Deterministic Modularity Optimization

We study community structure of networks. We have developed a scheme for maximizing the modularity Q based on mean field methods. Further, we have defined a simple family of random networks with community structure; we understand the behavior of these networks analytically. Using these networks, we show how the mean field methods display better performance than previously known deterministic methods for optimization of Q.Comment: 7 pages, 4 figures, minor change

Macrostate Data Clustering

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to the metastable macroscopic states (macrostates) of a diffusive system. A "minimum uncertainty criterion" determines the linear transformation from eigenvectors to cluster-defining window functions. Eigenspectrum gap and cluster certainty conditions identify the proper number of clusters. The physically motivated fuzzy representation and associated uncertainty analysis distinguishes macrostate clustering from spectral partitioning methods. Macrostate data clustering solves a variety of test cases that challenge other methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral graph theory, dynamic eigenvectors, machine learning, macrostates, classificatio

Computational protein biomarker prediction: a case study for prostate cancer

BACKGROUND: Recent technological advances in mass spectrometry pose challenges in computational mathematics and statistics to process the mass spectral data into predictive models with clinical and biological significance. We discuss several classification-based approaches to finding protein biomarker candidates using protein profiles obtained via mass spectrometry, and we assess their statistical significance. Our overall goal is to implicate peaks that have a high likelihood of being biologically linked to a given disease state, and thus to narrow the search for biomarker candidates. RESULTS: Thorough cross-validation studies and randomization tests are performed on a prostate cancer dataset with over 300 patients, obtained at the Eastern Virginia Medical School using SELDI-TOF mass spectrometry. We obtain average classification accuracies of 87% on a four-group classification problem using a two-stage linear SVM-based procedure and just 13 peaks, with other methods performing comparably. CONCLUSIONS: Modern feature selection and classification methods are powerful techniques for both the identification of biomarker candidates and the related problem of building predictive models from protein mass spectrometric profiles. Cross-validation and randomization are essential tools that must be performed carefully in order not to bias the results unfairly. However, only a biological validation and identification of the underlying proteins will ultimately confirm the actual value and power of any computational predictions

Review Article p16 INK4A and p14 ARF Gene Promoter Hypermethylation as Prognostic Biomarker in Oral and Oropharyngeal Squamous Cell Carcinoma: A Review

Head and neck squamous cell carcinoma is a heterogeneous group of tumors with each subtype having a distinct histopathological and molecular profile. Most tumors share, to some extent, the same multistep carcinogenic pathways, which include a wide variety of genetic and epigenetic changes. Epigenetic alterations represent all changes in gene expression patterns that do not alter the actual DNA sequence. Recently, it has become clear that silencing of cancer related genes is not exclusively a result of genetic changes such as mutations or deletions, but it can also be regulated on epigenetic level, mostly by means of gene promoter hypermethylation. Results from recent studies have demonstrated that DNA methylation patterns contain tumor-type-specific signatures, which could serve as biomarkers for clinical outcome in the near future. The topic of this review discusses gene promoter hypermethylation in oral and oropharyngeal squamous cell carcinoma (OSCC). The main objective is to analyse the available data on gene promoter hypermethylation of the cell cycle regulatory proteins p16 INK4A and p14 ARF and to investigate their clinical significance as novel biomarkers in OSCC. Hypermethylation of both genes seems to possess predictive properties for several clinicopathological outcomes. We conclude that the methylation status of p16 INK4A is definitely a promising candidate biomarker for predicting clinical outcome of OSCC, especially for recurrence-free survival

Ensemble approach for generalized network dismantling

Finding a set of nodes in a network, whose removal fragments the network below some target size at minimal cost is called network dismantling problem and it belongs to the NP-hard computational class. In this paper, we explore the (generalized) network dismantling problem by exploring the spectral approximation with the variant of the power-iteration method. In particular, we explore the network dismantling solution landscape by creating the ensemble of possible solutions from different initial conditions and a different number of iterations of the spectral approximation.Comment: 11 Pages, 4 Figures, 4 Table

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

A theoretical model of inflammation- and mechanotransduction- driven asthmatic airway remodelling

Inflammation, airway hyper-responsiveness and airway remodelling are well-established hallmarks of asthma, but their inter-relationships remain elusive. In order to obtain a better understanding of their inter-dependence, we develop a mechanochemical morphoelastic model of the airway wall accounting for local volume changes in airway smooth muscle (ASM) and extracellular matrix in response to transient inflammatory or contractile agonist challenges. We use constrained mixture theory, together with a multiplicative decomposition of growth from the elastic deformation, to model the airway wall as a nonlinear fibre-reinforced elastic cylinder. Local contractile agonist drives ASM cell contraction, generating mechanical stresses in the tissue that drive further release of mitogenic mediators and contractile agonists via underlying mechanotransductive signalling pathways. Our model predictions are consistent with previously described inflammation-induced remodelling within an axisymmetric airway geometry. Additionally, our simulations reveal novel mechanotransductive feedback by which hyper-responsive airways exhibit increased remodelling, for example, via stress-induced release of pro-mitogenic and procontractile cytokines. Simulation results also reveal emergence of a persistent contractile tone observed in asthmatics, via either a pathological mechanotransductive feedback loop, a failure to clear agonists from the tissue, or a combination of both. Furthermore, we identify various parameter combinations that may contribute to the existence of different asthma phenotypes, and we illustrate a combination of factors which may predispose severe asthmatics to fatal bronchospasms

On some properties of the Laplacian matrix revealed by the RCM algorithm

In this paper we present some theoretical results about the irreducibility of the Laplacian matrix ordered by the Reverse Cuthill-McKee (RCM) algorithm. We consider undirected graphs with no loops consisting of some connected components. RCM is a well-known scheme for numbering the nodes of a network in such a way that the corresponding adjacency matrix has a narrow bandwidth. Inspired by some properties of the eigenvectors of a Laplacian matrix, we derive some properties based on row sums of a Laplacian matrix that was reordered by the RCM algorithm. One of the theoretical results serves as a basis for writing an easy MATLAB code to detect connected components, by using the function “symrcm” of MATLAB. Some examples illustrate the theoretical results.The research has been supported by Spanish DGI grant MTM2010-18674, Consolider Ingenio CSD2007-00022, PROMETEO 2008/051, OVAMAH TIN2009-13839-C03-01, and PAID-06-11-2084.Pedroche Sánchez, F.; Rebollo Pedruelo, M.; Carrascosa Casamayor, C.; Palomares Chust, A. (2016). On some properties of the Laplacian matrix revealed by the RCM algorithm. Czechoslovak Mathematical Journal. 66(3):603-620. doi:10.1007/s10587-016-0281-yS60362066