Nikolay Makarenko

Bio: Nikolay Makarenko is an academic researcher from Pulkovo Observatory. The author has contributed to research in topics: Flare & Sunspot. The author has an hindex of 3, co-authored 14 publications receiving 23 citations.

Magnetic field topology by MDI data: Active region

Abstract: Themain purpose of this paper is to describe the evolution of the magnetic field of active regions of the Sun in the context of Minkowski functionals: the Euler characteristic and perimeter calculated on the excursion set for a specified level. Themethods of geometry of random fields was applied to the MDI SOHO magnetogram, containing flaring active regions. The results demonstrated that morphological functional tracked the dynamic scenarios of the magnetic fields preceded by flares or accompanying them.

On Alternative Instruments for the fMRI Data Analysis: General Linear Model Versus Algebraic Topology Approach

Abstract: This work aimed at comparing two different approaches (classical general linear model based on the Bayesian approach and the method of algebraic topology) for fMRI data processing in a simple motor task. Subjects imposes block paradigm, consisting of three identical blocks. The duration of each block was 40 s (20 s of rest and 20 s of right hand fingers busting). To obtain statistically significant results were carried out 20 sessions of experiment. The results obtained by both methods were very close to each other, but correspondence between statistically significant changes in BOLD-signal was not quite complete. TDA (topologic data analyses) allocated additional voxels in Post central gyrus right. This region could be revealed with the changing in the level of confidence in the GLM model, but with this lower level of confidence too much additional voxels appeared. Combination of two approaches could be used for verification of results.

Dynamic Clustering of Connections Between fMRI Resting State Networks: A Comparison of Two Methods of Data Analysis

Abstract: In the present paper we describe an approach to the dynamical clustering of fMRI resting state networks and their connections, in which we use two known mathematical methods for data analysis: topological data analysis and k-means method. With these two methods we found about 4 stable states in group analysis. Dynamics of these states is characterized by periods of stability (blocks) with subsequent transition to another state. Topological data analysis method allowed us to find some regularity in subsequent transitions between blocks of states for individuals but it was not shown that the regularity repeats in all subjects. Topological method gives smoother distribution of dynamic states comparing to k-means method, highlighting about 4 dominant states in percentage, while k-means method gives 1–2 such states.

Analysis of the Solar magnetograms evolution using a spectral gap of critical nets

Abstract: Analyzing the dynamics of the photospheric magnetic field of the Sun is one of the most important problems in Solar Physics. Different estimates of the complexity of magnetograms of the Sun Active Regions (AR) are used to predict the time and the strength of the solar flares, but the quality of the forecasts are still insufficient. A magnetogram is a highly variable discrete image with a very large number of local extrema. We use an idea of extraction of stable critical points within a framework of the scale-space theory. Two sequential convolutions of the image with the same Gaussian kernel and calculating the difference between the produced images allow to get a stable estimation of the Laplacian of the image. A critical graph is constructed using maxima and minima of the Laplacian. Dynamics of critical graphs can be used for diagnostics of dynamical regimes of ARs. The so-called spectral gap is proposed to be used as a numerical descriptor. This is the difference between the two largest eigenvalues of the discrete Laplacian of the graph constructed on critical networks. We investigated several ARs and found that there was a sudden increase in the spectral gap values one or two days before the flares.

The new approach for dynamical regimes detection in geomagnetic time series

Abstract: We suggest the new approach that could be used in the task of geomagnetic indexes forecasting. This approach based on the topological structure of the time series. The hourly data of different geomagnetic indexes were analyzed. We split the whole series to the calm parts, and geomagnetic storm preceding parts and find that the main measure of the topological structure of the series which called topological persistence differ significantly between these two groups.

Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams

Abstract: The interstellar medium (ISM) is a magnetised system in which transonic or supersonic turbulence is driven by supernova explosions. This leads to the production of intermittent, filamentary structures in the ISM gas density, whilst the associated dynamo action also produces intermittent magnetic fields. The traditional theory of random functions, restricted to second-order statistical moments (or power spectra), does not adequately describe such systems. We apply topological data analysis (TDA), sensitive to all statistical moments and independent of the assumption of Gaussian statistics, to the gas density fluctuations in a magnetohydrodynamic (MHD) simulation of the multi-phase ISM. This simulation admits dynamo action, so produces physically realistic magnetic fields. The topology of the gas distribution, with and without magnetic fields, is quantified in terms of Betti numbers and persistence diagrams. Like the more standard correlation analysis, TDA shows that the ISM gas density is sensitive to the presence of magnetic fields. However, TDA gives us important additional information that cannot be obtained from correlation functions. In particular, the Betti numbers per correlation cell are shown to be physically informative. Magnetic fields make the ISM more homogeneous, reducing the abundance of both isolated gas clouds and cavities, with a stronger effect on the cavities. Remarkably, the modification of the gas distribution by magnetic fields is captured by the Betti numbers even in regions more than 300 pc from the midplane, where the magnetic field is weaker and correlation analysis fails to detect any signatures of magnetic effects.

Feasibility of topological data analysis for event-related fMRI

Abstract: Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representati...

Solar Flare Prediction Using SDO/HMI Vector Magnetic Field Data with a Machine-Learning Algorithm

Abstract: We attempt to forecast M- and X-class solar flares using a machine-learning algorithm, called support vector machine (SVM), and four years of data from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager, the first instrument to continuously map the full-disk photospheric vector magnetic field from space. Most flare forecasting efforts described in the literature use either line-of-sight magnetograms or a relatively small number of ground-based vector magnetograms. This is the first time a large data set of vector magnetograms has been used to forecast solar flares. We build a catalog of flaring and non-flaring active regions sampled from a database of 2071 active regions, comprised of 1.5 million active region patches of vector magnetic field data, and characterize each active region by 25 parameters. We then train and test the machine-learning algorithm and we estimate its performances using forecast verification metrics with an emphasis on the true skill statistic (TSS). We obtain relatively high TSS scores and overall predictive abilities. We surmise that this is partly due to fine-tuning the SVM for this purpose and also to an advantageous set of features that can only be calculated from vector magnetic field data. We also apply a feature selection algorithm to determine which of our 25 features are useful for discriminating between flaring and non-flaring active regions and conclude that only a handful are needed for good predictive abilities.

Methods of Computational Topology for the Analysis of Dynamics of Active Regions of the Sun

Abstract: The aim of this work is to diagnose pre-flare dynamics of magnetic fields in the active regions of the Sun on the HMI SDO magnetograms. We use a tool based on the methods of the geometry of random fields and computational topology. The results show that the proposed formalism allows one to find some precursors of major flares for practically significant time slots.