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After a review of the diagram method for continuous-time random walks on graphs with cycles, the method is extended to discrete-time random walks. The basic theorems carry over formally from continuous time to discrete time. Three problems in tennis probabilities are used to illustrate random walks on discrete-time diagrams with cycles.
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.
An algorithm using the graph theoretical approach to predict secondary structures of large nucleic acids is discussed. Reliability of prediction can be improved by incorporating available experimental data and sequence homology information. As a case study, this algorithm is applied to predict the secondary structure of the 16S-23S rRNA complex from E. coli. It was found that several structures of the complex can coexist. The computer program developed to predict the secondary structure of large RNAs can be run on IBM PC/AT compatible systems.
MOTIVATION: The pathogenesis of diseases is closely associated with genes, and the discovery of disease genes holds significant importance for understanding disease mechanisms and designing targeted therapeutics. However, biological validation of all genes for diseases is expensive and challenging. RESULTS: In this study, we propose DGP-AMIO, a computational method based on graph attention networks, to rank all unknown genes and identify potential novel disease genes by integrating multi-omics and gene interaction networks from multiple data sources. DGP-AMIO outperforms other methods significantly on 20 disease datasets, with an average AUROC and AUPR exceeding 0.9. The superior performance of DGP-AMIO is attributed to the integration of multiomics and gene interaction networks from multiple databases, as well as triGAT, a proposed GAT-based method that enables precise identification of disease genes in directed gene networks. Enrichment analysis conducted on the top 100 genes predicted by DGP-AMIO and literature research revealed that a majority of enriched GO terms, KEGG pathways and top genes were associated with diseases supported by relevant studies. We believe that our method can serve as an effective tool for identifying disease genes and guiding subsequent experimental validation efforts. AVAILABILITY AND IMPLEMENTATION: DGP-AMIO is publicly available at https://github.com/yangkaiyuan1027/DGP-AMIO.
MOTIVATION: Developing computational tools for integrative analysis across multiple types of omics data has been of immense importance in cancer molecular biology and precision medicine research. While recent advancements have yielded integrative prediction solutions for multi-omics data, these methods lack a comprehensive and cohesive understanding of the rationale behind their specific predictions. To shed light on personalized medicine and unravel previously unknown characteristics within integrative analysis of multi-omics data, we introduce a novel integrative neural network approach for cancer molecular subtype and biomedical classification applications, named Integrative Graph Convolutional Networks (IGCN). RESULTS: To demonstrate the superiority of IGCN, we compare its performance with other state-of-the-art approaches across different cancer subtype and biomedical classification tasks. Our experimental results show that our proposed model outperforms the state-of-the-art and baseline methods. IGCN identifies which types of omics data receive more emphasis for each patient when predicting a specific class. Additionally, IGCN has the capability to pinpoint significant biomarkers from a range of omics data types. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/bozdaglab/IGCN.
SUMMARY: Ancestral recombination graphs (ARGs) represent the interwoven paths of genetic ancestry of a set of recombining sequences. The ability to capture the evolutionary history of samples makes ARGs valuable in a wide range of applications in population and statistical genetics. ARG-based approaches are increasingly becoming a part of genetic data analysis pipelines due to breakthroughs enabling ARG inference at biobank-scale. However, there is a lack of visualization tools, which are crucial for validating inferences and generating hypotheses. We present tsbrowse, an open-source, web-based Python application for the interactive visualization of the fundamental building blocks of ARGs, i.e. nodes, edges and mutations. We demonstrate the application of tsbrowse to various data sources and scenarios, and highlight its key features of browsability along the genome, user interactivity, and scalability to very large sample sizes. AVAILABILITY AND IMPLEMENTATION: Tsbrowse is installed as a Python package from PyPI (https://pypi.org/project/tsbrowse/), while a development version is maintained at https://github.com/tskit-dev/tsbrowse. Documentation is available at https://tskit.dev/tsbrowse/docs/. Source code is archived on Zenodo with DOI, https://doi.org/10.5281/zenodo.15683039.
MOTIVATION: Short tandem repeats (STRs) are abundant in protein sequences and play important role in determining their structures and functions. Strikingly, the unusual compositional characteristics of tandem repeats break classical sequence analysis tools. RESULTS: Here, we establish the first algorithm to effectively identify and cluster STRs: Graph-Based Sequence Clustering (GBSC) features linear time complexity, and clusters protein sequence fragments based on their STRs, while allowing for insertions and mutations and supporting the analysis of imperfect or cryptic repeats. Due to its computational efficacy, our algorithm can be used to systematically scan for patterns in large datasets. We compare our method both to state-of-the-art methods for identifying STRs in proteins and alternative clustering approaches. Unlike existing STR analysis methods, GBSC clusters repeat patterns rather than raw sequences, operating at the level of structural repeat identity, while tolerating biological variations and preventing erroneous merging of structurally and functionally distinct motifs. Whereas functional annotation is typically only available at the protein level, the functions of individual STRs and sequences of adjacent STRs remain largely unknown. On a challenging use case we here demonstrate and discuss how our method can be used to associate previously unannotated repetitive protein fragments with similar ones, allowing the transfer of annotation by similarity. For the first time, GBSC offers a tool that systematically extends this fundamental bioinformatics principle to low-complexity regions across large datasets. AVAILABILITY AND IMPLEMENTATION: GBSC is available at GitHub https://github.com/patryk-jarnot/GBSC and https://doi.org/10.5281/zenodo.18965247. The data and scripts to reproduce the analysis are available at https://doi.org/10.5281/zenodo.16906653.
MOTIVATION: Recent advances in inference of the ancestral recombination graph (ARG), which describes how segments of chromosomes trace back through recombination and shared lineages, have made it possible to reconstruct genome-wide genealogies for large cohorts, but it remains difficult to summarize and use this information for population genetic analyses. RESULTS: We present ARGformer, an encoder-only transformer that learns context-dependent embeddings with a self-supervised masked objective finetuned with contrastive learning for downstream retrieval tasks. We train ARGformer on genealogies from coalescent simulations and on genealogies inferred from ancient and present-day Homo sapiens genomes. Using only these learned embeddings, without access to genotype matrices, ARGformer captures patterns of global population structure and supports ancestry inference through clustering and nearest-neighbor retrieval. On genealogies that include archaic hominins, ARGformer can highlight Denisovan-derived segments in Oceanian genomes and reveals Oceanian-like ancestry in South American Indigenous populations. AVAILABILITY AND IMPLEMENTATION: ARGformer is available at https://github.com/AI-sandbox/ARGformer.
MOTIVATION: Ancestral Recombination Graphs (ARGs) provide a comprehensive representation of genetic ancestry and underpin analyses of natural selection, disease association, and population history. However, existing visualization tools are limited in scalability and interactivity, making ARGs difficult to explore at biobank scale. RESULTS: We introduce Lorax, a GPU-accelerated, web-native platform for real-time visualization of population-scale ARGs. Lorax integrates genomic position, coalescent time, local genealogy, and metadata, enabling interactive exploration of ancestry and variant inheritance in biobank-scale datasets. AVAILABILITY AND IMPLEMENTATION: Lorax is freely available as a live demo at https://lorax.ucsc.edu/ and as a Python package "lorax-arg" on PyPI. The source code and documentation are available on GitHub at https://github.com/pratikkatte/lorax.
The objective of this study was to develop and investigate an approach to optimally detect, rank, display, and analyze patterns of differential growth inhibition among cultured cell lines. Such patterns of cellular responsiveness are produced by substances tested in vitro against disease-oriented panels of human tumor cell lines in a new anticancer screening model under development by the National Cancer Institute. In the first phase of the study, we developed a key methodological tool, the mean graph, which allowed the transformation of the numerical cell line response data into graphic patterns. These patterns were particularly expressive of differential cell growth inhibition and were conveniently amenable to further analyses by an algorithm we devised and implemented in the COMPARE computer program.
