MIGSAA - Computational Modelling Reading Group, Thursdays 14.00-16.00

19 January 2017 - Aleksandra Plochocka

Explanation of variability and removal of confounding factors from data through optimal transport

Location: EMB (Earl Mountbatten) Room 1.58, 14.00-16.00

paper link

Abstract: A methodology based on the theory of optimal transport is devel- oped to attribute variability in data sets to known and unknown factors and to remove such attributable components of the variability from the data. Denoting by x the quantities of interest and by z the explanatory factors, the procedure transforms x into filtered variables y through a z-dependent map, so that the conditional probability distributions rho(x|z) are pushed forward into a target distribution mu(y), independent of z. Among all maps and target distributions that achieve this goal, the procedure selects the one that minimally distorts the original data: the barycenter of the rho(x|z). Connections are found to unsupervised learning - particularly simple instances of the methodology are shown to be equivalent to k-means and principal component analysis - and to fundamental problems in statistics such as conditional density estimation and sampling. An applications is shown to a time-series of ground temperature hourly data across the United States.

2 February 2017 - Matt Graham

Asymptotically exact inference in likelihood-free models

Location: JCMB 5215, 14.00-16.00

paper link

Abstract: Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class of 'likelihood-free' simulator models. We present a method for performing efficient MCMC inference in such models when conditioning on observations of the model output. For some models this offers an asymptotically exact inference method where Approximate Bayesian Computation might otherwise be employed. We use the intuition that inference corresponds to integrating a density across the manifold corresponding to the set of inputs consistent with the observed outputs. This motivates the use of a constrained variant of Hamiltonian Monte Carlo which leverages the smooth geometry of the manifold to coherently move between inputs exactly consistent with observations. We validate the method by performing inference tasks in a diverse set of models.

16 February 2017 - Gissell Estrada

Levy walks; E. coli Superdiffusion and Chemotaxis—Search Strategy, Precision, and Motility

Location: EMB (Earl Mountbatten) Room 1.58, 14.00-16.00
paper link

Note: I'll first talk about the characteristics of a Levy walk and how the fractional Laplacian could be derived from a long jump random walk. This paper is just one of many examples that evidences the presence of Levy walk motion in biology.

Abstract: Escherichia coli motion is characterized by a sequence of consecutive tumble-and-swim events. In the absence of chemical gradients, the length of individual swims is commonly believed to be distributed exponentially. However, recently there has been experimental indication that the swim-length distribution has the form of a power-law, suggesting that bacteria might perform superdiffusive Le´vy-walk motion. In E. coli, the power-law behavior can be induced through stochastic fluctuations in the level of CheR, one of the key enzymes in the chemotaxis signal transmission pathway. We use a mathematical model of the chemotaxis signaling pathway to study the influence of these fluctuations on the E. coli behavior in the absence and presence of chemical gradients. We find that the population with fluctuating CheR performs Le´vy-walks in the absence of chemoattractants, and therefore might have an advantage in environments where nutrients are sparse. The more efficient search strategy in sparse environments is accompanied by a generally larger motility, also in the presence of chemoattractants. The tradeoff of this strategy is a reduced precision in sensing and following gradients, as well as a slower adaptation to absolute chemoattractant levels.

2 March 2017 - Tim Hurst

Neighbor List Collision-Driven Molecular Dynamics Simulation for Nonspherical Hard Particles. I. Algorithmic Details

Location: JCMB 4325B, 14.00-16.00
paper link

Abstract: In this first part of a series of two papers, we present in considerable detail a collision-driven molecular dynamics algorithm for a system of non-spherical particles, within a parallelepiped simulation domain, under both periodic or hard-wall boundary conditions. The algorithm extends previous event-driven molecular dynamics algorithms for spheres, and is most efficient when applied to systems of particles with relatively small aspect ratios and with small variations in size. We present a novel partial-update near-neighbor list (NNL) algorithm that is superior to previous algorithms at high densities, without compromising the correctness of the algorithm. This efficiency of the algorithm is further increased for systems of very aspherical particles by using bounding sphere complexes (BSC). These tech- niques will be useful in any particle-based simulation, including Monte Carlo and time-driven molecular dynamics. Additionally, we allow for a non-vanishing rate of deformation of the boundary, which can be used to model macro- scopic strain and also alleviate boundary effects for small systems. In the second part of this series of papers we spe- cialize the algorithm to systems of ellipses and ellipsoids and present performance results for our implementation, demonstrating the practical utility of the algorithm.

