A Simple Approach to Maximum Intractable Likelihood Estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios

About the holographic pseudo-Goldstone boson

Pseudo-Goldstone bosons in 4D strongly coupled theories have a dual description in terms of 5D gauge theories in warped backgrounds. We introduce systematic methods of computing the pseudo-Goldstone potential for an arbitrary warp factor in 5D. When applied to electroweak symmetry breaking, our approach clarifies the relation of physical observables to geometrical quantities in five dimensions.Comment: 16 page

Millisecond single-molecule localization microscopy combined with convolution analysis and automated image segmentation to determine protein concentrations in complexly structured, functional cells, one cell at a time

We present a single-molecule tool called the CoPro (Concentration of Proteins) method that uses millisecond imaging with convolution analysis, automated image segmentation and super-resolution localization microscopy to generate robust estimates for protein concentration in different compartments of single living cells, validated using realistic simulations of complex multiple compartment cell types. We demonstrates its utility experimentally on model Escherichia coli bacteria and Saccharomyces cerevisiae budding yeast cells, and use it to address the biological question of how signals are transduced in cells. Cells in all domains of life dynamically sense their environment through signal transduction mechanisms, many involving gene regulation. The glucose sensing mechanism of S. cerevisiae is a model system for studying gene regulatory signal transduction. It uses the multi-copy expression inhibitor of the GAL gene family, Mig1, to repress unwanted genes in the presence of elevated extracellular glucose concentrations. We fluorescently labelled Mig1 molecules with green fluorescent protein (GFP) via chromosomal integration at physiological expression levels in living S. cerevisiae cells, in addition to the RNA polymerase protein Nrd1 with the fluorescent protein reporter mCherry. Using CoPro we make quantitative estimates of Mig1 and Nrd1 protein concentrations in the cytoplasm and nucleus compartments on a cell-by-cell basis under physiological conditions. These estimates indicate a 4-fold shift towards higher values in concentration of diffusive Mig1 in the nucleus if the external glucose concentration is raised, whereas equivalent levels in the cytoplasm shift to smaller values with a relative change an order of magnitude smaller. This compares with Nrd1 which is not involved directly in glucose sensing, which is almost exclusively localized in the nucleus under high and..

Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture

We address special cases of a question of Eisenbud on the ideals of secant varieties of Veronese re-embeddings of arbitrary varieties. Eisenbud's question generalizes a conjecture of Eisenbud, Koh and Stillman (EKS) for curves. We prove that set-theoretic equations of small secant varieties to a high degree Veronese re-embedding of a smooth variety are determined by equations of the ambient Veronese variety and linear equations. However this is false for singular varieties, and we give explicit counter-examples to the EKS conjecture for singular curves. The techniques we use also allow us to prove a gap and uniqueness theorem for symmetric tensor rank. We put Eisenbud's question in a more general context about the behaviour of border rank under specialisation to a linear subspace, and provide an overview of conjectures coming from signal processing and complexity theory in this context.Comment: 21 pages; presentation improved as suggested by the referees; To appear in Journal of London Mathematical Societ

Calculating Non-adiabatic Pressure Perturbations during Multi-field Inflation

Isocurvature perturbations naturally occur in models of inflation consisting of more than one scalar field. In this paper we calculate the spectrum of isocurvature perturbations generated at the end of inflation for three different inflationary models consisting of two canonical scalar fields. The amount of non-adiabatic pressure present at the end of inflation can have observational consequences through the generation of vorticity and subsequently the sourcing of B-mode polarisation. We compare two different definitions of isocurvature perturbations and show how these quantities evolve in different ways during inflation. Our results are calculated using the open source Pyflation numerical package which is available to download.Comment: v2: Typos fixed, references and comments added; v1: 8 pages, 10 figures, software available to download at http://pyflation.ianhuston.ne

Supersymmetric extensions of K field theories

We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.Comment: Contribution to the Proceedings of QTS7, Prague, August 201