Nitrogen availability and cell density each affects growth and cellular astaxanthin content of Haematococcus pluvialis, but possible combined effects of these two factors on the content and productivity of astaxanthin, especially under outdoor culture conditions, is less understood. In this study, the effects of the initial biomass densities IBDs of 0.1, 0.5, 0.8, 1.5, 2.7, 3.5, and 5.0 g L-1 DW and initial nitrogen concentrations of 0, 4.4, 8.8, and 17.6 mM nitrate on growth and cellular astaxanthin content of H. pluvialis Flotow K-0084 were investigated in outdoor glass column photobioreactors in a batch culture mode. A low IBD of 0.1 g L-1 DW led to photo-bleaching of the culture within 1-2 days. When the IBD was 0.5 g L-1 and above, the rate at which the increase in biomass density and the astaxanthin content on a per cell basis was higher at lower IBD. When the IBD was optimal (i.e., 0.8 g L-1), the maximum astaxanthin content of 3.8% of DW was obtained in the absence of nitrogen, whereas the maximum astaxanthin productivity of 16.0 mg L-1 d(-1) was obtained in the same IBD culture containing 4.4 mM nitrogen. The strategies for achieving maximum Haematococcus biomass productivity and for maximum cellular astaxanthin content are discussed.

We study the so-called Descent, or [bar over Q], Equation for the null polygonal supersymmetric Wilson loop in the framework of the pentagon operator product expansion. To properly address this problem, one requires to restore the cyclicity of the loop broken by the choice of OPE channels. In the course of the study, we unravel a phenomenon of twist enhancement when passing to a cyclically shifted channel. Currently, we focus on the consistency of the all-order Descent Equation for the particular case relating the NMHV heptagon to MHV hexagon. We find that the equation establishes a relation between contributions of different twists and successfully verify it in perturbation theory making use of available bootstrap predictions for elementary pentagons.

Cerebral small-vessel damage manifests as white matter hyperintensities and cerebral atrophy on brain MRI and is associated with aging, cognitive decline and dementia. We sought to examine the interrelationship of these imaging biomarkers and the influence of hypertension in older individuals. We used a multivariate spatial covariance neuroimaging technique to localize the effects of white matter lesion load on regional gray matter volume and assessed the role of blood pressure control, age and education on this relationship. Using a case-control design matching for age, gender, and educational attainment we selected 64 participants with normal blood pressure, controlled hypertension or uncontrolled hypertension from the Northern Manhattan Study cohort. We applied gray matter voxel-based morphometry with the scaled subprofile model to (1) identify regional covariance patterns of gray matter volume differences associated with white matter lesion load, (2) compare this relationship across blood pressure groups, and (3) relate it to cognitive performance. In this group of participants aged 60–86 years, we identified a pattern of reduced gray matter volume associated with white matter lesion load in bilateral temporal-parietal regions with relative preservation of volume in the basal forebrain, thalami and cingulate cortex. This pattern was expressed most in the uncontrolled hypertension group and least in the normotensives, but was also more evident in older and more educated individuals. Expression of this pattern was associated with worse performance in executive function and memory. In summary, white matter lesions from small-vessel disease are associated with a regional pattern of gray matter atrophy that is mitigated by blood pressure control, exacerbated by aging, and associated with cognitive performance.

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N = 4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N = 4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N = 4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N = 4SYM that should be valid at any coupling and away from the planar limit.

We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N = 4 super-Yang–Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.

We study event shapes in N = 4SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N = 4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N = 4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.

The utility of plasma amyloid beta (Aβ) and tau levels for the clinical diagnosis of Alzheimer’s disease (AD) dementia has been controversial. The main objective of this study was to compare Aβ42 and tau levels measured by the ultra-sensitive immunomagnetic reduction (IMR) assays in plasma samples collected at the Banner Sun Health Institute (BSHRI) (United States) with those from the National Taiwan University Hospital (NTUH) (Taiwan). Significant increase in tau levels were detected in AD subjects from both cohorts, while Aβ42 levels were increased only in the NTUH cohort. A regression model incorporating age showed that tau levels identified probable ADs with 81 and 96% accuracy in the BSHRI and NTUH cohorts, respectively, while computed products of Aβ42 and tau increased the accuracy to 84% in the BSHRI cohorts. Using 382.68 (pg/ml)² as the cut-off value, the product achieved 92% accuracy in identifying AD in the combined cohorts. Overall findings support that plasma Aβ42 and tau assayed by IMR technology can be used to assist in the clinical diagnosis of AD.

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to-two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.

We address the near-collinear expansion of multiparticle NMHV amplitudes, namely, the heptagon and octagons in the dual language of null polygonal super Wilson loops. In particular, we verify multiparticle factorization of charged pentagon transitions in terms of pentagons for single flux-tube excitations within the framework of refined operator product expansion. We find a perfect agreement with available tree and one-loop data.