Probabilistic methods in the analysis of protein interaction networks

Imperial Users onl

Statistical analysis of network data and evolution on GPUs: High-performance statistical computing

Network analysis typically involves as set of repetitive tasks that are particularly amenable to poor-man's parallelization. This is therefore an ideal application are for GPU architectures, which help to alleviate the tedium inherent to statistically sound analysis of network data. Here we will illustrate the use of GPUs in a range of applications, which include percolation processes on networks, the evolution of protein-protein interaction networks, and the fusion of different types of biomedical and disease data in the context of molecular interaction networks. We will pay particular attention to the numerical performance of different routines that are frequently invoked in network analysis problems. We conclude with a review over recent developments in the generation of random numbers that address the specific requirements posed by GPUs and high-performance computing needs

Displacement Profile of Charge Density Waves and Domain Walls at Critical Depinning

The influence of a strong surface potential on the critical depinning of an elastic system driven in a random medium is considered. If the surface potential prevents depinning completely the elastic system shows a parabolic displacement profile. Its curvature $\mathcal{C}$ exhibits at zero temperature a pronounced rhombic hysteresis curve of width $2f_c$ with the bulk depinning threshold $f_c$. The hysteresis disappears at non-zero temperatures if the driving force is changed adiabatically. If the surface depins by the applied force or thermal creep, $\mathcal{C}$ is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, flux-line lattices and charge-density waves.Comment: 4 pages, 2 figure

Multigrid with Cache Optimizations on Adaptive Mesh Refinement Hierarchies

This dissertation presents a multilevel algorithm to solve constant and variable coeffcient elliptic boundary value problems on adaptively refined structured meshes in 2D and 3D. Cacheaware algorithms for optimizing the operations to exploit the cache memory subsystem areshown. Keywords: Multigrid, Cache Aware, Adaptive Mesh Refinement, Partial Differential Equations, Numerical Solution

Stochastic Process Algebra Models of a Circadian Clock

We present stochastic process algebra models of a Circadian clock mechanism used in many biological organisms to regulate time-based behaviour. We compare modelling techniques from different modelling paradigms, PEPA and stochastic $pi$-calculus

Observed changes in surface atmospheric energy over land

The temperature of the surface atmosphere over land has been rising during recent decades. But surface temperature, or, more accurately, enthalpy which can be calculated from temperature, is only one component of the energy content of the surface atmosphere. The other parts include kinetic energy and latent heat. It has been advocated in certain quarters that ignoring additional terms somehow calls into question global surface temperature analyses. Examination of all three of these components of atmospheric energetics reveals a significant increase in global surface atmospheric energy since the 1970s. Kinetic energy has decreased but by over two orders of magnitude less than the increases in both enthalpy and latent heat which provide approximately equal contributions to the global increases in heat content. Regionally, the enthalpy or the latent heat component can dominate the change in heat content. Although generally changes in latent heat and enthalpy act in concert, in some regions they can have the opposite signs

Rare event ABC-SMC2^{2}

Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but the likelihood cannot easily be pointwise evaluated. A fundamental property of standard ABC approaches is that the number of Monte Carlo points required to achieve a given accuracy scales exponentially with the dimension of the data. Prangle et al. (2018) proposes a Markov chain Monte Carlo (MCMC) method that uses a rare event sequential Monte Carlo (SMC) approach to estimating the ABC likelihood that avoids this exponential scaling, and thus allows ABC to be used on higher dimensional data. This paper builds on the work of Prangle et al. (2018) by using the rare event SMC approach within an SMC algorithm, instead of within an MCMC algorithm. The new method has a similar structure to SMC$^{2}$ (Chopin et al., 2013), and requires less tuning than the MCMC approach. We demonstrate the new approach, compared to existing ABC-SMC methods, on a toy example and on a duplication-divergence random graph model used for modelling protein interaction networks

General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes

We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic MHD fluid in a dynamical spacetime characterized by a strong gravitational field.Comment: 8 pages; scheduled for March 10 issue of Ap

Derivative processes for modelling metabolic fluxes.

MOTIVATION: One of the challenging questions in modelling biological systems is to characterize the functional forms of the processes that control and orchestrate molecular and cellular phenotypes. Recently proposed methods for the analysis of metabolic pathways, for example, dynamic flux estimation, can only provide estimates of the underlying fluxes at discrete time points but fail to capture the complete temporal behaviour. To describe the dynamic variation of the fluxes, we additionally require the assumption of specific functional forms that can capture the temporal behaviour. However, it also remains unclear how to address the noise which might be present in experimentally measured metabolite concentrations. RESULTS: Here we propose a novel approach to modelling metabolic fluxes: derivative processes that are based on multiple-output Gaussian processes (MGPs), which are a flexible non-parametric Bayesian modelling technique. The main advantages that follow from MGPs approach include the natural non-parametric representation of the fluxes and ability to impute the missing data in between the measurements. Our derivative process approach allows us to model changes in metabolite derivative concentrations and to characterize the temporal behaviour of metabolic fluxes from time course data. Because the derivative of a Gaussian process is itself a Gaussian process, we can readily link metabolite concentrations to metabolic fluxes and vice versa. Here we discuss how this can be implemented in an MGP framework and illustrate its application to simple models, including nitrogen metabolism in Escherichia coli. AVAILABILITY AND IMPLEMENTATION: R code is available from the authors upon request