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At least 253 records · Page 14Linked to original sources

PubMedDate not supplied

Prediction of aquatic toxicity: use of optimization of correlation weights of local graph invariants.

Quantitative structure-activity relationships (QSARs) were developed for three sets of toxicity data. Chemicals in each set represented a number of narcoses and electrophilic mechanisms of toxic action. A series of quantitative structure-toxicity models correlating toxic potency with a number of optimization of correlation weights of local graph invariants were developed. In the case of the toxicity of a heterogeneous set of benzene derivatives to Tetrahymena pyriformis, the QSARs were based on the Descriptor of Correlation Weights (DCW) using atoms and extended connectivity (EC) graph invariants. The model [log (IGC(50)(-1)) = 0.0813 DCW(a(k),(3)EC(k)) + 2.636; n = 157, r(2) = 0.883, s = 0.27, F = 1170, Pr > F = 0.0001] based on third-order EC of 89 descriptors was observed to be best for the benzene data. However, fits for these data of > 0.800 were achieved ECs with as few as 23 variables. The relationship between the toxicity predicted by this model and experimental toxicity values for the test set [obs. log(IGC(50)(-1))) = 0.991 (pred. (log(IGC(50)(-1))) - 0.012; n = 60, r(2) = 0.863, s = 0.28, F = 372, Pr > F = 0.0001] is excellent. The utility of the approach was demonstrated by the model [log (IGC(50)(-1)) = 0.1744(DCW (a(k), (2)EC) - 3.505; n = 39, r(2) = 0.900, s = 0.35, F = 333, Pr > F = 0.0001] for the toxicity data for T. pyriformis exposed to halo-substituted aliphatic compounds and the model [log (IC(50)(-1)) = 0.1699(DCW (a(k), (2)EC)) - 2.610; n = 66, r(2) = 0.901, s = 0.31, F = 583, Pr > F = 0.0001] for the Vibrio fischeri toxicity data.

Animals↗

PubMed2000

Walk counts, labyrinthicity, and complexity of acyclic and cyclic graphs and molecules

It is demonstrated how the complexity of a (molecular) graph can be quantified in terms of the walk counts, extremely easily obtained graph invariants that depend on size, branching, cyclicity, and edge and vertex weights (unsaturation, heteroatoms). The influence of symmetry is easily accounted for. The term labyrinthicity is proposed for what is measured by walk counts alone, neglecting symmetry. The total walk count and recently advanced measures of labyrinthicity or complexity are compared with respect to the ordering of structures and to the computational effort required to obtain numerical values.

Journal Article↗

PubMed2000

Prognostic value of graph theory-based tissue architecture analysis in carcinomas of the tongue.

Several studies on oral squamous cell carcinomas (OSCC) suggest that the clinical value of traditional histologic grading is limited both by poor reproducibility and by low prognostic impact. However, the prognostic potential of a strictly quantitative and highly reproducible assessment of the tissue architecture in OSCC has not been evaluated. Using image analysis, in 193 cases of T1-2 (Stage I-II) OSCC we retrospectively investigated the prognostic impact of two graph theory-derived structural features: the average Delaunay Edge Length (DEL_av) and the average homogeneity of the Ulam Tree (ELH_av). Both structural features were derived from subgraphs of the Voronoi Diagram. The geometric centers of the cell nuclei were computed, generating a two-dimensional swarm of point-like seeds from which graphs could be constructed. The impact on survival of the computed values of ELH_av and DEL_av was estimated by the method of Kaplan and Meier, with relapse-free survival and overall survival as end-points. The prognostic values of DEL_av and ELH_av as computed for the invasive front, the superficial part of the carcinoma, the total carcinoma, and the normal-appearing oral mucosa were compared. For DEL_av, significant prognostic information was found in the invasive front (p < 0.001). No significant prognostic information was found in superficial part of the carcinoma (p = 0.34), in the carcinoma as a whole (p = 0.35), or in the normal-appearing mucosa (p = 0.27). For ELH_av, significant prognostic information was found in the invasive front (p = 0.01) and, surprisingly, in putatively normal mucosa (p = 0.03). No significant prognostic information was found in superficial parts of the carcinoma (p = 0.34) or in the total carcinoma (p = 0.11). In conclusion, strictly quantitative assessment of tissue architecture in the invasive front of OSCC yields highly prognostic information.

Aged↗

PubMed1997

[Inclination of the Hess-Weiss coordimetric graph. An indirect sign of ocular torsion?].

BACKGROUND: The coordimetric examinations according to Hess-Weiss (HW) and Hess-Lancaster produce the bidimensional graphic demonstration of eye deviations. The horizontal and vertical deviations can be shown easily, whereas cyclotorsion cannot be detected readily. Clinical experience has suggested, however, that there may be an association between rotation of the HW graph and cyclotorsion. The question is, how much can the bidimensional presentation be influenced by the cyclotorsion? METHODS: 48 patients with posttraumatic superior oblique palsy were investigated. The cyclotropia measured at the tangent scale of Harms (dark-red glass method) was compared to the rotation of the HW graph. Patients were divided into 2 groups: 27 unilateral and 21 bilateral palsy. CONCLUSION: The association between the two examination parameters was significant in both patient groups (Group 1 p < 0.01, Group 2 p < 0.05).

Adolescent↗

PubMedDate not supplied

[Percentile graphs in the documentation of acetabular angle in children with hip dysplasia. A tool in the diagnosis and quality control of its treatment].

The acetabular index (AI; Hilgenreiner 1925) has proven to be a reliable parameter for the radiological diagnosis of developmental hip dysplasia (DDH). Age-dependent normal values and ranges of the AI are well documented. These data, however, have so far not been presented graphically in a way which would have made them suitable for patient data documentation on a routine basis (calculation of percentiles, time-axis with log scale, smoothing). We have therefore created graphs meeting these requirements, based on a previous examination of the AI of 719 girls and 428 boys (Tönnis and Brunken 1968). These graphs have meanwhile proven to be a useful and time-saving tool for the diagnosis as well as quality control of the treatment in children with DDH.

Acetabulum↗

PubMed2002

Random graph models of social networks.

We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world social networks and find that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

Humans↗

PubMed1988

Interrelations between random walks on diagrams (graphs) with and without cycles.

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Algorithms↗

PubMed2000

Bounds for cell entries in contingency tables given marginal totals and decomposable graphs.

Upper and lower bounds on cell counts in cross-classifications of nonnegative counts play important roles in a number of practical problems, including statistical disclosure limitation, computer tomography, mass transportation, cell suppression, and data swapping. Some features of the Frechet bounds are well known, intuitive, and regularly used by those working on disclosure limitation methods, especially those for two-dimensional tables. We previously have described a series of results relating these bounds to theory on loglinear models for cross-classified counts. This paper provides the actual theory and proofs for the special case of decomposable loglinear models and their related independence graphs. It also includes an extension linked to the structure of reducible graphs and a discussion of the relevance of other results linked to nongraphical loglinear models.

Journal Article↗

PubMed1994

Integration of graph theory and quantum chemistry for structure-activity relationships.

The objective of this article is to outline both graph-theoretically based and quantum chemically based structural indices of potential use in quantitative structure activity correlations. We consider graph-theoretical indices such as the connectivity index, topological index, Wiener index and molecular ID indices. Several structural and geometry-dependent indices can be derived from semiempirical and ab initio quantum calculations based on the charge densities, overlap matrices, frontier orbitals, molecular hardness, free valence, density matrices, quantum spectral difference indices, quantum spectral indices and bond matrices. Finally, the use of electrostatic potentials and charge densities for the prediction of reactive sites will be discussed.

Butadienes↗

PubMed1992

Timing of physiodesis in limb length inequality. The Straight Line Graph applied in 30 patients.

In a prospective study 30 children underwent 33 physiodeses for lower limb length inequality (LLI). Timing of surgery was based on (bi)annual orthoradiographic measurements and skeletal age, and in accordance with Moseley's Straight Line Graph. The mean predicted LLI was 5.2 (3.0-11) cm and the mean LLI at the end of growth was 1.4 (0.0-4.3) cm. In 9 patients final LLI exceeded 1.5 cm, and one of these patients was operated on twice. In total, secondary operations were performed three times. After analysis of the failures it is concluded that the accuracy of the Straight Line Graph is mainly limited by the pattern of skeletal maturation. Recommendations to prevent failures from other causes are given.

Adolescent↗

PubMed1994

An algorithm based on graph theory for the assembly of contigs in physical mapping of DNA.

An algorithm is described for mapping DNA contigs based on an interval graph (IG) representation. In general terms, the input to the algorithm is a set of binary overlapping relations among finite intervals spread along a real line, from which the algorithm generates sets of ordered overlapping fragments spanning that line. The implications of a more general case of the IG, called a probe interval graph (PIG), in which only a subset of cosmids are used as probes, are also discussed. In the specific case of cosmids hybridizing to regions of a YAC, the algorithm takes cross-hybridization information using the cosmids as probes, and orders them along the YAC; if gaps exist due to insufficient coverage of cosmid contigs along the length of the YAC, repetitive use of the algorithm generates sets of ordered overlapping fragments. Both the IG and the PIG can expose problems caused by false overlaps, such as hybridizations due to repetitive elements. The algorithm, has been coded in C; CPU time is essentially linear with respect to the number of cosmids analyzed. Results are presented for the application of a PIG to cosmid contig assembly along a human chromosome 13-specific YAC. An alignment of 67 cosmids spanning a YAC took 0.28 seconds of CPU time on a Convex 220 computer.

Algorithms↗

PubMed1999

Revealing hidden interval graph structure in STS-content data.

MOTIVATION: STS-content data for genomic mapping contain numerous errors and anomalies resulting in cross-links among distant regions of the genome. Identification of contigs within the data is an important and difficult problem. RESULTS: This paper introduces a graph algorithm which creates a simplified view of STS-content data. The shape of the resulting structure graph provides a quality check - coherent data produce a straight line, while anomalous data produce branches and loops. In the latter case, it is sometimes possible to disentangle the various paths into subsets of the data covering contiguous regions of the genome, i.e. contigs. These straight subgraphs can then be analyzed in standard ways to construct a physical map. A theoretical basis for the method is presented along with examples of its application to current STS data from human genome centers. AVAILABILITY: Freely available on request.

