Aromatic 19F–13C TROSY—[19F, 13C]‐Pyrimidine Labeling for NMR Spectroscopy of RNA

We present the access to [5‐¹⁹F, 5‐¹³C]‐uridine and ‐cytidine phosphoramidites for the production of site‐specifically modified RNAs up to 65 nucleotides (nts). The amidites were used to introduce [5‐¹⁹F, 5‐¹³C]‐pyrimidine labels into five RNAs—the 30 nt human immunodeficiency virus trans activation response (HIV TAR) 2 RNA, the 61 nt human hepatitis B virus ? (hHBV ?) RNA, the 49 nt SAM VI riboswitch aptamer domain from B. angulatum, the 29 nt apical stem loop of the pre‐microRNA (miRNA) 21 and the 59 nt full length pre‐miRNA 21. The main stimulus to introduce the aromatic ¹⁹F–¹³C‐spin topology into RNA comes from a work of Boeszoermenyi et al., in which the dipole‐dipole interaction and the chemical shift anisotropy relaxation mechanisms cancel each other leading to advantageous TROSY properties shown for aromatic protein sidechains. This aromatic ¹³C–¹⁹F labeling scheme is now transferred to RNA. We provide a protocol for the resonance assignment by solid phase synthesis based on diluted [5‐¹⁹F, 5‐¹³C]/[5‐¹⁹F] pyrimidine labeling. For the 61 nt hHBV ? we find a beneficial ¹⁹F–¹³C TROSY enhancement, which should be even more pronounced in larger RNAs and will facilitate the NMR studies of larger RNAs. The [¹⁹F, ¹³C]‐labeling of the SAM VI aptamer domain and the pre‐miRNA 21 further opens the possibility to use the biorthogonal stable isotope reporter nuclei in in vivo NMR to observe ligand binding and microRNA processing in a biological relevant setting.     

Cationic beta-cyclodextrin bilayer vesicles

Cationic amphiphilic beta-cyclodextrins, substituted with hydrophobic n-alkylthio chains at the primary hydroxyl side and hydrophilic omega-amino-oligo(ethylene glycol) units at the secondary side, form bilayer vesicles with a diameter of 30-35 nm (when alkyl = hexadecyl) or nanoparticles with a diameter of ca. 120 nm (when alkyl = hexyl) in water.     

Primordial Black Holes: Pair Creation, Lorentzian Condition, and Evaporation

The wave function of the universe is usuallytaken to be a functional of the threemetric on aspacelike section, , which is measured. It issometimes better, however, to work in the conjugaterepresentation, where the wave function depends on a quantityrelated to the second fundamental form of . Thismakes it possible to ensure that is part of aLorentzian universe by requiring that the argument of the wave function be purely imaginary. Wedemonstrate the advantages of this formalism first inthe well-known examples of the nucleation of a de Sitteror a Nariai universe. We then use it to calculate the pair creation rate for submaximal blackholes in de Sitter space, which had been thought tovanish semiclassically. We also study the quantumevolution of asymptotically de Sitter black holes. Forblack holes whose size is comparable to that of thecosmological horizon, this process differs significantlyfrom the evaporation of asymptotically flat black holes.Our model includes the one-loop effective action in the s-wave and large-N approximation.Black holes of the maximal mass are in equilibrium.Unexpectedly, we find that nearly maximal quantumSchwarzschild–de Sitter black holes antievaporate.However, there is a different perturbative mode thatleads to evaporation. We show that this mode will alwaysbe excited when a pair of maximal cosmological blackholes nucleates.     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.     

Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation

We consider finite time blow up solutions to the critical nonlinear Schrödinger equation For a suitable class of initial data in the energy space H¹, we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L² mass at the blow up point, the second part corresponds to the regular part and has a strong L² limit at blow up time.Part of this work has been supported by grant DMS-0111298.     

On universality of blow-up profile for <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> critical nonlinear Schrödinger equation

We consider finite time blow-up solutions to the critical nonlinear Schrödinger equation iu_t=-u-|u|^4/Nu with initial condition u₀H¹. Existence of such solutions is known, but the complete blow-up dynamic is not understood so far. For a specific set of initial data, finite time blow-up with a universal sharp upper bound on the blow-up rate has been proved in [22], [23].We establish in this paper the existence of a universal blow-up profile which attracts blow-up solutions in the vicinity of blow-up time. Such a property relies on classification results of a new type for solutions to critical NLS. In particular, a new characterization of soliton solutions is given, and a refined study of dispersive effects of (NLS) in L² will remove the possibility of self similar blow-up in energy space H¹.     

Unbounded Entropy in Spacetimes with Positive Cosmological Constant

In theories of gravity with a positive cosmological constant, we consider product solutions with flux, of the form (A)dS _p ×S ^q . Most solutions are shown to be perturbatively unstable, including all uncharged dS _p ×S ^q spacetimes. For dimensions greater than four, the stable class includes universes whose entropy exceeds that of de Sitter space, in violation of the conjectured N-bound. Hence, if quantum gravity theories with finite-dimensional Hilbert space exist, the specification of a positive cosmological constant will not suffice to characterize the class of spacetimes they describe.