Institute of Computer Science

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2021-09-26
00:06
Assessment of Independent EEG Components Obtained by Different Methods for BCI Based on Motor Imagery
Húsek, Dušan ; Frolov, A. A. ; Kerechanin, J. V. ; Bobrov, P.D.
Eight methods of decomposition of a multichannel EEG signal are compared in terms of their ability to identify the most physiologically significant components. The criterion for the meaningfulness of a method is its ability to reduce mutual information between components; to create components that can be attributed to the activity of dipoles located in the cerebral cortex; find components that are provided by other methods and for this case; and at the same time, these components should most contribute to the accuracy of the BCI based on imaginary movement. Independent component analysis methods AMICA, RUNICA and FASTICA outperform others in the first three criteria and are second only to the Common Spatial Patterns method in the fourth criterion. The components created by all methods for 386 experimental sessions of 27 subjects were combined into more than 100 clusters containing more than 10 elements. Additionally, the components of the 12 largest clusters were analyzed. They have proven to be of great importance in controlling BCI, their origins can be modeled using dipoles in the brain, and they have been detected by several degradation methods. Five of the 12 selected components have been identified and described in our previous articles. Even if the physiological and functional origins of the rest of identified components’ are to be the subject of further research, we have shown that their physiological nature is at least highly probable.\n

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2021-08-22
00:07
Nearly All Reals Can Be Sorted with Linear Time Complexity
Jiřina, Marcel
We propose a variant of the counting sort modified for sorting reals in a linear time. It is assumed that the sorting key and pointers to the items being sorted are moved and individual items remain at the same place in the memory (in place sorting). In this case, the space complexity of the new variant of the algorithm is the same as the complexity of the quicksort. We also quantify the practical limits for possible sorting reals in a linear time. This possibility is assured under additional assumptions on the distribution of the sorting key, mainly the independence and identity of the distribution. Here we give a more general criteria easily applicable in practice. We also show that the algorithm is applicable for data that do not fulfill criteria for linear time complexity but even that the computation is faster than the system quicksort. A new, faster version of the algorithm is attached.

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2021-05-02
00:01
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix
Turčičová, Marie ; Mandel, J. ; Eben, Kryštof
We present an ensemble filter that provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. We use a linear model for the precision matrix (inverse of covariance) and estimate its parameters together with the analysis mean by the Score Matching method. This procedure provides an explicit expression for parameter estimators. The resulting analysis step formula is the same as in the traditional ensemble Kalman filter.

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2021-02-24
00:43
Visual Images Segmentation based on Uniform Textures Extraction
Goltsev, A. ; Gritsenko, V. ; Húsek, Dušan
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. The main advantages of the proposed procedure are as follows. It is completely unsupervised, that is, it processes the input image without any prior knowledge of either the type of textures or the number of texture segments in the image. In addition, the procedure segments arbitrary images of all types. This means that no changes to the procedure parameters are required to switch from one image type to another. Another major advantage of the procedure is that in most cases it extracts the uniform ne-grained texture segments present in the image, just as humans do. This result is supported by series of experiments that demonstrate the ability of the procedure to delineate uniform ne-grained texture segments over a wide range of images. At a minimum, image processing according to the proposed technique leads to a signficant reduction in the uncertainty of the internal structure of the analyzed image.

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2021-02-24
00:43
City simulation software for modeling, planning, and strategic assessment of territorial city units
Svítek, M. ; Přibyl, O. ; Vorel, J. ; Garlík, B. ; Resler, Jaroslav ; Kozhevnikov, S. ; Krč, Pavel ; Geletič, Jan ; Daniel, Milan ; Dostál, R. ; Janča, T. ; Myška, V. ; Aralkina, O. ; Pereira, A. M.
SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software for modeling, planning, and strategic assessment of territorial city units. 1.1. Prague: CTU & ICS CAS, 2021. Technical Report. ABSTRACT: The Smart Resilience City concept is a new vision of a city as a digital platform and eco-system of smart services where agents of people, things, documents, robots, and other entities can directly negotiate with each other on resource demand principals providing the best possible solution. It creates the smart environment making possible self-organization in sustainable or, when needed, resilient way of individuals, groups and the whole system objectives.

