Fine-grained, nonlinear image registration of live cell movies reveals spatiotemporal organization of diffuse molecular processes

We present an application of non-linear Image registration that allows spatiotemporal analysis of extremely noisy and diffuse molecular processes across the entire cell. To produce meaningful local tracking of the spatially coherent portion of diffuse protein dynamics, we improved upon existing nonlinear image registration to compensate for cell movement and deformation. The registration relies on a subcellular fiducial marker, a cell motion mask, and a topological regularization that enforces diffeomorphism on the registration without significant loss of granularity. We demonstrate the potential of this approach in conjunction with stochastic time-series analysis through the discovery of distinct zones of coherent Profillin dynamics in symmetry-breaking U2OS cells. Further analysis of the resulting Profilin dynamics revealed strong relationships with the underlying actin organization. This study thus provides a framework for extracting functional interactions between cell morphodynamics, protein distributions, and signaling in cells undergoing continuous shape changes.

Differences and similarities between precipitation patterns of different climates

In recent years water-related issues are increasing globally, some researchers even argue that the global hydrological cycle is accelerating, while the number of meteorological extremities is growing. With the help of large number of available measured data, these changes can be examined with advanced mathematical methods. In the outlined research we were able to collect long precipitation datasets from two different climatical regions, one sample area being Ecuador, the other one being Kenya. Using the methodology of spectral analysis based on the discrete Fourier-transformation, several deterministic components were calculated locally in the otherwise stochastic time series, while by the comparison of the results, also with previous calculations from Hungary, several global precipitation cycles were defined in the time interval between 1980 and 2019. The results of these calculations, the described local, regional, and global precipitation cycles can be a helpful tool for groundwater management, as precipitation is the major resource of groundwater recharge, as well as with the help of these deterministic cycles, precipitation forecasts can be delivered for the areas.

Characterization of Export Regimes in Concentration–Discharge Plots via an Advanced Time-Series Model and Event-Based Sampling Strategies

Currently, the export regime of a catchment is often characterized by the relationship between compound concentration and discharge in the catchment outlet or, more specifically, by the regression slope in log-concentrations versus log-discharge plots. However, the scattered points in these plots usually do not follow a plain linear regression representation because of different processes (e.g., hysteresis effects). This work proposes a simple stochastic time-series model for simulating compound concentrations in a river based on river discharge. Our model has an explicit transition parameter that can morph the model between chemostatic behavior and chemodynamic behavior. As opposed to the typically used linear regression approach, our model has an additional parameter to account for hysteresis by including correlation over time. We demonstrate the advantages of our model using a high-frequency data series of nitrate concentrations collected with in situ analyzers in a catchment in Germany. Furthermore, we identify event-based optimal scheduling rules for sampling strategies. Overall, our results show that (i) our model is much more robust for estimating the export regime than the usually used regression approach, and (ii) sampling strategies based on extreme events (including both high and low discharge rates) are key to reducing the prediction uncertainty of the catchment behavior. Thus, the results of this study can help characterize the export regime of a catchment and manage water pollution in rivers at lower monitoring costs.

On analysis of signals of seismic acoustic emission of surface sedimentary rocks in Kamchatka

На Камчатке в пункте наблюдений “Карымшина” при помощи измерительной системы на основе трехкомпонентного пьезокерамического сейсмоприемника проводится мониторинг сигналов сейсмоакустической эмиссии приповерхностных осадочных пород. На выходе измерительной системы регистрируется колебательное ускорение в частотном диапазоне 0.5–400 Гц. Анализ проводится на основе записей сейсмоакустических сигналов от группы региональных землетрясений 2019 года с энергетическим классом Ks > 10.0. Функция распределения плотности вероятностей такого сигнала не всегда описывается нормальным законом распределения, поэтому для исследования подобных стохастических временных рядов подходят методы статистической физики, в рамках которых рассматриваются свойства автомодельности этих сигналов. In Kamchatka, at the observation point “Karymshina”, using a measuring system based on a three-component piezoceramic seismic receiver, the signals of seismoacoustic emission of near-surface sedimentary rocks are monitored. At the output of the measuring system, an oscillatory acceleration is recorded in the frequency range of 0.5-400 Hz. The analysis is based on records of seismoacoustic signals from several regional earthquakes in 2019 with an energy class of Ks > 10:0. The probability density distribution function of such a signal is not always described by the normal distribution law; therefore, statistical physics methods are suitable for studying such stochastic time series, within which the properties of self-similarity of these signals are considered.

