Preparative isolation of (+)-beta-eudesmol fromAmyris balsamifera

Summary Optically pure (+)-beta-eudesmol is a possible starting material for the synthesis of several termite defense compounds. A two step procedure for the isolation of gram quantities of (+)-beta-eudesmol from commercially availableAmyris balsamifera oil (syn. West Indian sandalwood oil), containing 8% beta-eudesmol, was developed. Step one consisted of an efficient vacuum distillation of the total oil. Step two was a medium pressure LC separation with an AgNO₃ impregnated silica gel stationary phase. Several other separation procedures failed due to the presence of many closely related sesquiterpene alcohols (75% of the oil).     

Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?

Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.     

Relativistic chaos is coordinate invariant

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.     

Extraction and derivatization of polar herbicides for GC-MS analyses

A sample preparation procedure including a simultaneous microwave-assisted (MA) extraction and derivatization for the determination of chlorophenoxy acids in soil samples is presented. For a selective and sensitive measurement, an analytical technique such as GC coupled with MS needs to be adopted. For GC analyses, chlorophenoxy acids have to be converted into more volatile and thermally stable derivatives. Derivatization by means of microwave radiation offers new alternatives in terms of shorter derivatization time and reduces susceptibility for the formation of artefacts. Extraction and derivatization into methyl esters (ME) were performed with sulphuric acid and methanol. Due to the novelty of the simultaneous extraction and derivatization assisted by means of microwave radiation, a careful investigation and optimization of influential reaction parameters was necessary. It could be shown that the combination of sulphuric acid and methanol provides a fast sample preparation including an efficient clean up procedure. The data obtained by the described method are in good agreement with those published for the reference material. Finally, compared to conventional heating and also to the standard procedure of the EPA, the sample preparation time could be considerably shortened.     

Universality in active chaos

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).     

Cascade control and defense in complex networks

Complex networks with a heterogeneous distribution of loads may undergo a global cascade of overload failures when highly loaded nodes or edges are removed due to attacks or failures. Since a small attack or failure has the potential to trigger a global cascade, a fundamental question regards the possible strategies of defense to prevent the cascade from propagating through the entire network. Here we introduce and investigate a costless strategy of defense based on a selective further removal of nodes and edges, right after the initial attack or failure. This intentional removal of network elements is shown to drastically reduce the size of the cascade.     

Identifying Trends in Word Frequency Dynamics

The word-stock of a language is a complex dynamical system in which words can be created, evolve, and become extinct. Even more dynamic are the short-term fluctuations in word usage by individuals in a population. Building on the recent demonstration that word niche is a strong determinant of future rise or fall in word frequency, here we introduce a model that allows us to distinguish persistent from temporary increases in frequency. Our model is illustrated using a 10⁸-word database from an online discussion group and a 10¹¹-word collection of digitized books. The model reveals a strong relation between changes in word dissemination and changes in frequency. Aside from their implications for short-term word frequency dynamics, these observations are potentially important for language evolution as new words must survive in the short term in order to survive in the long term.     

Sample-to-sample fluctuations in real-network ensembles

Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is indeed the case for uncorrelated networks with minimum degree ≥ 3. Here, we focus on real networks, which generally have both structural correlations and low-degree nodes. We show that: (i) the ensemble distribution of the dynamically most important eigenvalues can be not only broad and far apart from the real eigenvalue but also highly structured, often with a multimodal rather than a bell-shaped form; (ii) these interesting properties are found to be due to low-degree nodes, mainly those with degree ≤ 3, and network communities, which is a common form of structural correlation found in real networks. In addition to having implications for ensemble-based approaches, this shows that low-degree nodes may have a stronger influence on collective dynamics than previously anticipated from the study of computer-generated networks.     

Ensemble averageability in network spectra

The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by ensemble averages. Here we investigate this question explicitly and validate the concept of ensemble averageability in random scale-free networks by showing that the ensemble distributions of extreme eigenvalues converge to peaked distributions as the system size increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.