Branching Random Walks in Space–Time Random Environment: Survival Probability,Global and Local Growth Rates

We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time–space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environment (DPRE), for which the quantity called the free energy is well studied. We discuss the survival probability (both global and local) for BRWRE and give a criterion for its positivity in terms of the free energy of the associated DPRE. We also show that the global growth rate for the number of particles in BRWRE is given by the free energy of the associated DPRE, though the local growth rate is given by the directional free energy.     

Group topologies coarser than the Isbell topology

The Isbell, compact-open and point-open topologies on the set C(X,R) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α(X) of compact families of open subsets of a topological space X. Those α(X) for which addition is jointly continuous at the zero function in Cα(X,R) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α(X) for which Cα(X,R) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, that Cα(X,R) can be strictly finer than the compact-open topology, are given. To our knowledge, this is the first example of a splitting group topology strictly finer than the compact-open topology.     

On the Cohomology of the Invariant Euler–Lagrange Complex

Given a Lie group action G we show, using the method of equivariant moving frames, that the local cohomology of the invariant Euler–Lagrange complex is isomorphic to the Lie algebra cohomology of G.     

An infraconsonant nonconsonant completely regular space

Let R denote the real numbers. We construct in ZFC a countable space X such that X has exactly one non-isolated point, X is infraconsonant, and X is not consonant. We conclude that X is a completely regular space such that Isbell topology on C(X,R) is a group topology that coincides with the natural (finest splitting) topology on C(X,R), but the Isbell and compact-open topologies on C(X,R) do not coincide. The example answers two open problems in the literature.     

Leptospermum petersonii as a Potential Natural Food Preservative

Leptospermum petersonii (family Myrtaceae) is often cultivated for ornamental purposes but also serves as a rich source of bioactive essential oils. While several studies focused on the activities of the essential oils, this study analysed the potential of spent L. petersonii leaves as a natural food preservative. Method: We investigated the in vitro antioxidant and antimicrobial activities of crude L. petersonii extracts against activities of the purified isolated flavonoid, 6-methyltectochrysin, which was characterized using spectroscopic methods. The antioxidant assays followed ORAC, FRAP and TEAC tests. The antimicrobial activities of the extract and purified flavonoid were analysed against six multi-drug resistant microbial strains in broth dilution assays. Result: The results revealed that both the crude extracts and isolated 6-methyltectochrysin exhibited positive radical ion scavenging antioxidant potential, however the crude extract was about 6-fold more potent antioxidant than the purified 6-methyltectochrysin. The crude extract also showed strong antimicrobial activities against Bacillus cereus, and even more potent antimicrobial agent than the reference ampicillin antibiotic against Klebsiella pneumoniae subsp. pneumoniae. A higher resistance was observed for the tested Gram-negative strains than for the Gram-positive ones. 6-methyltectochrysin was generally inactive in the antimicrobial assays. Conclusion: The crude methanolic extract showed significant bioactivity which validates the medicinal relevance of the plant. The observed biological activities, especially against a notorious strain of B. cereus, suggest that L. petersonii could be a promising natural source of food preservatives.     

Chemical Proteomics and Phenotypic Profiling Identifies the Aryl Hydrocarbon Receptor as a Molecular Target of the Utrophin Modulator Ezutromid

Duchenne muscular dystrophy (DMD) is a fatal muscle‐wasting disease arising from mutations in the dystrophin gene. Upregulation of utrophin to compensate for the missing dystrophin offers a potential therapy independent of patient genotype. The first‐in‐class utrophin modulator ezutromid/SMT C1100 was developed from a phenotypic screen through to a Phase 2 clinical trial. Promising efficacy and evidence of target engagement was observed in DMD patients after 24 weeks of treatment, however trial endpoints were not met after 48 weeks. The objective of this study was to understand the mechanism of action of ezutromid which could explain the lack of sustained efficacy and help development of new generations of utrophin modulators. Using chemical proteomics and phenotypic profiling we show that the aryl hydrocarbon receptor (AhR) is a target of ezutromid. Several lines of evidence demonstrate that ezutromid binds AhR with an apparent K_D of 50 nm  and behaves as an AhR antagonist. Furthermore, other reported AhR antagonists also upregulate utrophin, showing that this pathway, which is currently being explored in other clinical applications including oncology and rheumatoid arthritis, could also be exploited in future DMD therapies.     