The genetic code doublets can be divided into two octets of completely degenerate and ambiguous coding dinucleotides. These two octets have the algebraic property of lying on continuously connected planes on the group graph (a tesseract) of the Cartesian product of two Klein 4-groups of nucleotide exchange operators. The K X K group can also be broken into four cosets, one of which has completely degenerate coding elements, and another that has completely ambiguous coding elements. The two octets of coding doublets have the further algebraic property that the product of their internal exchange operators naturally divide into two exactly equivalent sets. These properties of the genetic code are relevant to unraveling error-detecting and error-correcting (proof-reading) aspects of the genetic code and may be helpful in understanding the context-sensitive grammar of genetic language.
The first application of a novel technique for the identification of common folding motifs in proteins is presented. Using techniques derived from graph theory, developed in order to compare secondary structure motifs in proteins, we have established that there is a striking resemblance in the tertiary fold of the Salmonella typhimurium Che Y chemotaxis protein and that of the GDP-binding domain of Escherichia coli elongation factor Tu (EF Tu). These two protein structures are representatives of two major macromolecular classes: CheY is a signal-transduction protein with sequence homologies to a wide range of bacterial proteins involved in regulation of chemotaxis, membrane synthesis and sporulation; whilst EF Tu is one of a family of guanosine-nucleotide-binding proteins which include the ras oncogene proteins and signal-transducing G proteins. The similarity we have found extends far beyond the previously recognized resemblances of each protein's fold to that of a generic nucleotide-binding domain. The lack of significant sequence homology between the two classes of proteins may mean that the common fold of the two proteins constitutes a particularly stable folding motif. However, an alternative possibility is that the strong three-dimensional structural resemblance may be indicative of a remote shared common ancestry between the bacterial signal-transduction proteins and the GDP-binding proteins.
A graphic format is presented for the display and storage of data relating to gestational age. The graph permits rapid retrieval and synthesis of often confusion information and is thereby useful in the management of complicated pregnancies.
A method is presented based on graph theory for categorizing hydrogen-bond motifs in such a way that complex hydrogen-bond patterns can be disentangled, or decoded, systematically and consistently. This method is based on viewing hydrogen-bond patterns topologically as if they were intertwined nets with molecules as the nodes and hydrogen bonds as the lines. Surprisingly, very few parameters are needed to define the hydrogen-bond motifs comprising these networks. The methods for making these assignments, and examples of their chemical utility are given.
This paper describes a new method of data reduction and classification in a multidimensional symptom space for diagnostic aid of congenital heart diseases. The algorithm developed here is to reduce interactively a multidimensional symptom space to sectorial regions representing each disease in a semicircle using the modified constellation graph method. This method enables us to classify patients using the angle in the semicircle as a single classifying parameter with an accuracy of about 90%, that is, with little overlapping between disease sectors. Comparing this method with conventional factor analysis, we have found the former far more effective than the latter for disease region separation.
Graphs of labeled mitoses, derived from autoradiographs of cell populations with (3)H-thymidine, show depressions in the curves at their midpoints. These depressions reflect interruption of DNA synthesis midway through S phase. Such interruptions revealed by the method of labeled mitoses should be considered when determining cell-cycle times.
Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically.
Pangenome graphs capture extensive structural diversity, but resolving complex loci from shallow sequencing remains challenging, particularly when samples are of low quality such as in ancient DNA. We introduce COSIGT (COsine SImilarity-based GenoTyper), which assigns diploid genotypes by matching read-depth distributions to haplotype paths via cosine similarity. Because this metric evaluates relative coverage profiles rather than absolute read counts, COSIGT substantially outperforms existing likelihood-based tools at low coverage (1-2X). We demonstrate scalability to thousands of modern and ancient genomes, enabling robust, population-scale analyses of complex variation directly from low-coverage datasets.