Bilinear forms on Grothendieck groups of triangulated categories

We extend the theory of bilinear forms on the Green ring of a finite group developed by Benson and Parker to the context of the Grothendieck group of a triangulated category with Auslander-Reiten triangles, taking only relations given by direct sum decompositions. We examine the non-degeneracy of the bilinear form given by dimensions of homomorphisms, and show that the form may be modified to give a Hermitian form for which the standard basis given by indecomposable objects has a dual basis given by Auslander-Reiten triangles. An application is given to the homotopy category of perfect complexes over a symmetric algebra, with a consequence analogous to a result of Erdmann and Kerner.Comment: arXiv admin note: substantial text overlap with arXiv:1301.470

Ultrasensitive force and displacement detection using trapped ions

The ability to detect extremely small forces is vital for a variety of disciplines including precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1 $aN/\sqrt{Hz}$ (atto $=10^{-18}$) through coupling of micro or nanofabricated mechanical resonators to a variety of physical systems including single-electron transistors, superconducting microwave cavities, and individual spins. These experiments have allowed for probing studies of a variety of phenomena, but sensitivity requirements are ever-increasing as new regimes of physical interactions are considered. Here we show that trapped atomic ions are exquisitely sensitive force detectors, with a measured sensitivity more than three orders of magnitude better than existing reports. We demonstrate detection of forces as small as 174 $yN$ (yocto $=10^{-24}$), with a sensitivity 390$\pm150$ $yN/\sqrt{Hz}$ using crystals of $n=60$ $^{9}$Be$^{+}$ ions in a Penning trap. Our technique is based on the excitation of normal motional modes in an ion trap by externally applied electric fields, detection via and phase-coherent Doppler velocimetry, which allows for the discrimination of ion motion with amplitudes on the scale of nanometers. These experimental results and extracted force-detection sensitivities in the single-ion limit validate proposals suggesting that trapped atomic ions are capable of detecting of forces with sensitivity approaching 1 $yN/\sqrt{Hz}$. We anticipate that this demonstration will be strongly motivational for the development of a new class of deployable trapped-ion-based sensors, and will permit scientists to access new regimes in materials science.Comment: Expanded introduction and analysis. Methods section added. Subject to press embarg

(Non)-Renormalization of the Chiral Vortical Effect Coefficient

We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula $\sum_{n=1}^\infty n=-1/12$. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large $N$ limit.Comment: 11 pages, 3 figures. Version 2 corrects an error and calculates leading radiative correctio

Sea anemones may thrive in a high CO2 world

Increased seawater pCO 2, and in turn 'ocean acidification' (OA), is predicted to profoundly impact marine ecosystem diversity and function this century. Much research has already focussed on calcifying reef-forming corals (Class: Anthozoa) that appear particularly susceptible to OA via reduced net calcification. However, here we show that OA-like conditions can simultaneously enhance the ecological success of non-calcifying anthozoans, which not only play key ecological and biogeochemical roles in present day benthic ecosystems but also represent a model organism should calcifying anthozoans exist as less calcified (soft-bodied) forms in future oceans. Increased growth (abundance and size) of the sea anemone (Anemonia viridis) population was observed along a natural CO 2 gradient at Vulcano, Italy. Both gross photosynthesis (P G) and respiration (R) increased with pCO 2 indicating that the increased growth was, at least in part, fuelled by bottom up (CO 2 stimulation) of metabolism. The increase of P G outweighed that of R and the genetic identity of the symbiotic microalgae (Symbiodinium spp.) remained unchanged (type A19) suggesting proximity to the vent site relieved CO 2 limitation of the anemones' symbiotic microalgal population. Our observations of enhanced productivity with pCO 2, which are consistent with previous reports for some calcifying corals, convey an increase in fitness that may enable non-calcifying anthozoans to thrive in future environments, i.e. higher seawater pCO 2. Understanding how CO 2-enhanced productivity of non- (and less-) calcifying anthozoans applies more widely to tropical ecosystems is a priority where such organisms can dominate benthic ecosystems, in particular following localized anthropogenic stress. © 2012 Blackwell Publishing Ltd

Low plasma neurofilament light levels associated with raised cortical microglial activation suggest inflammation acts to protect prodromal Alzheimer's disease

BACKGROUND: Plasma and cerebrospinal fluid levels of neurofilament light (NfL), a marker of axonal degeneration, have previously been reported to be raised in patients with clinically diagnosed Alzheimer's disease (AD). Activated microglia, an intrinsic inflammatory response to brain lesions, are also known to be present in a majority of Alzheimer or mild cognitive impaired (MCI) subjects with raised β-amyloid load on their positron emission tomography (PET) imaging. It is now considered that the earliest phase of inflammation may be protective to the brain, removing amyloid plaques and remodelling synapses. Our aim was to determine whether the cortical inflammation/microglial activation load, measured with the translocator protein marker 11C-PK11195 PET, was correlated with plasma NfL levels in prodromal and early Alzheimer subjects. METHODS: Twenty-seven MCI or early AD cases with raised cortical β-amyloid load had 11C-(R)-PK11195 PET, structural and diffusion magnetic resonance imaging, and levels of their plasma NfL measured. Correlation analyses were performed using surface-based cortical statistics. RESULTS: Statistical maps localised areas in MCI cases where levels of brain inflammation correlated inversely with plasma NfL levels. These areas were localised in the frontal, parietal, precuneus, occipital, and sensorimotor cortices. Brain inflammation correlated negatively with mean diffusivity (MD) of water with regions overlapping. CONCLUSION: We conclude that an inverse correlation between levels of inflammation in cortical areas and plasma NfL levels indicates that microglial activation may initially be protective to axons in AD. This is supported by the finding of an inverse association between cortical water diffusivity and microglial activation in the same regions. Our findings suggest a rationale for stimulating microglial activity in early and prodromal Alzheimer cases-possibly using immunotherapy. Plasma NfL levels could be used as a measure of the protective efficacy of immune stimulation and for monitoring efficacy of putative neuroprotective agents