**1619**

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**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.

2021 - English
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.
Keywords:
*Smart city; City simulation; Energy resource-demand modelling; Environmental modelling; Synthetic population; Transport modelling*
Available on request at various institutes of the ASCR
City simulation software for modeling, planning, and strategic assessment of territorial city units

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 ...

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**Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix**

Turčičová, Marie; Mandel, J.; Eben, Kryštof

2021 - English
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.
Keywords:
*Score matching; ensemble filter; Gaussian Markov random field; covariance modelling*
Available in digital repository of the ASCR
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

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 ...

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**Nearly All Reals Can Be Sorted with Linear Time Complexity**

Jiřina, Marcel

2021 - English
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.
Keywords:
*sorting; algorithm; real sorting key; time complexity; linear complexity*
Available in digital repository of the ASCR
Nearly All Reals Can Be Sorted with Linear Time Complexity

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 ...

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**Visual Images Segmentation based on Uniform Textures Extraction**

Goltsev, A.; Gritsenko, V.; Húsek, Dušan

2020 - English
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.
Keywords:
*Texture feature; Texture window; Homogeneous ne-grained texture segment; Texture segment extraction; Texture segmentation*
Available at various institutes of the ASCR
Visual Images Segmentation based on Uniform Textures Extraction

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. ...

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**Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations**

Vlček, Jan; Lukšan, Ladislav

2020 - English
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
Keywords:
*unconstrained minimization; variable metric methods; limited-memory methods; variationally derived methods; global convergence; numerical results*
Available in a digital repository NRGL
Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations

Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey ...

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**Linear-time Algorithms for Largest Inscribed Quadrilateral**

Keikha, Vahideh

2020 - English
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.
Keywords:
*Maximum-area quadrilateral; extreme area k-gon*
Available in a digital repository NRGL
Linear-time Algorithms for Largest Inscribed Quadrilateral

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 ...

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**Least Weighted Absolute Value Estimator with an Application to Investment Data**

Vidnerová, Petra; Kalina, Jan

2020 - English
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.
Keywords:
*robust regression; regression median; implicit weighting; computational aspects; nonparametric bootstrap*
Fulltext is available at external website.
Least Weighted Absolute Value Estimator with an Application to Investment Data

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 ...

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**On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles**

Kalina, Jan; Janáček, Patrik

2020 - English
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.
Keywords:
*tourism infrastructure; human resources; regression; robustness; regression quantiles*
Fulltext is available at external website.
On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles

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 ...

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**Regression for High-Dimensional Data: From Regularization to Deep Learning**

Kalina, Jan; Vidnerová, Petra

2020 - English
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.
Keywords:
*regression; neural networks; robustness; high-dimensional data; regularization*
Fulltext is available at external website.
Regression for High-Dimensional Data: From Regularization to Deep Learning

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. ...

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**The scalar-valued score functions of continuous probability distribution**

Fabián, Zdeněk

2019 - English
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalar-valued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalar-valued score function of distribution.
Keywords:
*Shortcomings of probability theory; Scalar-valued score functions; Characteristics of continous random variables; Parametric estimation; Transformed distributions; Skew-symmetric distributions*
Available at various institutes of the ASCR
The scalar-valued score functions of continuous probability distribution

In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not ...

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