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On avoiding Ostrogradski instabilities within Asymptotic Safety
We study the renormalization group flow of gravity coupled to scalar matter
using functional renormalization group techniques. The novel feature is the
inclusion of higher-derivative terms in the scalar propagator. Such terms give
rise to Ostrogradski ghosts which signal an instability of the system and are
therefore dangerous for the consistency of the theory. Since it is expected
that such terms are generated dynamically by the renormalization group flow
they provide a potential threat when constructing a theory of quantum gravity
based on Asymptotic Safety. Our work then establishes the following picture:
upon incorporating higher-derivative terms in the scalar propagator the flow of
the gravity-matter system possesses a fixed point structure suitable for
Asymptotic Safety. This structure includes an interacting renormalization group
fixed point where the Ostrogradski ghosts acquire an infinite mass and decouple
from the system. Tracing the flow towards the infrared it is found that there
is a subset of complete renormalization group trajectories which lead to stable
renormalized propagators. This subset is in one-to-one correspondence to the
complete renormalization group trajectories obtained in computations which do
not track of the higher-derivative terms. Thus our asymptotically safe
gravity-matter systems are not haunted by Ostrogradski ghosts.Comment: 35 pages, 10 figure
Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
One-dimensional spinor gases with strong delta interaction fermionize and
form a spin chain. The spatial degrees of freedom of this atom chain can be
described by a mapping to spinless noninteracting fermions and the spin degrees
of freedom are described by a spin-chain model with nearest-neighbor
interactions. Here, we compute momentum and occupation-number distributions of
up to 16 strongly interacting spinor fermions and bosons as a function of their
spin imbalance, the strength of an externally applied magnetic field gradient,
the length of their spin, and for different excited states of the multiplet. We
show that the ground-state momentum distributions resemble those of the
corresponding noninteracting systems, apart from flat background distributions,
which extend to high momenta. Moreover, we show that the spin order of the spin
chain---in particular antiferromagnetic spin order---may be deduced from the
momentum and occupation-number distributions of the system. Finally, we present
efficient numerical methods for the calculation of the single-particle
densities and one-body density matrix elements and of the local exchange
coefficients of the spin chain for large systems containing more than 20
strongly interacting particles in arbitrary confining potentials.Comment: See the ancillary files for the Mathematica notebook used to
calculate the results of this paper, the derivation of the formula for the
one-body density matrix elements, given by Eq. (22), and a table with the
local exchange coefficients of up to 60 harmonically trapped particles. A
less efficient method for calculating the exchange coefficients was given in
the 2nd version of this manuscrip
Dynamic changes in connexin expression correlate with key events in the wound healing process.
Wound healing is a complex process requiring communication for the precise co-ordination of different cell types. The role of extracellular communication through growth factors in the wound healing process has been extensively documented, but the role of direct intercellular communication via gap junctions has scarcely been investigated. We have examined the dynamics of gap junction protein (Connexins 26, 30, 31.1 and 43) expression in the murine epidermis and dermis during wound healing, and we show that connexin expression is extremely plastic between 6 hours and 12 days post-wounding. The immediate response (6 h) to wounding is to downregulate all connexins in the epidermis, but thereafter the expression profile of each connexin changes dramatically. Here, we correlate the changing patterns of connexin expression with key events in the wound healing process
Immuno-electron microscopic quantification of the fucoxanthin chlorophyll a/c binding polypeptides Fcp2, Fcp4, and Fcp6 of Cyclotella cryptica grown under low- and high-light intensities
The diatom Cyclotella cryptica was grown under low- and highintensity white light of 50 and 500 Ī¼mol photons mā2 sā1, respectively. Western immunoblotting showed that the diatom adapted its light-harvesting apparatus, giving rise to different amounts of distinct fucoxanthin chlorophyll a/c binding polypeptides (Fcp). The amount of Fcp2 was approximately two-fold higher under low-light than under high-light conditions, whereas the amount of Fcp6 increased four- to five-fold under high-light conditions. For Fcp4, no significant differences were detected in response to either light regime. Cells of Cyclotella grown under high- and low-light intensity were subjected to immunoelectron microscopy. Quantification of the gold label, expressed as gold particles per Ī¼m2, confirmed the results obtained by Western immunoblotting. Exposure to low light resulted in the detection of approximately six times more Fcp2-bound gold particles per Ī¼m2 in thylakoid membranes, whereas in cells grown under high light the number of Fcp6- bound gold particles increased ten-fold. For Fcp4, similar amounts of gold particles per Ī¼m2 were counted under the two light regimes. These immunocytochemical results confirmed molecular data derived from phylogenetic analyses of the sequences of genes encoding fucoxanthin chlorophyll a/c binding polypeptides (fcp genes) and from measurements of steady-state fcp mRNA concentrations. The results show that Fcp2 and Fcp6 accumulate under low- and high-light intensity, respectively, whereas Fcp4 seems to be constitutively synthesized. [Int Microbiol 2006; 9(1):29-36
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