Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators.

Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.

Time to revisit? A predator's previous successes and failures in prey capture determine its return time to patches.

In a heterogeneous environment containing multiple patches that may deplete and renew, a forager should be able to detect the quality of food resources within and among patches and choose to exploit them to best maximize returns. From the predator's perspective, the behavioral responses of the prey in a patch will be perceived as depletion when they retreat to refuge and renewal when they reemerge. A predator encountering responsive prey should manage predation risk, and thus behavioral resource depression, by optimally timing its return time to the patch based on prey behavior. We evaluated the foraging decisions of a predator that encountered patches differing in size of the refuge and prey density. We used little egrets and goldfish as predators and prey in an environment that contained three patches (pools). We manipulated prey density and refuge size and availability (using covers) and observed predator foraging behavior. When the egret had previously caught a fish it did not discriminate between the pools, and the return time was similar for all cover types. The fish densities also did not affect the egret decisions to return to pools. However, when it failed to catch fish, it returned sooner to the pool containing the small cover than the larger one. Additionally, after failing to catch fish in patches containing the highest prey density, the egrets subsequently preferred to return to such patches sooner. We show experimentally that previous failures influence the foraging decisions of a predator choosing how quickly to return to a previously visited patch.

Temporal scale dependent interactions between multiple environmental disturbances in microcosm ecosystems.

Global environmental change has negative impacts on ecological systems, impacting the stable provision of functions, goods, and services. Whereas effects of individual environmental changes (e.g. temperature change or change in resource availability) are reasonably well understood, we lack information about if and how multiple changes interact. We examined interactions among four types of environmental disturbance (temperature, nutrient ratio, carbon enrichment, and light) in a fully factorial design using a microbial aquatic ecosystem and observed responses of dissolved oxygen saturation at three temporal scales (resistance, resilience, and return time). We tested whether multiple disturbances combine in a dominant, additive, or interactive fashion, and compared the predictability of dissolved oxygen across scales. Carbon enrichment and shading reduced oxygen concentration in the short term (i.e. resistance); although no other effects or interactions were statistically significant, resistance decreased as the number of disturbances increased. In the medium term, only enrichment accelerated recovery, but none of the other effects (including interactions) were significant. In the long term, enrichment and shading lengthened return times, and we found significant two-way synergistic interactions between disturbances. The best performing model (dominant, additive, or interactive) depended on the temporal scale of response. In the short term (i.e. for resistance), the dominance model predicted resistance of dissolved oxygen best, due to a large effect of carbon enrichment, whereas none of the models could predict the medium term (i.e. resilience). The long-term response was best predicted by models including interactions among disturbances. Our results indicate the importance of accounting for the temporal scale of responses when researching the effects of environmental disturbances on ecosystems.

IDV Typer: An Automated Tool for Lineage Typing of Influenza D Viruses Based on Return Time Distribution.

Influenza D virus (IDV) is the most recent addition to the Orthomyxoviridae family and cattle serve as the primary reservoir. IDV has been implicated in Bovine Respiratory Disease Complex (BRDC), and there is serological evidence of human infection of IDV. Evolutionary changes in the IDV genome have resulted in the expansion of genetic diversity and the emergence of multiple lineages that might expand the host tropism and potentially increase the pathogenicity to animals and humans. Therefore, there is an urgent need for automated, accurate and rapid typing tools for IDV lineage typing. Currently, IDV lineage typing is carried out using BLAST-based searches and alignment-based molecular phylogeny of the hemagglutinin-esterase fusion (HEF) gene sequences, and lineage is assigned to query sequences based on sequence similarity (BLAST search) and proximity to the reference lineages in the tree topology, respectively. To minimize human intervention and lineage typing time, we developed IDV Typer server, implementing alignment-free method based on return time distribution (RTD) of k-mers. Lineages are assigned using HEF gene sequences. The server performs with 100% sensitivity and specificity. The IDV Typer server is the first application of an RTD-based alignment-free method for typing animal viruses.

Bursting Rate Variability.

In this paper, a new electromyographic phenomenon, referred to as Bursting Rate Variability (BRV), is reported. Not only does it manifest itself visually as a train of short periods of accrued surface electromyographic (sEMG) activity in the traces, but it has a deeper underpinning because the sEMG bursts are synchronous with wavelet packets in the D8 subband of the Daubechies 3 (db3) wavelet decomposition of the raw signal referred to as "D8 doublets"-which are absent during muscle relaxation. Moreover, the db3 wavelet decomposition reconstructs the entire sEMG bursts with two contiguous relatively high detail coefficients at level 8, suggesting a high incidence of two consecutive neuronal discharges. Most importantly, the timing between successive bursts shows some variability, hence the BRV acronym. Contrary to Heart Rate Variability (HRV), where the R-wave is easily identified, here, time-localization of the burst requires a statistical waveform matching between the "D8 doublet" and the burst in the raw sEMG signal. Furthermore, statistical fitting of the empirical distribution of return times shows a striking difference between control and quadriplegic subjects. Finally, the BRV rate appears to be within 60-88 bursts per minute on average among 9 human subjects, suggesting a possible connection between BRV and HRV.

The Impact of Spatial and Temporal Dimensions of Disturbances on Ecosystem Stability.

Ecosystems constantly face disturbances which vary in their spatial and temporal features, yet little is known on how these features affect ecosystem recovery and persistence, i.e., ecosystem stability. We address this issue by considering three ecosystem models with different local dynamics, and ask how their stability properties depend on the spatial and temporal properties of disturbances. We measure the spatial dimension of disturbances by their spatial extent while controlling for their overall strength, and their temporal dimension by the average frequency of random disturbance events. Our models show that the return to equilibrium following a disturbance depends strongly on the disturbance's extent, due to rescue effects mediated by dispersal. We then reveal a direct relation between the temporal variability caused by repeated disturbances and the recovery from an isolated disturbance event. Although this could suggest a trivial dependency of ecosystem response on disturbance frequency, we find that this is true only up to a frequency threshold, which depends on both the disturbance spatial features and the ecosystem dynamics. Beyond this threshold the response changes qualitatively, displaying spatial clusters of disturbed regions, causing an increase in variability, and even a system-wide collapse for ecosystems with alternative stable states. Thus, spanning the spatial dimension of disturbances is a way to probe the underlying dynamics of an ecosystem. Furthermore, considering spatial and temporal dimensions of disturbances in conjunction is necessary to predict ecosystem responses with dramatic ecological consequences, such as regime shifts or population extinction.

WNV Typer: a server for genotyping of West Nile viruses using an alignment-free method based on a return time distribution.

West Nile virus (WNV), genus Flavivirus, family Flaviviridae, is a major cause of viral encephalitis with broad host range and global spread. The virus has undergone a series of evolutionary changes with emergence of various genotypic lineages that are known to differ in type and severity of the diseases caused. Currently, genotyping is carried out using molecular phylogeny of complete coding sequences and genotype is assigned based on proximity to reference genotypes in tree topology. Efficient epidemiological surveillance of WNVs demands development of objective criteria for typing. An alignment-free approach based on return time distribution (RTD) of k-mers has been validated for genotyping of WNVs. The RTDs of complete genome sequences at k=7 were found to be optimum for classification of the known lineages of WNVs as well as for genotyping. It provides time and computationally efficient alternative for genome based annotation of WNV lineages. The development of a WNV Typer server based on RTD is described (http://bioinfo.net.in/wnv/homepage.html). Both the method and the server have 100% sensitivity and specificity.

A methodology for stochastic analysis of share prices as Markov chains with finite states.

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.