On the algebraic structure ofN=2 string theory

InN=2 string theory the chiral algebra expresses the generations and anti-generations of the theory and the Yukawa couplings among them and is thus crucial to the phenomenological properties of the theory. Also the connection with complex geometry is largely through the algebras. These algebras are systematically investigated in this paper. A solution for the algebras is found in the context of rational conformal field theory based on Lie algebras. A statistical mechanics interpretation for the chiral algebra is given for a large family of theories and is used to derive a rich structure of equivalences among the theories (dihedralities). The Poincaré polynomials are shown to obey a resolution series which cast these in a form which is a sum of complete intersection Poincaré polynomials. It is suggested that the resolution series is the proper tool for studying allN=2 string theories and, in particular, exposing their geometrical nature.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

The crystal structure of the inorganic surface films formed on Mg and Li intercalation compounds and the electrode performance

A crystallographic approach was applied to elucidate the influence of the nature of the surface films on the electrochemical behavior of Li and Mg intercalation compounds. This paper presents two examples: (1) protection of graphite electrodes by Li₂CO₃ surface films, and (2) the unique electrochemical behavior of Mg-containing Chevrel phases (MgCP) obtained by different synthetic routes. In the former case, the elucidation of the protection mechanism and the explanation of the high performance of such protected electrodes are based on the analysis of possible Li-ion motion in the carbonate crystal structure. In the latter case, a combination of synthesis, electrochemistry and XRD analysis was used to explain an unusual phenomenon: the difference between the excellent electrochemical behavior of the Chevrel phase (CP) based on Cu-leached Cu₂Mo₆S₈ (CuCP), and the poor electrochemical activity of the high-temperature synthesized MgCP, with the same phase composition. It is shown that this phenomenon is caused by MgO formation on the surface of the latter material. The different surface chemistry of the MgCPs obtained by the two different synthetic routes was substantiated by revealing the correlation between the electrochemical activity and the chemical stability of these materials under ambient atmosphere conditions. Dedicated to Prof. Mikhail A. Vorotyntsev on the occasion of his 60th birthday.     

Templating S100A9 amyloids on Aβ fibrillar surfaces revealed by charge detection mass spectrometry,microscopy, kinetic and microfluidic analyses

The mechanism of amyloid co-aggregation and its nucleation process are not fully understood in spite of extensive studies. Deciphering the interactions between proinflammatory S100A9 protein and Aβ₄₂ peptide in Alzheimer''s disease is fundamental since inflammation plays a central role in the disease onset. Here we use innovative charge detection mass spectrometry (CDMS) together with biophysical techniques to provide mechanistic insight into the co-aggregation process and differentiate amyloid complexes at a single particle level. Combination of mass and charge distributions of amyloids together with reconstruction of the differences between them and detailed microscopy reveals that co-aggregation involves templating of S100A9 fibrils on the surface of Aβ₄₂ amyloids. Kinetic analysis further corroborates that the surfaces available for the Aβ₄₂ secondary nucleation are diminished due to the coating by S100A9 amyloids, while the binding of S100A9 to Aβ₄₂ fibrils is validated by a microfluidic assay. We demonstrate that synergy between CDMS, microscopy, kinetic and microfluidic analyses opens new directions in interdisciplinary research.

Templating mechanism of S100A9 amyloids on Aβ fibrillar surfaces during amyloid co-aggregation process was revealed by synergy of biophysical methods including charge detection mass spectrometry, microscopy, kinetic and microfluidic analyses.     

Reduced Endocannabinoid Tone in Saliva of Chronic Orofacial Pain Patients

Background: the endocannabinoid system (ECS) participates in many physiological and pathological processes including pain generation, modulation, and sensation. Its involvement in chronic orofacial pain (OFP) in general, and the reflection of its involvement in OFP in salivary endocannabinoid (eCBs) levels in particular, has not been examined. Objectives: to evaluate the association between salivary (eCBs) levels and chronic OFP. Methods: salivary levels of 2 eCBs, anandamide (AEA), 2-arachidonoylglycerol (2-AG), 2 endocannabinoid-like compoundsN-palmitoylethanolamine (PEA), N-oleoylethanolamine (OEA), and their endogenous precursor and breakdown product, arachidonic acid (AA), were analyzed using liquid chromatography/tandem mass spectrometry in 83 chronic OFP patients and 43 pain-free controls. The chronic OFP patients were divided according to diagnosis into musculoskeletal, neurovascular/migraine, and neuropathic pain types. Results: chronic OFP patients had lower levels of OEA (p = 0.02) and 2-AG (p = 0.01). Analyzing specific pain types revealed lower levels of AEA and OEA in the neurovascular group (p = 0.04, 0.02, respectively), and 2-AG in the neuropathic group compared to controls (p = 0.05). No significant differences were found between the musculoskeletal pain group and controls. Higher pain intensity was accompanied by lower levels of AA (p = 0.028), in neuropathic group. Conclusions: lower levels of eCBs were found in the saliva of chronic OFP patients compared to controls, specifically those with neurovascular/migraine, and neuropathic pain. The detection of changes in salivary endocannabinoids levels related to OFP adds a new dimension to our understanding of OFP mechanisms, and may have diagnostic as well as therapeutic implications for pain.     

Redox Potential and Crystal Chemistry of Hexanuclear Cluster Compounds

Most of TM₆-cluster compounds (TM = transition metal) are soluble in polar solvents, in which the cluster units commonly remain intact, preserving the same atomic arrangement as in solids. Consequently, the redox potential is often used to characterize structural and electronic features of respective solids. Although a high lability and variety of ligands allow for tuning of redox potential and of the related spectroscopic properties in wide ranges, the mechanism of this tuning is still unclear. Crystal chemistry approach was applied for the first time to clarify this mechanism. It was shown that there are two factors affecting redox potential of a given metal couple: Lever’s electrochemical parameters of the ligands and the effective ionic charge of TM, which in cluster compounds differs effectively from the formal value due to the bond strains around TM atoms. Calculations of the effective ionic charge of TMs were performed in the framework of bond valence model, which relates the valence of a bond to its length by simple Pauling relationship. It was also shown that due to the bond strains the charge depends mainly on the atomic size of the inner ligands.     

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.