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A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law < r(2)(t)> similar or equal to Dt yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.
A considerable number of systems have recently been reported in which
Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
The author shows the strong relation between political developments, frontiers and their graphical representation on maps. Human rights, economic globalisation and the European integration process do change national policy and erode classical border lines. Still today, maps with lines and colours as their main graphic elements represent the world of the 19th century with separate national states in atlases, schoolbooks and electronic media. The main argument of the article insists on stressing the political character of maps and showing the contradiction between the cartographic picture of the world and the recent international transformations. The author concludes with the question of whether maps can reproduce these new developments at all.
Characterization of drought tolerance in potato cultivars for identification of molecular markers
(2014)
Potato (Solanum tuberosum L.) is one of the most important food crops worldwide. Current potato varieties are highly susceptible to drought stress. In view of global climate change, selection of cultivars with improved drought tolerance and high yield potential is of paramount importance. Drought tolerance breeding of potato is currently based on direct selection according to yield and phenotypic traits and requires multiple trials under drought conditions. Marker-assisted selection (MAS) is cheaper, faster and reduces classification errors caused by noncontrolled environmental effects. We analysed 31 potato cultivars grown under optimal and reduced water supply in six independent field trials. Drought tolerance was determined as tuber starch yield. Leaf samples from young plants were screened for preselected transcript and nontargeted metabolite abundance using qRT-PCR and GC-MS profiling, respectively. Transcript marker candidates were selected from a published RNA-Seq data set. A Random Forest machine learning approach extracted metabolite and transcript markers for drought tolerance prediction with low error rates of 6% and 9%, respectively. Moreover, by combining transcript and metabolite markers, the prediction error was reduced to 4.3%. Feature selection from Random Forest models allowed model minimization, yielding a minimal combination of only 20 metabolite and transcript markers that were successfully tested for their reproducibility in 16 independent agronomic field trials. We demonstrate that a minimum combination of transcript and metabolite markers sampled at early cultivation stages predicts potato yield stability under drought largely independent of seasonal and regional agronomic conditions.
Potato (Solanum tuberosum L.) is one of the most important food crops worldwide. Current potato varieties are highly susceptible to drought stress. In view of global climate change, selection of cultivars with improved drought tolerance and high yield potential is of paramount importance. Drought tolerance breeding of potato is currently based on direct selection according to yield and phenotypic traits and requires multiple trials under drought conditions. Marker‐assisted selection (MAS) is cheaper, faster and reduces classification errors caused by noncontrolled environmental effects. We analysed 31 potato cultivars grown under optimal and reduced water supply in six independent field trials. Drought tolerance was determined as tuber starch yield. Leaf samples from young plants were screened for preselected transcript and nontargeted metabolite abundance using qRT‐PCR and GC‐MS profiling, respectively. Transcript marker candidates were selected from a published RNA‐Seq data set. A Random Forest machine learning approach extracted metabolite and transcript markers for drought tolerance prediction with low error rates of 6% and 9%, respectively. Moreover, by combining transcript and metabolite markers, the prediction error was reduced to 4.3%. Feature selection from Random Forest models allowed model minimization, yielding a minimal combination of only 20 metabolite and transcript markers that were successfully tested for their reproducibility in 16 independent agronomic field trials. We demonstrate that a minimum combination of transcript and metabolite markers sampled at early cultivation stages predicts potato yield stability under drought largely independent of seasonal and regional agronomic conditions.
Climate models predict an increased likelihood of seasonal droughts for many areas of the world. Breeding for drought tolerance could be accelerated by marker-assisted selection. As a basis for marker identification, we studied the genetic variance, predictability of field performance and potential costs of tolerance in potato (Solanum tuberosum L.). Potato produces high calories per unit of water invested, but is drought-sensitive. In 14 independent pot or field trials, 34 potato cultivars were grown under optimal and reduced water supply to determine starch yield. In an artificial dataset, we tested several stress indices for their power to distinguish tolerant and sensitive genotypes independent of their yield potential. We identified the deviation of relative starch yield from the experimental median (DRYM) as the most efficient index. DRYM corresponded qualitatively to the partial least square model-based metric of drought stress tolerance in a stress effect model. The DRYM identified significant tolerance variation in the European potato cultivar population to allow tolerance breeding and marker identification. Tolerance results from pot trials correlated with those from field trials but predicted field performance worse than field growth parameters. Drought tolerance correlated negatively with yield under optimal conditions in the field. The distribution of yield data versus DRYM indicated that tolerance can be combined with average yield potentials, thus circumventing potential yield penalties in tolerance breeding.
