approaches. The advantages and disadvantages of the use of these approaches are analyzed on the basis of computational expenditure, i.e. computer time and memory, and the statistical quality, complexity, and structural interpretation of the models developed.

Journal Article↗