Convex Multi-View Clustering Via Robust Low Rank Approximation With Application to Multi-Omic Data.

Recent advances in high throughput technologies have made large amounts of biomedical omics data accessible to the scientific community. Single omic data clustering has proved its impact in the biomedical and biological research fields. Multi-omic data clustering and multi-omic data integration techniques have shown improved clustering performance and biological insight. Cancer subtype clustering is an important task in the medical field to be able to identify a suitable treatment procedure and prognosis for cancer patients. State of the art multi-view clustering methods are based on non-convex objectives which only guarantee non-global solutions that are high in computational complexity. Only a few convex multi-view methods are present. However, their models do not take into account the intrinsic manifold structure of the data. In this paper, we introduce a convex graph regularized multi-view clustering method that is robust to outliers. We compare our algorithm to state of the art convex and non-convex multi-view and single view clustering methods, and show its superiority in clustering cancer subtypes on publicly available cancer genomic datasets from the TCGA repository. We also show our method's better ability to potentially discover cancer subtypes compared to other state of the art multi-view methods.

A Low Dimensional Approximation For Competence In Bacillus Subtilis.

The behaviour of a high dimensional stochastic system described by a chemical master equation (CME) depends on many parameters, rendering explicit simulation an inefficient method for exploring the properties of such models. Capturing their behaviour by low-dimensional models makes analysis of system behaviour tractable. In this paper, we present low dimensional models for the noise-induced excitable dynamics in Bacillus subtilis, whereby a key protein ComK, which drives a complex chain of reactions leading to bacterial competence, gets expressed rapidly in large quantities (competent state) before subsiding to low levels of expression (vegetative state). These rapid reactions suggest the application of an adiabatic approximation of the dynamics of the regulatory model that, however, lead to competence durations that are incorrect by a factor of 2. We apply a modified version of an iterative functional procedure that faithfully approximates the time-course of the trajectories in terms of a two-dimensional model involving proteins ComK and ComS. Furthermore, in order to describe the bimodal bivariate marginal probability distribution obtained from the Gillespie simulations of the CME, we introduce a tunable multiplicative noise term in a two-dimensional Langevin model whose stationary state is described by the time-independent solution of the corresponding Fokker-Planck equation.

Dynamical System Approach for Edge Detection Using Coupled FitzHugh-Nagumo Neurons.

The prospect of emulating the impressive computational capabilities of biological systems has led to considerable interest in the design of analog circuits that are potentially implementable in very large scale integration CMOS technology and are guided by biologically motivated models. For example, simple image processing tasks, such as the detection of edges in binary and grayscale images, have been performed by networks of FitzHugh-Nagumo-type neurons using the reaction-diffusion models. However, in these studies, the one-to-one mapping of image pixels to component neurons makes the size of the network a critical factor in any such implementation. In this paper, we develop a simplified version of the employed reaction-diffusion model in three steps. In the first step, we perform a detailed study to locate this threshold using continuous Lyapunov exponents from dynamical system theory. Furthermore, we render the diffusion in the system to be anisotropic, with the degree of anisotropy being set by the gradients of grayscale values in each image. The final step involves a simplification of the model that is achieved by eliminating the terms that couple the membrane potentials of adjacent neurons. We apply our technique to detect edges in data sets of artificially generated and real images, and we demonstrate that the performance is as good if not better than that of the previous methods without increasing the size of the network.

Model of haplotype and phenotype in the evolution of a duplicated autoregulatory activator.

Gene duplication is believed to play a major role in the evolution of genomic complexity. The presence of a duplicate frees a gene from the constraint of natural selection, leading to its loss of function or the gain of a novel one. Alternately, a pleiotropic gene might partition its functions among its duplicates, thus preserving both copies. Such arguments invoking duplication for novelty or specialisation are not qualitatively true of diploid genotypes, but only of haplotypes. In this paper, we study the consequences of regulatory interactions in diploid genotypes and explore how the context of allelic interactions gives rise to dynamical phenotypes that enable duplicate genes to spread in a population. The regulatory network we study is that of a single autoregulatory activator gene, and the two copies of the gene diverge either as alleles in a diploid species or as duplicates in haploids. These differences are in their transcriptional ability-either via alterations to its activating domain, or to its cis-regulatory binding repertoire. When cis-regulatory changes are introduced that partition multiple regulatory triggers among the duplicates, it is shown that mutually exclusive expression states of the duplicates that emerge are accompanied by a back-up facility: when a highly expressed gene is deleted, the previously unexpressed duplicate copy compensates for it. The diploid version of the regulatory network model can account for allele-specific expression variants, and a model of inheritance of the haplotype network enables us to trace the evolutionary consequence of heterozygous phenotypes. This is modelled for the variations in the activating domain of one copy, whereby stable as well as transiently bursting oscillations ensue in single cells. The evolutionary model shows that these phenotypic states accessible to a diploid, heterozygous genotype enable the spread of a duplicated haplotype.

Correlated fluctuations carry signatures of gene regulatory network dynamics.

The dynamics of transcriptional control involve small numbers of molecules and result in significant fluctuations in protein and mRNA concentrations. The correlations between these intrinsic fluctuations then offer, via the fluctuation dissipation relation, the possibility of capturing the system's response to external perturbations, and hence the nature of the regulatory activity itself. We show that for simple regulatory networks of activators and repressors, the correlated fluctuations between molecular species show distinct characteristics for changes in regulatory mechanism and for changes to the topology of causal influence. Here, we do a stochastic analysis and derive time-dependent correlation functions between molecular species of regulatory networks and present analytical and numerical results on peaks and delays in correlations between proteins within networks. Upon using these values of peaks and delays as a two-dimensional feature space, we find that different regulatory mechanisms separate into distinct clusters. This indicates that experimentally observable pairwise correlations can distinguish between gene regulatory networks.