Up-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity

Liouville first passage percolation(LFPP) with the parameter ξ > 0 is the family of random distance functions ■ on the plane obtained by integrating ■along paths, where ■ is a smooth mollification of the planar Gaussian free field. Recent works have shown that for all ξ > 0, the LFPP metrics,appropriately re-scaled, admit non-trivial subsequential limiting metrics. In the case ξ < ξcrit≈ 0.41, it has been shown that the subsequential limit is unique and defines a metric on γ-Liouville q...     

A common repressor pool results in indeterminacy of extrinsic noise

For just over a decade, stochastic gene expression has been the focus of many experimental and theoretical studies. It is now widely accepted that noise in gene expression can be decomposed into extrinsic and intrinsic components, which have orthogonal contributions to the total noise. Intrinsic noise stems from the random occurrence of biochemical reactions and is inherent to gene expression. Extrinsic noise originates from fluctuations in the concentrations of regulatory components or random transitions in the cell's state and is imposed to the gene of interest by the intra- and extra-cellular environment. The basic assumption has been that extrinsic noise acts as a pure input on the gene of interest, which exerts no feedback on the extrinsic noise source. Thus, multiple copies of a gene would be uniformly influenced by an extrinsic noise source. Here, we report that this assumption falls short when multiple genes share a common pool of a regulatory molecule. Due to the competitive utilization of the molecules existing in this pool, genes are no longer uniformly influenced by the extrinsic noise source. Rather, they exert negative regulation on each other and thus extrinsic noise cannot be determined by the currently established method.     

Hyperconifold transitions,mirror symmetry,and string theory

Multiply-connected Calabi–Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli space) is an isolated singularity which is a finite cyclic quotient of the conifold; these were called hyperconifolds. It was also shown that if the order of the quotient group is even, such singular varieties have projective crepant resolutions, which are therefore smooth Calabi–Yau manifolds. The resulting topological transitions were called hyperconifold transitions, and change the fundamental group as well as the Hodge numbers. Here Batyrev?s construction of Calabi–Yau hypersurfaces in toric fourfolds is used to demonstrate that certain compact examples containing the remaining hyperconifolds — the Z₃${\mathbb{Z}}_3$ and Z₅${\mathbb{Z}}_5$ cases — also have Calabi–Yau resolutions. The mirrors of the resulting transitions are studied and it is found, surprisingly, that they are ordinary conifold transitions. These are the first examples of conifold transitions with mirrors which are more exotic extremal transitions. The new hyperconifold transitions are also used to construct a small number of new Calabi–Yau manifolds, with small Hodge numbers and fundamental group Z₃${\mathbb{Z}}_3$ or Z₅${\mathbb{Z}}_5$. Finally, it is demonstrated that a hyperconifold is a physically sensible background in Type IIB string theory. In analogy to the conifold case, non-perturbative dynamics smooth the physical moduli space, such that hyperconifold transitions correspond to non-singular processes in the full theory.     

Hexaphenylbenzene-based polymers of intrinsic microporosity

Microporous polymers derived from the 1,2- and 1,4-regioisomers of di(3',4'-dihydroxyphenyl)tetraphenylbenzene have very different properties with the former being composed predominantly of cyclic oligomers whereas the latter is of high molar mass suitable for the formation of robust solvent-cast films of high gas permeability.     

Partitioning the edges of a graph

For any integer m (≥2), it is known that there are simple graphs of maximum valence m whose edges cannot be coloured with m colours in such a way that adjacent edges shall have different colours. We find those values of m and k for which it is true that every simple graph whose maximum valence does not exceed mk can be coloured with m colours in such a way that no colour appears more than k times at any vertex.     

Uncatalyzed,Regioselective Oxidation of Saturated Hydrocarbons in an Ambient Corona Discharge

Atmospheric pressure chemical ionization (APCI) in air or in nitrogen with just traces of oxygen is shown to yield regioselective oxidation, dehydrogenation, and fragmentation of alkanes. Ozone is produced from ambient oxygen in situ and is responsible for the observed ion chemistry, which includes partial oxidation to ketones and C?C cleavage to give aldehydes. The mechanism of oxidation is explored and relationships between ionic species produced from individual alkanes are established. Unusually, dehydrogenation occurs by water loss. Competitive incorporation into the hydrocarbon chain of nitrogen versus oxygen as a mode of ionization is also demonstrated.     

Coiled coils 9-to-5: rational de novo design of α-helical barrels with tunable oligomeric states

The rational design of linear peptides that assemble controllably and predictably in water is challenging. Short sequences must encode unique target structures and avoid alternative states. However, the non-covalent forces that stabilize and discriminate between states are weak. Nonetheless, for α-helical coiled-coil assemblies considerable progress has been made in rational de novo design. In these, sequence repeats of nominally hydrophobic (h) and polar (p) residues, hpphppp, direct the assembly of amphipathic helices into dimeric to tetrameric bundles. Expanding this pattern to hpphhph can produce larger α-helical barrels. Here, we show that pentameric to nonameric barrels are accessed by varying the residue at one of the h sites. In peptides with four L/I–K–E–I–A–x–Z repeats, decreasing the size of Z from threonine to serine to alanine to glycine gives progressively larger oligomers. X-ray crystal structures of the resulting α-helical barrels rationalize this: side chains at Z point directly into the helical interfaces, and smaller residues allow closer helix contacts and larger assemblies.

Systematic de novo design of peptides that form α-helical barrels with functionalisable central channels with a range of internal diameters.     

Mechanistic studies of rearrangements during the ring expansions of cyclopropanated carbohydrates

Deuterium-labeling studies have been performed on the ring expansion of cyclopropanated carbohydrates. From these studies, mechanisms have been proposed for two unusual rearrangements. In addition, a selective deprotection of the 1,3-di-tert-butylsilyl ether protecting group at the secondary position versus the primary position has been observed. This is a high yielding transformation with the potential for general synthetic utility.