Birational maps from polarization and the preservation of measure and integrals

The main result of this paper is the discretization of Hamiltonian systems of the form $\ddot x = -K \nabla W(x)$, where $K$ is a constant symmetric matrix and $W\colon\mathbb{R}^n\to \mathbb{R}$ is a polynomial of degree $d\le 4$ in any number of variables $n$. The discretization uses the method of polarization and preserves both the energy and the invariant measure of the differential equation, as well as the dimension of the phase space. This generalises earlier work for discretizations of first order systems with $d=3$, and of second order systems with $d=4$ and $n=1$.Comment: Updated to final pre-publication versio

Volume preservation by Runge–Kutta methods

This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.apnum.2016.06.010It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge–Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and Tse and independently by Chartier and Murua that no B-Series method can be volume preserving for all volume preserving vector fields. In this paper, we show that despite this result, symplectic Runge–Kutta methods can be volume preserving for a much larger class of vector fields than Hamiltonian systems, and discuss how some Runge–Kutta methods can preserve a modified measure exactly.This research was supported by the Marie Curie International Research Staff Exchange Scheme, grant number DP140100640, within the 7th European Community Framework Programme; by the Australian Research Council grant number 269281; and by the UK Engineering and Physical Sciences Research Council grant EP/H023348/1 for the Cambridge Centre for Analysis

Exploring the pre-immune landscape of antigen-specific T cells

Abstract Background Adaptive immune responses to newly encountered pathogens depend on the mobilization of antigen-specific clonotypes from a vastly diverse pool of naive T cells. Using recent advances in immune repertoire sequencing technologies, models of the immune receptor rearrangement process, and a database of annotated T cell receptor (TCR) sequences with known specificities, we explored the baseline frequencies of T cells specific for defined human leukocyte antigen (HLA) class I-restricted epitopes in healthy individuals. Methods We used a database of TCR sequences with known antigen specificities and a probabilistic TCR rearrangement model to estimate the baseline frequencies of TCRs specific to distinct antigens epitopespecificT-cells. We verified our estimates using a publicly available collection of TCR repertoires from healthy individuals. We also interrogated a database of immunogenic and non-immunogenic peptides is used to link baseline T-cell frequencies with epitope immunogenicity. Results Our findings revealed a high degree of variability in the prevalence of T cells specific for different antigens that could be explained by the physicochemical properties of the corresponding HLA class I-bound peptides. The occurrence of certain rearrangements was influenced by ancestry and HLA class I restriction, and umbilical cord blood samples contained higher frequencies of common pathogen-specific TCRs. We also identified a quantitative link between specific T cell frequencies and the immunogenicity of cognate epitopes presented by defined HLA class I molecules. Conclusions Our results suggest that the population frequencies of specific T cells are strikingly non-uniform across epitopes that are known to elicit immune responses. This inference leads to a new definition of epitope immunogenicity based on specific TCR frequencies, which can be estimated with a high degree of accuracy in silico, thereby providing a novel framework to integrate computational and experimental genomics with basic and translational research efforts in the field of T cell immunology

Correction: Faught et al. “Socioeconomic Disadvantage across the Life Course is associated with Diet Quality in Young Adulthood” Nutrients, 2019, 11(2), 242

We noticed an error in the text that requires correcting as it may contribute to an incorrect understanding of our study’s scientific conclusions. In the text accompanying Table 4 (Section 3.3: Mediation Analysis (Pathways Hypothesis), page 11), the third sentence in the paragraph reads: “Adult SEP at the level of university education mediated associations between childhood SEP and mean adult HEI-2015 score (p < 0.001).” This should in fact read: “Adult SEP at the level of high school or less mediated associations between childhood SEP and mean adult HEI-2015 score (p < 0.001).” This correction is consistent with the results presented in Table 4, and in line with the scientific conclusions discussed in the article that a low socioeconomic position (SEP) in adulthood mediates associations between childhood SEP and adult diet quality. SEP at the level of university education was the reference group in this analysis

Divergent roles for antigenic drive in the aetiology of primary versus dasatinib-associated CD8(+) TCR-Vβ(+) expansions

CD8(+) T-cell expansions are the primary manifestation of T-cell large granular lymphocytic leukemia (T-LGLL), which is frequently accompanied by neutropenia and rheumatoid arthritis, and also occur as a secondary phenomenon in leukemia patients treated with dasatinib, notably in association with various drug-induced side-effects. However, the mechanisms that underlie the genesis and maintenance of expanded CD8(+) T-cell receptor (TCR)-V beta(+) populations in these patient groups have yet to be fully defined. In this study, we performed a comprehensive phenotypic and clonotypic assessment of expanded (TCR-V beta(+)) and residual (TCR-V beta(-)) CD8(+) T-cell populations in T-LGLL and dasatinib-treated chronic myelogenous leukemia (CML) patients. The dominant CD8(+) TCR-V beta(+) expansions in T-LGLL patients were largely monoclonal and highly differentiated, whereas the dominant CD8(+) TCR-V beta(+) expansions in dasatinib-treated CML patients were oligoclonal or polyclonal, and displayed a broad range of memory phenotypes. These contrasting features suggest divergent roles for antigenic drive in the immunopathogenesis of primary versus dasatinib-associated CD8(+) TCR-V beta(+) expansions.Peer reviewe

Correction to: Why public health matters today and tomorrow: the role of applied public health research.

The article "Why public health matters today and tomorrow: the role of applied public health research," written by Lindsay McLaren et al., was originally published Online First without Open Access