Dynamics of defect formation

A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as a function of the rate of increase of the critical parameter. The procedure is valid in both the overdamped and underdamped limits. In one space dimension, we perform quantitative comparison with numerical simulations of the nonlinear nonautonomous stochastic partial differential equation and report on signatures of underdamped dynamics.Comment: 4 pages, LaTeX, 4 figures. Submitted to Physical Revie

A new mechanism shapes the naïve CD8+ T cell repertoire: the selection for full diversity

During thymic T cell differentiation, TCR repertoires are shaped by negative, positive and agonist selection. In the thymus and in the periphery, repertoires are also shaped by strong inter-clonal and intra-clonal competition to survive death by neglect. Understanding the impact of these events on the T cell repertoire requires direct evaluation of TCR expression in peripheral naïve T cells. Several studies have evaluated TCR diversity, with contradictory results. Some of these studies had intrinsic technical limitations since they used material obtained from T cell pools, preventing the direct evaluation of clone sizes. Indeed with these approaches, identical TCRs may correspond to different cells expressing the same receptor, or to several amplicons from the same T cell. We here overcame this limitation by evaluating TCRB expression in individual naïve CD8+ T cells. Of the 2269 Tcrb sequences we obtained from 13 mice, 99% were unique. Mathematical analysis of this data showed that the average number of naïve peripheral CD8+ T cells expressing the same TCRB is 1.1 cell. Since TCRA co-expression studies could only increase repertoire diversity, these results reveal that the number of naïve T cells with unique TCRs approaches the number of naïve cells. Since thymocytes undergo multiple rounds of divisions after TCRB rearrangement; and 3–5% of thymocytes survive thymic selection events; the number of cells expressing the same TCRB was expected to be much higher. Thus, these results suggest a new repertoire selection mechanism, which strongly selects for full TCRB diversity

On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics (Dec 2011

Why are cell populations maintained via multiple compartments?

We consider the maintenance of ‘product’ cell populations from ‘progenitor’ cells via a sequence of one or more cell types, or compartments, where each cell’s fate is chosen stochastically. If there is only one compartment then large amplification, that is, a large ratio of product cells to progenitors comes with disadvantages. The product cell population is dominated by large families (cells descended from the same progenitor) and many generations separate, on average, product cells from progenitors. These disadvantages are avoided using suitably constructed sequences of compartments: the amplification factor of a sequence is the product of the amplification factors of each compartment, while the average number of generations is a sum over contributions from each compartment. Passing through multiple compartments is, in fact, an efficient way to maintain a product cell population from a small flux of progenitors, avoiding excessive clonality and minimizing the number of rounds of division en route. We use division, exit and death rates, estimated from measurements of single-positive thymocytes, to choose illustrative parameter values in the single-compartment case. We also consider a five-compartment model of thymocyte differentiation, from double-negative precursors to single-positive product cells

Counting defects with the two-point correlator

We study how topological defects manifest themselves in the equal-time two-point field correlator. We consider a scalar field with Z_2 symmetry in 1, 2 and 3 spatial dimensions, allowing for kinks, domain lines and domain walls, respectively. Using numerical lattice simulations, we find that in any number of dimensions, the correlator in momentum space is to a very good approximation the product of two factors, one describing the spatial distribution of the defects and the other describing the defect shape. When the defects are produced by the Kibble mechanism, the former has a universal form as a function of k/n, which we determine numerically. This signature makes it possible to determine the kink density from the field correlator without having to resort to the Gaussian approximation. This is essential when studying field dynamics with methods relying only on correlators (Schwinger-Dyson, 2PI).Comment: 11 pages, 7 figures

Neo-Atlantis: The Netherlands under a 5-m sea level rise

What could happen to the Netherlands if, in 2030, the sea level starts to rise and eventually, after 100 years, a sea level of 5 m above current level would be reached? This question is addressed by studying literature, by interviewing experts in widely differing fields, and by holding an expert workshop on this question. Although most experts believe that geomorphology and current engineering skills would enable the country to largely maintain its territorial integrity, there are reasons to assume that this is not likely to happen. Social processes that precede important political decisions - such as the growth of the belief in the reality of sea level rise and the framing of such decisions in a proper political context (policy window) - evolve slowly. A flood disaster would speed up the decision-making process. The shared opinion of the experts surveyed is that eventually part of the Netherlands would be abandoned. © 2008 The Author(s)

The Antarctic Impulsive Transient Antenna Ultra-high Energy Neutrino Detector Design, Performance, and Sensitivity for 2006-2007 Balloon Flight

We present a detailed report on the experimental details of the Antarctic Impulsive Transient Antenna (ANITA) long duration balloon payload, including the design philosophy and realization, physics simulations, performance of the instrument during its first Antarctic flight completed in January of 2007, and expectations for the limiting neutrino detection sensitivity. Neutrino physics results will be reported separately.Comment: 50 pages, 49 figures, in preparation for PR

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years