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2021-02-24
00:43
On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles
Kalina, Jan ; Janáček, Patrik
Tourism represents an important sector of the economy in many countries around the world. In this work, we are interested in the effect of the Human Resources and Labor Market pillar of the Travel and Tourism Competitiveness Index on tourist service infrastructure across 141 countries of the world. A regression analysis requires to handle heteroscedasticity in these data, which is not an uncommon situation in various available human capital studies. Our first task is focused on testing significance of individual variables in the model. It is illustrated here that significance tests are influenced by heteroscedasticity, which remains true also for tests for regression quantiles or robust regression estimators, resistant to a possible contamination of data by outliers. Only if a suitable model is considered, which takes heteroscedasticity into account, the effect of the Human Resources and Labor Market pillar turns out to be significant. Further, we propose and present a new diagnostic tool denoted as aquintile plot, allowing to interpret immediately the heteroscedastic structure of the linear regression model for possibly contaminated data.

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2021-02-24
00:43
Least Weighted Absolute Value Estimator with an Application to Investment Data
Vidnerová, Petra ; Kalina, Jan
While linear regression represents the most fundamental model in current econometrics, the least squares (LS) estimator of its parameters is notoriously known to be vulnerable to the presence of outlying measurements (outliers) in the data. The class of M-estimators, thoroughly investigated since the groundbreaking work by Huber in 1960s, belongs to the classical robust estimation methodology (Jurečková et al., 2019). M-estimators are nevertheless not robust with respect to leverage points, which are defined as values outlying on the horizontal axis (i.e. outlying in one or more regressors). The least trimmed squares estimator seems therefore a more suitable highly robust method, i.e. with a high breakdown point (Rousseeuw & Leroy, 1987). Its version with weights implicitly assigned to individual observations, denoted as the least weighted squares estimator, was proposed and investigated in Víšek (2011). A trimmed estimator based on the 𝐿1-norm is available as the least trimmed absolute value estimator (Hawkins & Olive, 1999), which has not however acquired attention of practical econometricians. Moreover, to the best of our knowledge, its version with weights implicitly assigned to individual observations seems to be still lacking.

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2021-02-24
00:43
Regression for High-Dimensional Data: From Regularization to Deep Learning
Kalina, Jan ; Vidnerová, Petra
Regression modeling is well known as a fundamental task in current econometrics. However, classical estimation tools for the linear regression model are not applicable to highdimensional data. Although there is not an agreement about a formal definition of high dimensional data, usually these are understood either as data with the number of variables p exceeding (possibly largely) the number of observations n, or as data with a large p in the order of (at least) thousands. In both situations, which appear in various field including econometrics, the analysis of the data is difficult due to the so-called curse of dimensionality (cf. Kalina (2013) for discussion). Compared to linear regression, nonlinear regression modeling with an unknown shape of the relationship of the response on the regressors requires even more intricate methods.

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2021-02-24
00:43
Linear-time Algorithms for Largest Inscribed Quadrilateral
Keikha, Vahideh
Let P be a convex polygon of n vertices. We present a linear-time algorithm for the problem of computing the largest-area inscribed quadrilateral of P. We also design the parallel version of the algorithm with O(log n) time and O(n) work in CREW PRAM model, which is quite work optimal. Our parallel algorithm also computes all the antipodal pairs of a convex polygon with O(log n) time and O(log2n+s) work, where s is the number of antipodal pairs, that we hope is of independent interest. We also discuss several approximation algorithms (both constant factor and approximation scheme) for computing the largest-inscribed k-gons for constant values of k, in both area and perimeter measures.
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2020-12-03
22:56
Special issue of the Conference Analytical Methods in Statistics (AMISTAT 2019)
Kalina, Jan ; Jurečková, Jana
IN: Applications of Mathematics. 2020, 65(3), 227-342. ISSN 0862-7940. doi: 10.21136/AM.2020.0106-20. ANNOTATION: This special issue of Applications of Mathematics is devoted to the third workshop on Analytical Methods in Statistics (AMISTAT 2019), which took place in Liberec on September 16–19, 2019. It was organized by the Department of Applied Mathematics at the Faculty of Science, Humanities and Education of the Technical University of Liberec. The workshop was held under the auspices of Miroslav Brzezina, Rector of the Technical University of Liberec.\n

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