Does it have to be trees? : Data-driven dependency parsing with incomplete and noisy training data
(2011)
We present a novel approach to training data-driven dependency parsers on incomplete annotations. Our parsers are simple modifications of two well-known dependency parsers, the transition-based Malt parser and the graph-based MST parser. While previous work on parsing with incomplete data has typically couched the task in frameworks of unsupervised or semi-supervised machine learning, we essentially treat it as a supervised problem. In particular, we propose what we call agnostic parsers which hide all fragmentation in the training data from their supervised components. We present experimental results with training data that was obtained by means of annotation projection. Annotation projection is a resource-lean technique which allows us to transfer annotations from one language to another within a parallel corpus. However, the output tends to be noisy and incomplete due to cross-lingual non-parallelism and error-prone word alignments. This makes the projected annotations a suitable test bed for our fragment parsers. Our results show that (i) dependency parsers trained on large amounts of projected annotations achieve higher accuracy than the direct projections, and that (ii) our agnostic fragment parsers perform roughly on a par with the original parsers which are trained only on strictly filtered, complete trees. Finally, (iii) when our fragment parsers are trained on artificially fragmented but otherwise gold standard dependencies, the performance loss is moderate even with up to 50% of all edges removed.
An efficient electrocatalytic biosensor for sulfite detection was developed by co-immobilizing sulfite oxidase and cytochrome c with polyaniline sulfonic acid in a layer-by-layer assembly. QCM, UV-Vis spectroscopy and cyclic voltammetry revealed increasing loading of electrochemically active protein with the formation of multilayers. The sensor operates reagentless at low working potential. A catalytic oxidation current was detected in the presence of sulfite at the modified gold electrode, polarized at +0.1 V ( vs. Ag/AgCl 1 M KCl). The stability of the biosensor performance was characterized and optimized. A 17-bilayer electrode has a linear range between 1 and 60 mu M sulfite with a sensitivity of 2.19 mA M-1 sulfite and a response time of 2 min. The electrode retained a stable response for 3 days with a serial reproducibility of 3.8% and lost 20% of sensitivity after 5 days of operation. It is possible to store the sensor in a dry state for more than 2 months. The multilayer electrode was used for determination of sulfite in unspiked and spiked samples of red and white wine. The recovery and the specificity of the signals were evaluated for each sample.
An efficient electrocatalytic biosensor for sulfite detection was developed by co-immobilizing sulfite oxidase and cytochrome c with polyaniline sulfonic acid in a layer-by-layer assembly. QCM, UV-Vis spectroscopy and cyclic voltammetry revealed increasing loading of electrochemically active protein with the formation of multilayers. The sensor operates reagentless at low working potential. A catalytic oxidation current was detected in the presence of sulfite at the modified gold electrode, polarized at +0.1 V ( vs. Ag/AgCl 1 M KCl). The stability of the biosensor performance was characterized and optimized. A 17-bilayer electrode has a linear range between 1 and 60 mu M sulfite with a sensitivity of 2.19 mA M-1 sulfite and a response time of 2 min. The electrode retained a stable response for 3 days with a serial reproducibility of 3.8% and lost 20% of sensitivity after 5 days of operation. It is possible to store the sensor in a dry state for more than 2 months. The multilayer electrode was used for determination of sulfite in unspiked and spiked samples of red and white wine. The recovery and the specificity of the signals were evaluated for each sample.
The Electrically Wired Molybdenum Domain of Human Sulfite Oxidase is Bioelectrocatalytically Active
(2015)
We report electron transfer between the catalytic molybdenum cofactor (Moco) domain of human sulfite oxidase (hSO) and electrodes through a poly(vinylpyridine)-bound [osmium(N,N'-methyl-2,2'-biimidazole)(3)](2+/3+) complex as the electron-transfer mediator. The biocatalyst was immobilized in this low-potential redox polymer on a carbon electrode. Upon the addition of sulfite to the immobilized separate Moco domain, the generation of a significant catalytic current demonstrated that the catalytic center is effectively wired and active. The bioelectrocatalytic current of the wired separate catalytic domain reached 25% of the signal of the wired full molybdoheme enzyme hSO, in which the heme b(5) is involved in the electron-transfer pathway. This is the first report on a catalytically active wired molybdenum cofactor domain. The formal potential of this electrochemical mediator is between the potentials of the two cofactors of hSO, and as hSO can occupy several conformations in the polymer matrix, it is imaginable that electron transfer from the catalytic site to the electrode through the osmium center occurs for the hSO molecules in which the Moco domain is sufficiently accessible. The observation of catalytic oxidation currents at low potentials is favorable for applications in bioelectronic devices.