The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Toward a theory of semantic representation

We present an account of semantic representation that focuses on distinct types of information from which word meanings can be learned. In particular, we argue that there are at least two major types of information from which we learn word meanings. The first is what we call experiential information. This is data derived both from our sensory-motor interactions with the outside world, as well as from our experience of own inner states, particularly our emotions. The second type of information is language-based. In particular, it is derived from the general linguistic context in which words appear. The paper spells out this proposal, summarizes research supporting this view and presents new predictions emerging from this framework.

Colloidal gas aphrons based separation process for the purification and fractionation of natural phenolic extracts

Following previous studies, the aim of this work is to further investigate the application of colloidal gas aphrons (CGA) to the recovery of polyphenols from a grape marc ethanolic extract with particular focus on exploring the use of a non-ionic food grade surfactant (Tween 20) as an alternative to the more toxic cationic surfactant CTAB. Different batch separation trials in a flotation column were carried out to evaluate the influence of surfactant type and concentration and processing parameters (such as pH, drainage time, CGA/extract volumetric and molar ratio) on the recovery of total and specific phenolic compounds. The possibility of achieving selective separation and concentration of different classes of phenolic compounds and non-phenolic compounds was also assessed, together with the influence of the process on the antioxidant capacity of the recovered compounds. The process led to good recovery, limited loss of antioxidant capacity, but low selectivity under the tested conditions. Results showed the possibility of using Tween 20 with a separation mechanism mainly driven by hydrophobic interactions. Volumetric ratio rather than the molar ratio was the key operating parameter in the recovery of polyphenols by CGA.

Separation of natural colorants from the fermented broth of filamentous fungi using colloidal gas aphrons

There is a worldwide interest in the development of processes for producing colorants from natural sources. Microorganisms provide an alternative source of natural colorants produced by cultivation technology and extracted from the fermented broth. The aim of the present work was to study the recovery of red colorants from the fermented broth of Talaromyces amestolkiae using the technique of colloidal gas aphrons (CGA) comprising surfactant-stabilized microbubbles. Preliminary experiments were performed to evaluate the red colorants’ solubility in different organic solvents, octanol/water partitioning, and their stability in surfactant solutions, namely hexadecyl trimethylammonium bromide (CTAB), sodium dodecyl sulfate (SDS), and polyoxyethylenesorbitan monolaurate (Tween 20), which are cationic, anionic and nonionic surfactants, respectively. The first recovery experiments were carried out using CGA generated by these surfactants at different volumetric ratios (VR, 3–18). Subsequently, two different approaches to generate CGA were investigated at VR values of 6 and 12: the first involved the use of CTAB at pH 6.9–10.0, and the second involved the use of Tween 20 using red colorants partially dissolved in ethanol and Tween 20. The characterization results showed that red colorants have a hydrophilic nature. The highest recoveries were obtained with Tween 20 (78%) and CTAB (70%). These results demonstrated that the recovery of the colorants was driven by both electrostatic and hydrophobic interactions. The VR was found to be an important operating parameter and at VR 12 with CTAB (at pH 9) maximum recovery, partitioning coefficient (K = 5.39) and selectivity in relation to protein and sugar (SP = 3.75 and SS = 7.20 respectively) were achieved. Furthermore, with Tween 20, the separation was driven mainly by hydrophobic interactions. Overall CGA show promise for the recovery of red colorants from a fermented broth. Although better results were obtained with CTAB than with Tween 20 the latter may be more suitable for some application due to its lower toxicity.

Positive phenotypic selection inferred from phylogenies

Rates of phenotypic evolution vary widely in nature and these rates may often reflect the intensity of natural selection. Here we outline an approach for detecting exceptional shifts in the rate of phenotypic evolution across phylogenies. We introduce a simple new branch-specific metric ∆V/∆B that divides observed phenotypic change along a branch into two components: (1) that attributable to the background rate (∆B), and (2) that attributable to departures from the background rate (∆V). Where the amount of expected change derived from variation in the rate of morphological evolution doubles that explained by to the background rate (∆V/∆B > 2), we identify this as positive phenotypic selection. We apply our approach to six datasets, finding multiple instances of positive selection in each. Our results support the growing appreciation that the traditional gradual view of phenotypic evolution is rarely upheld, with a more episodic view taking its place. This moves focus away from viewing phenotypic evolution as a simple homogeneous process and facilitates reconciliation with macroevolutionary interpretations from a genetic perspective, paving the way to novel insights into the link between genotype and phenotype. The ability to detect positive selection when genetic data are unavailable or unobtainable represents an attractive prospect for extant species, but when applied to fossil data it can reveal patterns of natural selection in deep time that would otherwise be impossible.

An example in Beurling's theory of generalised primes

In this paper we prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes.