Differentials of the second kind on mumford curves

We define ap-adic analytic Hodge decomposition for the cohomology of Mumford curves, with values in a local system. When the local system is trivial, we give a new proof of Gerritzen’s theorem, that this decomposition forms a variation of Hodge structure, in a family of Mumford curves.     

Search for supersymmetry at LEP-2

An extensive effort to search for a hint of a supersymmetric signal was carried out by the four LEP Collaborations. All LEP data, up to centre-of-mass energy of 209 GeV, was carefully analysed with no observed SUSY signal. In an attempt to further increase the sensitivity of the search, the four groups combined some of their searches, to no avail.     

Mediated talk

The notion of mediated talk in which players communicate through a mediator before starting the game is introduced. It is shown that a deterministic mechanized mediator receiving private inputs and producing public outputs can generate any rational correlated equilibrium with rational probabilities by a self-enforcing procedure.     

Bessel identities in the waldspurger correspondence over the real numbers

We prove certain identities between Bessel functions attached to irreducible unitary representations ofPGL ₂(R) and Bessel functions attached to irreducible unitary representations of the double cover ofSL ₂(R). These identities give a correspondence between such representations which turns out to be the Waldspurger correspondence. In the process we prove several regularity theorems for Bessel distributions which appear in the relative trace formula. In the heart of the proof lies a classical result of Weber and Hardy on a Fourier transform of classical Bessel functions. This paper constitutes the local (real) spectral theory of the relative trace formula for the Waldspurger correspondence for which the global part was developed by Jacquet. Research of first author was partially supported by NSF grant DMS-0070762. Research of second author was partially supported by NSF grant DMS-9729992 and DMS 9971003.     

Flat corannulene: when a transition state becomes a stable molecule

Flat corannulene has been considered so far only as a transition state of the bowl-to-bowl inversion process. This study was driven by the prediction that substituents with strong steric repulsion could destabilize the bowl-shaped conformation of this molecule to such an extent that the highly unstable planar geometry would become an isolable molecule. To examine the substituents'' effect on the corannulene bowl depth, optimized structures for the highly-congested decakis(t-butylsulfido)corannulene were calculated. The computations, performed with both the M06-2X/def2-TZVP and the B3LYP/def2-TZVP methods (the latter with and without Grimme''s D3 dispersion correction), predict that this molecule can achieve two minimum structures: a flat carbon framework and a bowl-shaped structure, which are very close in energy. This rather unusual compound was easily synthesized from decachlorocorannulene under mild reaction conditions, and X-ray crystallographic studies gave similar results to the theoretical predictions. This compound crystallized in two different polymorphs, one exhibiting a completely flat corannulene core and the other having a bowl-shaped conformation.

The first flat metal-free corannulene derivative was predicted by computations and achieved by synthesis.     

Co-Assembly between Fmoc Diphenylalanine and Diphenylalanine within a 3D Fibrous Viscous Network Confers Atypical Curvature and Branching

Supramolecular polymer co-assembly is a useful approach to modulate peptide nanostructures. However, the co-assembly scenario where one of the peptide building blocks simultaneously forms a hydrogel is yet to be studied. Herein, we investigate the co-assembly formation of diphenylalanine (FF), and Fmoc-diphenylalanine (FmocFF) within the 3D network of FmocFF hydrogel. The overlapping peptide sequence between the two building blocks leads to their co-assembly within the gel state modulating the nature of the FF crystals. We observe the formation of branched microcrystalline aggregates with an atypical curvature, in contrast to the FF assemblies obtained from aqueous solution. Optical microscopy reveal the sigmoidal kinetic growth profile of these aggregates. Microfluidics and ToF-SIMS experiments exhibit the presence of co-assembled structures of FF and FmocFF in the crystalline aggregates. Molecular dynamics simulation was used to decipher the mechanism of co-assembly formation.     

Dual‐Functional Semithiobambusurils

Semithiobambusurils, which represent a new family of macrocyclic host molecules, have been prepared by a convenient, scalable synthesis. These new cavitands are double functional: they strongly bind a broad variety of anions in their interiors and metal ions at their sulfur‐edged portals. The solid‐state structure of semithiobambus[4]uril with HgCl₂ demonstrates the ability of these compounds to form linear chains of coordination polymers with thiophillic metal ions. The crystal structure of semithiobambus[6]uril with tetraphenylphosphonium bromide exhibits the unique anion‐binding properties of the host cavity and the characteristics of the binding site.     

Repulsive interaction can be a key design element of molecular rotary motors

Low-barrier molecular rotary motors having rotaxane architecture can be constructed using a cucurbituril host and a polyyne guest serving as stator and rotator, respectively. The repulsive interaction between these components is supported by molecular mechanics calculations with model systems and experimentally verified by X-ray crystallography with several synthetic host-guest complexes, all suggesting that the diyne rod floats at the center of the macrocyclic host with no apparent van der Waals contacts between them. Further support for these interactions is suggested by microcalorimetry measurements.     

Cognitive‐Performance Recovery of Alzheimer's Disease Model Mice by Modulation of Early Soluble Amyloidal Assemblies

A rationally designed oligomerization inhibitor interacts with early intermediate assemblies of amyloid‐β polypeptide (Aβ) through the aromatic elements and inhibits their assembly into the toxic oligomers that cause Alzheimer's disease by a unique C^α‐methylation β‐breakage strategy. The electrostatic potential of the low‐energy conformation of the dipeptide inhibitor bound to Aβ is shown.

     

Synthesis and characterization of a new fluorogenic substrate for alpha-galactosidase

Alpha-galactosidase A hydrolyzes the terminal alpha-galactosyl moieties from glycolipids and glycoproteins in lysosomes. Mutations in α-galactosidase cause lysosomal accumulation of the glycosphingolipid, globotriaosylceramide, which leads to Fabry disease. Small-molecule chaperones that bind to mutant enzyme proteins and correct their misfolding and mistrafficking have emerged as a potential therapy for Fabry disease. We have synthesized a red fluorogenic substrate, resorufinyl α-d-galactopyranoside, for a new α-galactosidase enzyme assay. This assay can be measured continuously at lower pH values, without the addition of a stop solution, due to the relatively low pK _a of resorufin (~6). In addition, the assay emits red fluorescence, which can significantly reduce interferences due to compound fluorescence and dust/lint as compared to blue fluorescence. Therefore, this new red fluorogenic substrate and the resulting enzyme assay can be used in high-throughput screening to identify small-molecule chaperones for Fabry disease. Zhen-Dan Shi and Omid Motabar contributed equally to this work