Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele

We establish a connection between two recently-proposed approaches to the understanding of the geometric origin of the Fu-Kane-Mele invariant $\mathrm{FKM} \in \mathbb{Z}_2$, arising in the context of 2-dimensional time-reversal symmetric topological insulators. On the one hand, the $\mathbb{Z}_2$ invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes it is possible to provide an expression for $\mathrm{FKM}$ containing the square root of the Wess-Zumino amplitude for a certain $U(N)$-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above mentioned Wess-Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov-Wiegmann formula for fields $\mathbb{T}^2 \to U(N)$, of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.Comment: 23 pages, 1 figure. To appear in Letters in Mathematical Physic

Relativistic Binaries in Globular Clusters

Galactic globular clusters are old, dense star systems typically containing 10\super{4}--10\super{7} stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of hard binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct {\it N}-body integrations and Fokker--Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.Comment: 88 pages, 13 figures. Submitted update of Living Reviews articl

Primary progressive aphasia: a clinical approach

This work was supported by the Alzheimer’s Society (AS-PG-16-007), the National Institute for Health Research University College London Hospitals Biomedical Research Centre and the UCL Leonard Wolfson Experimental Neurology Centre (PR/ylr/18575). Individual authors were supported by the Leonard Wolfson Foundation (Clinical Research Fellowship to CRM), the National Institute for Health Research (NIHR Doctoral Training Fellowship to AV), the National Brain Appeal–Frontotemporal Dementia Research Fund (CNC) and the Medical Research Council (PhD Studentships to CJDH and RLB, MRC Research Training Fellowship to PDF, MRC Clinician Scientist to JDR). MNR and NCF are NIHR Senior Investigators. SJC is supported by Grants from ESRC-NIHR (ES/L001810/1), EPSRC (EP/M006093/1) and Wellcome Trust (200783). JDW was supported by a Wellcome Trust Senior Research Fellowship in Clinical Science (091673/Z/10/Z)

Early development of infant gut microbiota in relation to breastfeeding and human milk oligosaccharides.

Peer reviewed: TrueAcknowledgements: We thank study site staff for their cooperation. The participation of parents and infants in this study is greatly appreciated. We would like to thank all NIZO laboratory personnel, Dr. Sierra Durham (UC Davis) and Prof. Daniela Barile (UC Davis) for their contributions to the HMO analysis described in this manuscript. We acknowledge the CBGS research nurses Suzanne Smith, Anne-Marie Wardell, and Karen Forbes, all the families who contributed to the study, the staff at the National Institute for Health Research (NIHR) Cambridge/Wellcome Trust Clinical Research Facility, the NIHR Cambridge Comprehensive Biomedical Research Centre, the midwives at the Rosie Maternity Hospital, Cambridge, UK, and Karen Whitehead and Dianne Wingate at the Department of Paediatrics, University of Cambridge, for laboratory support.BACKGROUND: Infant gut microbiota composition is influenced by various factors early in life. Here, we investigate associations between infant gut microbiome development, infant age, breastfeeding duration, and human milk oligosaccharides (HMO) composition in breastmilk. METHODS: A total of 94 mother-infant pairs were recruited as part of the Cambridge Baby Growth and Breastfeeding Study (CBGS-BF) (Cambridge, UK). Infant stool samples (n = 337) were collected at 2 week, 6 week, 3 month, and 6 month of age. The 16S rRNA V3-V4 rRNA region was sequenced using MiSeq Illumina to determine microbiota composition and diversity. Mother's hindmilk samples were collected at birth, 2 week, 6 week, 3 month, and 6 month postpartum. Concentrations of five neutral [2'FL, 3'FL, lacto-N-fucopentaose 1 (LNFP1), LNnT, LNT] and two acidic (3'SL, and 6'SL) HMOs were measured in all milk samples using High-Performance Anion-Exchange Chromatography with Pulsed Amperometric Detection (HPAEC-PAD). We explored the associations between infant gut microbiome parameters and age, duration of exclusive breastfeeding (EBF), and levels of individual HMOs. RESULTS: Bifidobacterium was the most abundant genus in infant stool at all-time points, irrespective of breastfeeding duration, with an overall mean relative abundance of 70%. The relative abundance of B. bifidum in stool from infants who were breastfed for longer than 6 months was significantly higher compared to the infant breastfed up to 3 months (p = 0.0285). Alpha-diversity (both Shannon and ASV-level Richness) of infant gut microbiota showed a biphasic change with infant age, decreasing from 2 weeks until 3 months and then increasing until 6 months of age. Bifidobacterium relative abundance was associated with higher concentrations of 2'FL and LNFP1 in breastmilk across all time-points (p = 0.049 and 0.017, respectively), with trends toward a higher abundance of B. longum species. No significant association with Bifidobacterium was found for breastmilk LNnT, 3'SL, and 6'SL levels. CONCLUSION: Our study is in line with previous data demonstrating that EBF duration in the first months of life impacts infant gut microbiota composition. The observed links between specific HMOs in breastmilk and bacteria in infant stool provide evidence of how mother's milk affects infant microbiome development