A Statistical Method for Generating Temporally Downscaled Geochemical Tracers in Precipitation

Sampling intervals of precipitation geochemistry measurements are often coarser than those required by fine-scale hydrometeorological models. This study presents a statistical method to temporally downscale geochemical tracer signals in precipitation so that they can be used in high-resolution, tracer-enabled applications. In this method, we separated the deterministic component of the time series and the remaining daily stochastic component, which was approximated by a conditional multivariate Gaussian distribution. Specifically, statistics of the stochastic component could be explained from coarser data using a newly identified power-law decay function, which relates data aggregation intervals to changes in tracer concentration variance and correlations with precipitation amounts. These statistics were used within a copula framework to generate synthetic tracer values from the deterministic and stochastic time series components based on daily precipitation amounts. The method was evaluated at 27 sites located worldwide using daily precipitation isotope ratios, which were aggregated in time to provide low resolution testing datasets with known daily values. At each site, the downscaling method was applied on weekly, biweekly and monthly aggregated series to yield an ensemble of daily tracer realizations. Daily tracer concentrations downscaled from a biweekly series had average (+/- standard deviation) absolute errors of 1.69‰ (1.61‰) for δ2H and 0.23‰ (0.24‰) for δ18O relative to observations. The results suggest coarsely sampled precipitation tracers can be accurately downscaled to daily values. This method may be extended to other geochemical tracers in order to generate downscaled datasets needed to drive complex, fine-scale models of hydrometeorological processes.

Application of Neural Network Time Series (NNAR) and ARIMA to Forecast Infection Fatality Rate (IFR) of COVID-19 in Brazil

Forecasting is a method that is often used to view future events using past time data. Past time data have useful information to use in obtaining the future. The aim of this study was to forecast infection fatality rate (IFR) of COVID-19 in Brazil using NNAR and ARIMA. ARIMA and NNAR are used because (1) ARIMA is a simple stochastic time series method that can be used to train and predict future time points and ARIMA also capable of capturing dynamic interactions when it uses error terms and observations of lagged terms; (2) the Artificial Neural Network (ANN) is a technique capable of analyzing certain non-linear interactions between input regressor and responses, and Neural Network Time Series (NNAR) is one method of ANN in which lagged time series values were used as inputs to a neural network. Data included in this study were derived from the total data of confirmed cases and the total data of death of COVID-19. The data of COVID-19 in Brazil from February 15, 2020 to April 30, 2020 were collected from the Worldometer (https://www.worldometers.info/coronavirus/) and Microsoft Excel 2013 was used to build a time-series table. Forecasting was accomplished by means of a time series package (forecast package) in R Software. Neural Network Time Series and ARIMA models were applied to a dataset consisting of 76 days. The accuracy of forecasting was examined by means of an MSE. The forecast of IFR of COVID-19 in Brazil from May 01, 2020 to May 10, 2020 with NNAR (1,1) model was around in 6,85% and ARIMA (0,2,1) was around in 7.11%.

A unified and automated approach to attractor reconstruction

<p>Since acquisition costs for sensors and data collection decrease rapidly especially in the geo-scientific fields, researchers often have to deal with a large amount of multivariable data, which they would need to automatically analyze in an appropriate way. In nonlinear time series analysis, phase space reconstruction often makes the very first step of any sophisticated analysis, but the established methods are either unable to reliably automate the process or they can not handle multivariate time series input. Here we present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data.</p>