On the nonlinear mechanics of discrete networks

Summary A formulation of the equilibrium problem for nonlinear elastic networks is presented. Explicit necessary and sufficient conditions for minimum-energy configurations are derived. These are used to generate a relaxed formulation of the theory in which fibre slackening is accounted for automatically. For the relaxed problem, minimum-energy and uniqueness theorems are proved and used as the basis of a numerical method in which equilibrium configurations are recovered asymptotically in the long-time limit of an artificial dynamical problem. Such an approach is particularly useful for networks, as stiffness-based equilibrium formulations are known to suffer from ill-conditioning in a wide variety of applications. Several illustrative examples are discussed. Accepted for publication 22 June 1996     

Brownian Dynamics simulation of reversible polymeric networks

In this paper we describe the construction of a Brownian Dynamics simulation of reversibly cross-linked networks. The simulation differs from existing analytical approaches and computer simulations of networks in the sense that we also take the topology of the network into account. The motion of the junction points between different molecules is not prescribed but is calculated from a force balance. This makes it possible to measure the effect of network reorganisations on the stress relaxation. The response of networks to shear flow is measured and analysed in terms of transient network theory and within the framework of linear viscoelasticity. It is shown that the average motion of the junction is affine but that there is a long time diffusive process around the affine path. It was found that, even in systems with Gaussian chains and fixed association and disociation rates, a shear thickening of the viscosity and primary normal stress coefficient can occur. The reason was found to be that dangling segments are recaptured by the network before they had the opportunity to fully relax to the equilibrium state where the probability of reattachment to the network increases linearly with the length of a segment. Due to this mechanism the fraction of long segments present in the network is increased. This explanation of shear thickening seems to be consistent with experimental findings.     

Network regularised Cox regression and multiplex network models to predict disease comorbidities and survival of cancer

In cancer genomics, gene expression levels provide important molecular signatures for all types of cancer, and this could be very useful for predicting the survival of cancer patients. However, the main challenge of gene expression data analysis is high dimensionality, and microarray is characterised by few number of samples with large number of genes. To overcome this problem, a variety of penalised Cox proportional hazard models have been proposed. We introduce a novel network regularised Cox proportional hazard model and a novel multiplex network model to measure the disease comorbidities and to predict survival of the cancer patient. Our methods are applied to analyse seven microarray cancer gene expression datasets: breast cancer, ovarian cancer, lung cancer, liver cancer, renal cancer and osteosarcoma. Firstly, we applied a principal component analysis to reduce the dimensionality of original gene expression data. Secondly, we applied a network regularised Cox regression model on the reduced gene expression datasets. By using normalised mutual information method and multiplex network model, we predict the comorbidities for the liver cancer based on the integration of diverse set of omics and clinical data, and we find the diseasome associations (disease–gene association) among different cancers based on the identified common significant genes. Finally, we evaluated the precision of the approach with respect to the accuracy of survival prediction using ROC curves. We report that colon cancer, liver cancer and renal cancer share the CXCL5 gene, and breast cancer, ovarian cancer and renal cancer share the CCND2 gene. Our methods are useful to predict survival of the patient and disease comorbidities more accurately and helpful for improvement of the care of patients with comorbidity. Software in Matlab and R is available on our GitHub page: https://github.com/ssnhcom/NetworkRegularisedCox.git.     

Discovering DNA methylation patterns for long non-coding RNAs associated with cancer subtypes