Asymmetric Hydrogenation of Unfunctionalized Tetrasubstituted Acyclic Olefins

Asymmetric hydrogenation has evolved as one of the most powerful tools to construct stereocenters. However, the asymmetric hydrogenation of unfunctionalized tetrasubstituted acyclic olefins remains the pinnacle of asymmetric synthesis and an unsolved challenge. We report herein the discovery of an iridium catalyst for the first, generally applicable, highly enantio‐ and diastereoselective hydrogenation of such olefins and the mechanistic insights of the reaction. The power of this chemistry is demonstrated by the successful hydrogenation of a wide variety of electronically and sterically diverse olefins in excellent yield and high enantio‐ and diastereoselectivity.     

Distance-Dependent Electron Transfer Kinetics in Axially Connected Silicon Phthalocyanine-Fullerene Conjugates

The effect of donor-acceptor distance in controlling the rate of electron transfer in axially linked silicon phthalocyanine-C₆₀ dyads has been investigated. For this, two C₆₀-SiPc-C₆₀ dyads, 1 and 2 , varying in their donor-acceptor distance, have been newly synthesized and characterized. In the case of C₆₀-SiPc-C₆₀ 1 where the SiPc and C₆₀ are separated by a phenyl spacer, faster electron transfer was observed with k_cs equal to 2.7×10⁹ s⁻¹ in benzonitrile. However, in the case of C₆₀-SiPc-C₆₀ 2 , where SiPc and C₆₀ are separated by a biphenyl spacer, a slower electron transfer rate constant, k_cs=9.1×10⁸ s⁻¹, was recorded. The addition of an extra phenyl spacer in 2 increased the donor-acceptor distance by ∼4.3 Å, and consequently, slowed down the electron transfer rate constant by a factor of ∼3.7. The charge separated state lasted over 3 ns, monitoring time window of our femtosecond transient spectrometer. Complimentary nanosecond transient absorption studies revealed formation of ³SiPc* as the end product and suggested the final lifetime of the charge separated state to be in the 3–20 ns range. Energy level diagrams established to comprehend these mechanistic details indicated that the comparatively high-energy SiPc^.+-C₆₀^.− charge separated states (1.57 eV) populated the low-lying ³SiPc* (1.26 eV) prior returning to the ground state.     

Phenothiazine–BODIPY–Fullerene Triads as Photosynthetic Reaction Center Models: Substitution and Solvent Polarity Effects on Photoinduced Charge Separation and Recombination

Novel photosynthetic reaction center model compounds of the type donor₂–donor₁–acceptor, composed of phenothiazine, BF₂‐chelated dipyrromethene (BODIPY), and fullerene, respectively, have been newly synthesized using multistep synthetic methods. X‐ray structures of three of the phenothiazine‐BODIPY intermediate compounds have been solved to visualize the substitution effect caused by the phenothiazine on the BODIPY macrocycle. Optical absorption and emission, computational, and differential pulse voltammetry studies were systematically performed to establish the molecular integrity of the triads. The N‐substituted phenothiazine was found to be easier to oxidize by 60 mV compared to the C‐substituted analogue. The geometry and electronic structures were obtained by B3LYP/6‐31G(dp) calculations (for H, B, N, and O) and B3LYP/6‐31G(df) calculations (for S) in vacuum, followed by a single‐point calculation in benzonitrile utilizing the polarizable continuum model (PCM). The HOMO?1, HOMO, and LUMO were, respectively, on the BODIPY, phenothiazine and fullerene entities, which agreed well with the site of electron transfer determined from electrochemical studies. The energy‐level diagram deduced from these data helped in elucidating the mechanistic details of the photochemical events. Excitation of BODIPY resulted in ultrafast electron transfer to produce PTZ–BODIPY^.+–C₆₀^.?; subsequent hole shift resulted in PTZ^.+–BODIPY–C₆₀^.? charge‐separated species. The return of the charge‐separated species was found to be solvent dependent. In nonpolar solvents the PTZ^.+–BODIPY–C₆₀^.? species populated the ³C₆₀* prior to returning to the ground state, while in polar solvent no such process was observed due to relative positioning of the energy levels. The ¹BODIPY* generated radical ion‐pair in these triads persisted for few nanoseconds due to electron transfer/hole‐shift mechanism.