Algorithms↗

PubMed2025

monarchr: an R package for querying biomedical knowledge graphs.

SUMMARY: Biomedical knowledge graphs (KGs) aggregate and provide a wealth of information, linking genes and their variants, diseases, phenotypes, and much more. While these data are available in raw and API-hosted form, to date, functionality for working with KGs in the R programming language has been limited. We introduce monarchr, a package for querying and manipulating KG data. Support for the expansive Monarch Initiative KG is built in, and monarchr can accommodate any KG in the Knowledge Graph eXchange (KGX) format. This tidy-inspired interface offers researchers an intuitive, iterative approach to querying and visualizing KG data. AVAILABILITY AND IMPLEMENTATION: Source code, documentation, and installation instructions are available at https://github.com/monarch-initiative/monarchr.

Software↗

PubMed2026

EPIC: Event Prototyping via Information Constrained graph learning for personalized cancer driver gene prediction.

MOTIVATION: Precision oncology relies on accurately distinguishing patient-specific driver mutations from the vast background of passenger alterations. While graph-based computational methods have emerged as powerful tools for this task, they often struggle to preserve the distinct genomic context of individual mutations within complex biological networks. Consequently, subtle patient-specific driver signals are frequently obscured by dominant topological patterns, critically impeding the identification of individualized oncogenic events essential for personalized cancer therapy. RESULTS: To address this, we propose EPIC, a novel framework for Event Prototyping via Information Constrained Graph Learning. Unlike traditional node-centric approaches, EPIC redefines driver prediction as a metric learning task in an event embedding space. We introduce an information-constrained learning strategy that imposes explicit geometric constraints on feature variance, effectively preventing feature collapse and ensuring that low-frequency driver signals are distinctively preserved. Experiments on large-scale cancer cohorts demonstrate that EPIC significantly outperforms established baselines. Notably, the model prioritizes low-frequency driver variants typically overlooked by population-based methods, mapping them to critical oncogenic mechanisms associated with drug resistance and metastasis. Furthermore, clinical actionability analysis confirms that EPIC substantially expands the patient population eligible for targeted therapies. EPIC provides a robust and context-aware solution for personalized cancer driver discovery, bridging the gap between genomic data and actionable therapeutic insights. AVAILABILITY AND IMPLEMENTATION: The source code and datasets are available at https://github.com/spcho-dev/EPIC.

Humans↗

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↗

PubMed2026

GT-Mamba: a Topology-Aware Graph-State space model for robust and interpretable epigenetic age prediction.

MOTIVATION: Current epigenetic clocks face a trade-off between predictive accuracy and biological interpretability, often relying on dataset-specific correction to generalize across cohorts. We propose GT-Mamba, a novel architecture that integrates a Structure-Aware Graph Transformer with the Mamba state space model. This design captures CpG topological correlations and genome-wide long-range dependencies. RESULTS: GT-Mamba demonstrates strong out-of-the-box robustness across heterogeneous independent validation cohorts, achieving a weighted average MAE of 4.43 years. Notably, it effectively generalizes to EPIC 850k arrays despite partial feature missingness, and maintains consistent performance across homologous age distribution shifts (MAE 2.94 years in a young cohort). Ablation studies confirm that graph topology contributes to improved robustness against noise. Mechanistic analysis suggests that the model captures methylation patterns associated with both developmental and functional processes. AVAILABILITY: Source code and pre-trained models are freely available at https://github.com/NENUBioCompute/GT-Mamba and archived on Zenodo (DOI: 10.5281/zenodo.19703155).

Epigenesis, Genetic↗

PubMed1990

A computer designed graph for administration of atracurium by i.v. infusion.

A bi-exponential mathematical computer model was used to develop a guidance graph for atracurium infusions. The model permitted variation in infusion rates, in pharmacokinetic parameters and in "effect" thresholds. Systematic experiments revealed a relationship between the rate of recovery from a fixed bolus loading dose and the most appropriate initial infusion rate. This relationship was expressed as a guidance graph or "ready reckoner". The quality of guidance was assessed in 50 anaesthetics, given consecutively. In 39 patients optimal myoneural block for surgery was maintained for the duration of the infusion without adjustments or supplementary bolus doses. The mean operating time was 92 min and the mean duration of infusion was 59 min.

Adult↗

PubMed1988

A box-graph method for illustrating relative-size relationships in a 2 x 2 table.

The proportional relationships of the four numbers in a 2 x 2 table can be displayed using two types of box graphs. In one approach, a 'unitary square' is first divided according to the denominator proportions of the two groups formed in a cohort or case-control study, and then re-divided according to the numerator proportions in each group. In the second method, the numbers are arranged as four squares, proportionately sized according to the square root of each number, and contiguously adjacent to a central reference point. The methods offer a pictorial format for showing contingency counts in a manner analogous to the graphs used for other forms of data.

Data Interpretation, Statistical↗