Despite growing evidence demonstrates that the long non-coding ribonucleic acids (lncRNAs) are critical modulators for cancers, the knowledge about the DNA methylation patterns of lncRNAs is quite limited. We develop a systematic analysis pipeline to discover DNA methylation patterns for lncRNAs across multiple cancer subtypes from probe, gene and network levels. By using The Cancer Genome Atlas (TCGA) breast cancer methylation data, the pipeline discovers various DNA methylation patterns for lncRNAs across four major subtypes such as luminal A, luminal B, her2-enriched as well as basal-like. On the probe and gene level, we find that both differentially methylated probes and lncRNAs are subtype specific, while the lncRNAs are not as specific as probes. On the network level, the pipeline constructs differential co-methylation lncRNA network for each subtype. Then, it identifies both subtype specific and common lncRNA modules by simultaneously analyzing multiple networks. We show that the lncRNAs in subtype specific and common modules differ greatly in terms of topological structure, sequence conservation as well as expression. Furthermore, the subtype specific lncRNA modules serve as biomarkers to improve significantly the accuracy of breast cancer subtypes prediction. Finally, the common lncRNA modules associate with survival time of patients, which is critical for cancer therapy.     

Protection of flows under targeted attacks

We present a new robust optimization model for the problem of maximizing the amount of flow surviving the attack of an interdictor. Given some path flow, our model allows the interdictor to specify the amount of flow removed from each path individually. In contrast to previous models, for which no efficient algorithms are known, the most important basic variants of our model can be solved in poly-time. We also consider extensions where there is a budget to set the interdiction costs.     

A network model with free-strand dynamics for polymer melts

 A network model for polymer melts is presented in which disentangled strands relax under flow conditions and may rejoin the network before complete relaxation. For simplicity, we study Gaussian strands that move affinely when incorporated in the network. Network strands are created and lost according to a time constant λ. Free strands have their dynamics given by the Bird-DeAguiar model as a crude representation of reptation and the hindered rotation experienced by polymer strands in melts. The model yields a shear-thinning viscosity with overshoot in the start-up viscosity η⁺ (t). The double-step strain results compare well with available experimental data. Received: 10 July 2000 Accepted: 10 July 2001     

High-dimensional generation of Bernoulli random vectors

The objective of this paper is to explore different modeling strategies to generate high-dimensional Bernoulli vectors. We discuss the multivariate Bernoulli (MB) distribution, probe its properties and examine three models for generating random vectors. A latent multivariate normal model whose bivariate distributions are approximated with Plackett distributions with univariate normal distributions is presented. A conditional mean model is examined where the conditional probability of success depends on previous history of successes. A mixture of beta distributions is also presented that expresses the probability of the MB vector as a product of correlated binary random variables. Each method has a domain of effectiveness. The latent model offers unpatterned correlation structures while the conditional mean and the mixture model provide computational feasibility for high-dimensional generation of MB vectors.     

Practical extensions to a minimum cost flow model for level of repair analysis

The level of repair analysis (LORA) gives answers to three questions that are posed when deciding on how to maintain capital goods: (1) which components to repair upon failure and which to discard, (2) at which locations in the repair network to perform each type of repairs, and (3) at which locations in the network to deploy resources, such as test equipment. The goal is to achieve the lowest possible life cycle costs. Various models exist for the LORA problem. However, they tend to be restrictive in that specific business situations cannot be incorporated, such as having repair equipment with finite capacity or the occurrence of unsuccessful repairs or no-fault-founds. We discuss and model such practically relevant extensions to an existing minimum cost flow formulation for the LORA problem. In an extensive numerical experiment, we show that incorporating the model refinements leads to a substantial change in the costs in general. The repair strategy changes substantially only when incorporating finite resource capacities or a probability of unsuccessful repair that is decreasing with an increasing echelon level.     

The Transit Route Arc-Node Service Maximization problem

This article presents a new method for determining optimal transit routes. The Transit Route Arc-Node Service Maximization model is a mathematical model that maximizes the service value of a route, rather than minimizing cost. Cost (distance) is considered as a budget constraint on the extent of the route. The mathematical formulation modifies and exploits the structure of linear programming problems designed for the traveling salesman problem. An innovative divide-and-conquer solution procedure is presented that not only makes the transit routing problem tractable, but also provides a range of high-quality alternate routes for consideration, some of which have substantially varying geometries. Variant formulations are provided for several common transit route types. The model is tested through its application to an existing street network in Richardson, TX. Optimal numeric results are obtained for several problem instances, and these results demonstrate that increased route cost is not correlated with increased service provision.