Sets of integers avoiding congruent subsets

Consider the sets of integers $A$ that avoid any arrangement of $g$ congruent $h$-subsets. Our findings refine and improve upon some results by Erd\H{o}s and Harzheim about these sets.Comment: Several typos correcte

Dense infinite Bh sequences

For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x√(h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences

Fire-resistant materials for aircraft passenger seat construction

The thermal response characteristics of fabric and fabric-foam assemblies are described. The various aspects of the ignition behavior of contemporary aircraft passenger seat upholstery fabric materials relative to fabric materials made from thermally stable polymers are evaluated. The role of the polymeric foam backing on the thermal response of the fabric-foam assembly is also ascertained. The optimum utilization of improved fire-resistant fabric and foam materials in the construction of aircraft passenger seats is suggested

Dense infinite Bh sequences

For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x√(h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences

Cero vs. lo en español andino (Chinchero, Cuzco)

The goal of this study is to analyse both the use of lo and null object to refer to third person direct objects in an oral corpus of Quechua-Spanish bilinguals from the district of Chinchero (Cuzco). The analysis was performed through qualitative and quantitative methods that allowed us to show which parameters favour their use. We set this goal because our corpus’s direct object marking system is characterized by two variants: the use of lo as the only third person direct object pronoun, i.e. as an invariable morph, and its omission, i.e., the production of a zero morph. Through a multivariate statistical analysis we tried to predict the factors favouring the use of the full form and the null morpheme, and also to create a scale to account for the weight of each factor. The results show that the selection of lo or zero is triggered by different semantic, syntactic, and discursive factors. This reveals the existence of a highly productive and efficient discursive resource. Finally, we put forward that these changes belong to a pronominal system reorganization process caused by the bilingual situation of the region, and an intense contact with Quechua. In this context, we believe that both linguistic and social factors are essential to the development and diffusion of these changes.El objeto del presente estudio es analizar el empleo de lo y cero para la marcación del objeto directo de tercera persona en un corpus oral de bilingües quechua-español recogido en el distrito de Chinchero (Cuzco), mediante un análisis cualitativo y cuantitativo que nos permita mostrar qué parámetros favorecen el uso de ambos. Nos marcamos dicho objetivo pues el sistema de marcación de objeto directo de nuestro corpus se caracteriza básicamente por dos fenómenos: el empleo de una única forma lo invariable que ha perdido la morfología de género y número, o la omisión de la misma, esto es, un cero fonético. Mediante un análisis estadístico multivariado hemos tratado de predecir no solo los factores que favorecen el uso de la forma plena o su omisión, sino crear una escala en la que se pueda apreciar el peso específico de cada factor. Los resultados muestran que la selección de lo o cero está favorecida por varios factores semánticos, sintácticos y discursivos, lo que pone de manifiesto que se trata de un recurso altamente productivo y eficaz en el discurso. Finalmente desde estas páginas defendemos que estos cambios se enmarcan dentro de un proceso de reorganización del sistema pronominal que se ha producido debido a la situación de bilingüismo y contacto intenso con el quechua, donde tanto los factores puramente lingüísticos como los sociales se revelan fundamentales en el desarrollo y extensión del mismo

Nondeterministic self-assembly with asymmetric interactions.

We investigate general properties of nondeterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter can lead to self-limiting cluster growth. Furthermore, by adjusting the relative abundance of self-assembly particles in a two-particle mixture, we are able to tune the final sizes of these clusters. We show that this is a fundamental property of asymmetric interactions, which has potential applications in bioengineering, and provides insights into the study of diseases caused by protein aggregation.Winton Programme for the Physics of Sustainability, Gates Cambridge, Oppenheimer PhD studentship, NanoDTC Cambridge (Grant ID: EP/L015978/1), Engineering and Physical Sciences Research Council (Grant ID: EP/L504920/1), Royal SocietyThis is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.94.02240