16 March 2017 - Lyonell Boulton

Growth and decay of random Fibonacci sequences

Location: EMB (Earl Mountbatten) Room 1.58, 14.00-16.00
paper link

Abstract:For 0 < β < β∗ ≈ 0.702 58, solutions to the random recurrence xn+1 = xn ± βxn−1 decay exponentially as n → ∞ with probability one, whereas for β > β∗, they grow exponentially. By formulating the problem as a Markov chain involving ran- dom matrix products and computing its invariant measure—a fractal—the Lyapunov constant σ(β) = limn→∞ |xn|1/n is determined numerically for a wide range of val- ues β, and its dependence on β is observed to be non-smooth. (The limit is defined in the almost sure sense.) This generalizes recent work of Viswanath, who proved σ(1) = 1.131 988 24 . . . . By a simple rescaling, these results also apply to the more general random recurrence xn+1 = αxn ± βxn−1 for fixed α and β. These random recurrence relations have links with many fields, including ergodic theory, dynamical systems, heavy-tailed statistics, spectral theory, continued fractions, and condensed matter physics.

30 March 2017 - Anton Martinsson

Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials

Location: JCMB 4325B, 14.00-16.00
paper link

Abstract: Replica exchange molecular dynamics (REMD) becomes more efficient as the frequency of swap between the temperatures is increased. Recently Plattner et al. [J. Chem. Phys. 135, 134111 (2011)] proposed a method to implement infinite swapping REMD in practice. Here we introduce a natural modification of this method that involves molecular dynamics simulations over a mixture potential. This modification is both simple to implement in practice and provides a better, energy based under- standing of how to choose the temperatures in REMD to optimize efficiency. It also has implications for generalizations of REMD in which the swaps involve other parameters than the temperature.

13 April 2017 - Francesco Ungolo - CANCELLED

Location: EMB (Earl Mountbatten) Room 1.58, 14.00-16.00

Abstract:

27 April 2017 - Daniella Ayala Garcia

Location: JCMB 4325B, 14.00-16.00

Abstract:

11 May 2017 - Stuart Campbell

SPARSE TENSOR MULTI-LEVEL MONTE CARLO FINITE VOLUME METHODS FOR HYPERBOLIC CONSERVATION LAWS WITH RANDOM INITIAL DATA

Location: EMB (Earl Mountbatten) Room 1.58, 14.00-16.00
paper link

I will start the discussion by introducing MLMC for SDE's, as it was originally done by Giles, and then move over to cover the PDE side in the paper.

Abstract:We consider scalar hyperbolic conservation laws in spatial dimension d >= 1 with stochastic initial data. We prove existence and uniqueness of a random-entropy solution and give sufficient conditions on the initial data that ensure the existence of statistical moments of any order k of this random entropy solution. We present a class of numerical schemes of multi-level Monte Carlo Finite Volume (MLMC-FVM) type for the approximation of the ensemble average of the random entropy solutions as well as of their k-point space-time correlation functions. These schemes are shown to obey the same accuracy vs. work estimate as a single application of the finite volume solver for the corresponding deterministic problem. Numerical experiments demonstrating the efficiency of these schemes are presented. In certain cases, statistical moments of discontinuous solutions are found to be more regular than pathwise solutions.

25 May 2017 - Lyuba Chumakova

Location: JCMB 4325B, 14.00-16.00

Abstract: