On robust estimation of low-frequency variability trends in discrete Markovian sequences of atmospheric circulation patterns

Identification and analysis of temporal trends and low-frequency variability in discrete time series is an important practical topic in understanding and predic- tion of many atmospheric processes, for example, in analysis of climate change. Widely used numerical techniques of trend identification (like local Gaussian ker- nel smoothing) impose some strong mathematical assumptions on the analyzed data and are not robust to model sensitivity. The latter becomes crucial when analyzing historical observation data with a short record. Two global robust nu- merical methods for the trend estimation in discrete non-stationary Markovian data based on different sets of implicit mathematical assumptions are introduced and compared here. The methods are first compared on a simple model exam- ple, the importance of mathematical assumptions on the data is explained and numerical problems of local Gaussian kernel smoothing are demonstrated. Pre- sented methods are applied to analysis of the historical sequence of atmospheric circulation patterns over UK between 1946-2007. It is demonstrated that the influence of the seasonal pattern variability on transition processes is dominated by the long-term effects revealed by the introduced methods. Despite of the dif- ferences in the mathematical assumptions implied by both presented methods, almost identical symmetrical changes of the cyclonic and anticyclonic pattern probabilities are identified in the analyzed data, with the confidence intervals being smaller then in the case of the local Gaussian kernel smoothing algorithm. Analysis results are investigated with respect to model sensitivity and compared to standard analysis technique based on a local Gaussian kernel smoothing. Finally, the implications of the discussed strategies on long-range predictability of the data-fitted Markovian models are discussed

On the identification of non-stationary factor models and their application to atmospherical data analysis

A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences

On metastable conformational analysis of non-equilibrium biomolecular time series

We present a {recently} developed clustering method and specify it for the problem of identification of metastable conformations in {non-equilibrium} biomolecular time series. The approach is based on variational minimization of some novel regularized clustering functional. In context of conformational analysis, it allows to combine {the features of} standard \emph{geometrical clustering techniques} (like the K-Means algorithm), \emph{dimension reduction methods} (like principle component analysis (PCA)) and \emph{dynamical machine learning approaches} like Hidden Markov Models (HMMs). In contrast to the HMM-based approaches, no a priori assumptions about Markovianity of the underlying process and regarding probability distribution of the observed data are needed. The application of the computational framework is exemplified by means of conformational analysis of some penta-peptide torsion angle time series from a molecular dynamics simulation. Comparison of different versions of the presented algorithm is performed wrt. the \emph{metastability} and \emph{geometrical resolution} of the resulting conformations

On Clustering of Non-stationary Meteorological Time Series

A method for clustering of multidimensional non-stationary meteorological time series is presented. The approach is based on optimization of the regularized averaged clustering functional describing the quality of data representation in terms of several regression models and a metastable hidden process switching between them. Proposed numerical clustering algorithm is based on application of the finite element method (FEM) to the problem of non-stationary time series analysis. The main advantage of the presented algorithm compared to Hidden Markov Models (HMMs) and to finite mixture models is that no a priori assumptions about the probability model for the hidden and observed processes (e.g., Markovianity or stationarity) are necessary for the proposed method. Another attractive numerical feature of the discussed algorithm is the possibility to choose the optimal number of metastable clusters and a natural opportunity to control the fuzziness of the resulting decomposition a posteriory, based on the statistical distinguishability of the resulting persistent cluster states. The resulting FEM-K-trends algorithm is compared with some standard fuzzy clustering methods on toy model examples and on analysis of multidimensional historical temperature data locally in Europe and on the global temperature data set

Історичний досвід рабства у романі Удварда Джоунза «Знаний світ»

У статті розглянуто історичний досвід рабства у романі Едварда Джоунза «Знаний світ». Роман Ед. Джоунза продовжує традицію афро-американської словесності у зображенні неоднозначності як індивідуальної ідентичності чорношкірих американців, так і проблематизування їхнього колективного минулого. (The article deals with the historical experience of slavery in Edward Jones’ novel ‘The known world’. Jones’ novel continues the tradition of African-American literature in the imaging the ambiguity of individual identity of Afro-Americans and problematics of their collective past.

Improving clustering by imposing network information

Cluster analysis is one of the most popular data analysis tools in a wide range of applied disciplines. We propose and justify a computationally efficient and straightforward-to-implement way of imposing the available information from networks/graphs (a priori available in many application areas) on a broad family of clustering methods. The introduced approach is illustrated on the problem of a noninvasive unsupervised brain signal classification. This task is faced with several challenging difficulties such as nonstationary noisy signals and a small sample size, combined with a high-dimensional feature space and huge noise-to-signal ratios. Applying this approach results in an exact unsupervised classification of very short signals, opening new possibilities for clustering methods in the area of a noninvasive brain-computer interface