Instantons at Angles

We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The superposition of each pair of four-dimensional instantons is associated with four angles which depend on some of the ADHM parameters. All these solutions are associated with the group $Sp(k)$ and are examples of Hermitian-Einstein connections on \bE^{4k}. We show that the eight-dimensional solutions preserve 3/16 of the ten-dimensional N=1 supersymmetry. We argue that under the correspondence between the BPS states of Yang-Mills theory and those of M-theory that arises in the context of Matrix models, the instantons at angles configuration corresponds to the longitudinal intersecting 5-branes on a string at angles configuration of M-theory.Comment: 17 pages, phyzzx, many changes and a new section was adde

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural entropy obtained by computing the approximate entropy of the so called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erd\H{o}s-R\'enyi networks. By using classical results of Pincus, we show that our entropy measure converges with network size to a certain binary Shannon entropy. On a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs permit to naturally associate to a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.Comment: 11 pages, 5 EPS figure

Intra-tumour signalling entropy determines clinical outcome in breast and lung cancer.

The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample's genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers

Cell-type deconvolution in epigenome-wide association studies: a review and recommendations

A major challenge faced by epigenome-wide association studies (EWAS) is cell-type heterogeneity. As many EWAS have already demonstrated, adjusting for changes in cell-type composition can be critical when analyzing and interpreting findings from such studies. Because of their importance, a great number of different statistical algorithms, which adjust for cell-type composition, have been proposed. Some of the methods are ‘reference based’ in that they require a priori defined reference DNA methylation profiles of cell types that are present in the tissue of interest, while other algorithms are ‘reference free.’ At present, however, it is unclear how best to adjust for cell-type heterogeneity, as this may also largely depend on the type of tissue and phenotype being considered. Here, we provide a critical review of the major existing algorithms for correcting cell-type composition in the context of Illumina Infinium Methylation Beadarrays, with the aim of providing useful recommendations to the EWAS community

Network Transfer Entropy and Metric Space for Causality Inference

A measure is derived to quantify directed information transfer between pairs of vertices in a weighted network, over paths of a specified maximal length. Our approach employs a general, probabilistic model of network traffic, from which the informational distance between dynamics on two weighted networks can be naturally expressed as a Jensen Shannon Divergence (JSD). Our network transfer entropy measure is shown to be able to distinguish and quantify causal relationships between network elements, in applications to simple synthetic networks and a biological signalling network. We conclude with a theoretical extension of our framework, in which the square root of the JSD induces a metric on the space of dynamics on weighted networks. We prove a convergence criterion, demonstrating that a form of convergence in the structure of weighted networks in a family of matrix metric spaces implies convergence of their dynamics with respect to the square root JSD metric.Comment: 14 pages, 5 figure

Distinctive topology of age-associated epigenetic drift in the human interactome

Recently, it has been demonstrated that DNA methylation, a covalent modification of DNA that can regulate gene expression, is modified as a function of age. However, the biological and clinical significance of this age-associated epigenetic drift is unclear. To shed light on the potential biological significance, we here adopt a systems approach and study the genes undergoing age-associated changes in DNA methylation in the context of a protein interaction network, focusing on their topological properties. In contrast to what has been observed for other age-related gene classes, including longevity- and disease-associated genes, as well as genes undergoing age-associated changes in gene expression, we here demonstrate that age-associated epigenetic drift occurs preferentially in genes that occupy peripheral network positions of exceptionally low connectivity. In addition, we show that these genes synergize topologically with disease and longevity genes, forming unexpectedly large network communities. Thus, these results point toward a potentially distinct mechanistic and biological role of DNA methylation in dictating the complex aging and disease phenotypes

Stochastic epigenetic outliers can define field defects in cancer

BACKGROUND: There is growing evidence that DNA methylation alterations may contribute to carcinogenesis. Recent data also suggest that DNA methylation field defects in normal pre-neoplastic tissue represent infrequent stochastic “outlier” events. This presents a statistical challenge for standard feature selection algorithms, which assume frequent alterations in a disease phenotype. Although differential variability has emerged as a novel feature selection paradigm for the discovery of outliers, a growing concern is that these could result from technical confounders, in principle thus favouring algorithms which are robust to outliers. RESULTS: Here we evaluate five differential variability algorithms in over 700 DNA methylomes, including two of the largest cohorts profiling precursor cancer lesions, and demonstrate that most of the novel proposed algorithms lack the sensitivity to detect epigenetic field defects at genome-wide significance. In contrast, algorithms which recognise heterogeneous outlier DNA methylation patterns are able to identify many sites in pre-neoplastic lesions, which display progression in invasive cancer. Thus, we show that many DNA methylation outliers are not technical artefacts, but define epigenetic field defects which are selected for during cancer progression. CONCLUSIONS: Given that cancer studies aiming to find epigenetic field defects are likely to be limited by sample size, adopting the novel feature selection paradigm advocated here will be critical to increase assay sensitivity

Epigenetic and genetic deregulation in cancer target distinct signaling pathway domains

Cancer is characterized by both genetic and epigenetic alterations. While cancer driver mutations and copy-number alterations have been studied at a systems-level, relatively little is known about the systems-level patterns exhibited by their epigenetic counterparts. Here we perform a pan-cancer wide systems-level analysis, mapping candidate cancer-driver DNA methylation (DNAm) alterations onto a human interactome. We demonstrate that functional DNAm alterations in cancer tend to map to nodes of lower connectivity and inter-connectivity, compared to the corresponding alterations at the genomic level. We find that epigenetic alterations are relatively over-represented in extracellular and transmembrane signaling domains, whereas cancer genes undergoing amplification or deletion tend to be enriched within the intracellular domain. A pan-cancer wide meta-analysis identifies WNT and chemokine signaling, as two key pathways where epigenetic deregulation preferentially targets extracellular components. We further pinpoint specific chemokine ligands/receptors whose epigenetic deregulation associates with key epigenetic enzymes, representing potential targets for epigenetic therapy. Our results suggest that epigenetic deregulation in cancer not only targets tissue-specific transcription factors, but also modulates signaling within the extra-cellular domain, providing novel system-level insight into the potential distinctive role of genetic and epigenetic alterations in cancer

Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome

The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes