Phase transitions in graphs on orientable surfaces

Let be the orientable surface of genus and denote by the class of all graphs on vertex set with edges embeddable on . We prove that the component structure of a graph chosen uniformly at random from features two phase transitions. The first phase transition mirrors the classical phase transition in the Erd?s‐Rényi random graph chosen uniformly at random from all graphs with vertex set and edges. It takes place at , when the giant component emerges. The second phase transition occurs at , when the giant component covers almost all vertices of the graph. This kind of phenomenon is strikingly different from and has only been observed for graphs on surfaces.     

Solidifying framework nucleic acids

正Living organisms have developed their unique strategies during the natural evolution for building hard tissues with minerals, including silica, calcium carbonate, calcium phosphate, and ferric oxide [1]. Such biomineralized materials generally have complex hierarchical structures with excellent mechanical properties. Although bioinspired approaches have led to the creation of well-defined synthetic structural materials ranging from micro to macro scales, the rational design of discrete biomimetic structures at the nanoscale remains a grand challenge.     

Effects of multiple delays on dynamics of a five-neuron network model

A five-neuron network model with multiple delays is proposed. This paper presents the combined effect of different delays on the dynamics of the proposed network. Pitchfork bifurcation is discussed in detail with the variation of the value of coupled weight or attenuation rate of internal neurons. By analyzing the corresponding characteristic equation, some stable criteria on delay-dependence and delay-independence are derived including multiple delays and coupled weights and the periodic oscillation arises bifurcated from the trivial equilibrium after the network loses its stability. Stable regions on delay-dependence are displayed in the two delayed parameter plane. It is shown that multiple delays can produce stability switching between resting state and periodic activity. Finally, theoretical results are justified by providing two illustrative examples.     

Infinitely many reducts of homogeneous structures

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.     

A Highly Lewis Acidic Strontium ansa-Arene Complex for Lewis Acid Catalysis and Isobutylene Polymerization

The potential of a dicationic strontium ansa-arene complex for Lewis acid catalysis has been explored. The key to its synthesis was a simple salt metathesis from SrI₂ and 2 Ag[Al(OR^F)₄], giving the base-free strontium-perfluoroalkoxyaluminate Sr[Al(OR^F)₄]₂ (OR^F=OC(CF₃)₃). Addition of an ansa-arene yielded the highly Lewis acidic, dicationic strontium ansa-arene complex. In preliminary experiments, the complex was successfully applied as a catalyst in CO₂-reduction to CH₄ and a surprisingly controlled isobutylene polymerization reaction.     

Volatile organic compounds in head and neck squamous cell carcinoma—An in vitro pilot study

Owing to the lack of specific symptoms, diagnosis of head and neck squamous cell carcinoma (HNSCC) may be delayed. We evaluated volatile organic compounds in tumor samples from patients suffering from HNSCC and tested the hypothesis that there is a characteristic altered composition in the headspace of HNSCC compared with control samples from the same patient with normal squamous epithelium. These results provide the basis for future noninvasive breath analysis in HNSCC. Headspace air of suspected tumor and contralateral control samples in 20 patients were analyzed using ion-mobility spectrometry. Squamous cell carcinoma was diagnosed in 16 patients. In total, we observed 93 different signals in headspace measurements. Squamous cell carcinomas revealed significantly higher levels of volatile cyclohexanol (0.54 ppb_v, 25th to 75th percentiles 0.35–0.86) compared with healthy squamous epithelium (0.24 ppb_v, 25th to 75th percentiles 0.12–0.3; p < 0.001). In conclusion, head and neck squamous cell carcinoma emitted significantly higher levels of volatile cyclohexanol in headspace compared with normal squamous epithelium. These findings form the basis for future breath analysis for diagnosis, therapy control and the follow-up of HNSSC to improve therapy and aftercare.