**632**

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**Some modiﬁcations of the limited-memory variable metric optimization methods**

Vlček, Jan; Lukšan, Ladislav

2023 - English
Several modiﬁcations of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modiﬁed to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new eﬃcient way how to realize the limited-memory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard L-BFGS and BNS methods is given.
Keywords:
*unconstrained minimization; variable metric methods; limited-memory methods; variationally derived methods; arithmetic operations reduction; global convergence*
Available in a digital repository NRGL
Some modiﬁcations of the limited-memory variable metric optimization methods

Several modiﬁcations of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric ...

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**Spatio-Spectral EEG Patterns in the Source-Reconstructed Space and Relation to Resting-State Networks: An EEG-fMRI Study**

Jiříček, Stanislav; Koudelka, V.; Mantini, D.; Mareček, R.; Hlinka, Jaroslav

2022 - English
In this work, we present and evaluate a novel EEG-fMRI integration approach combining a spatio-spectral decomposition method and a reliable source localization technique. On the large 72 subjects resting- state hdEEG-fMRI data set we tested the stability of the proposed method in terms of both extracted spatio-spectral patterns(SSPs) as well as their correspondence to the BOLD signal. We also compared the proposed method with the spatio-spectral decomposition in the electrode space as well as well-known occipital alpha correlate in terms of the explained variance of BOLD signal. We showed that the proposed method is stable in terms of extracted patterns and where they correlate with the BOLD signal. Furthermore, we show that the proposed method explains a very similar level of the BOLD signal with the other methods and that the BOLD signal in areas of typical BOLD functional networks is explained significantly more than by a chance. Nevertheless, we didn’t observe a significant relation between our source-space SSPs and the BOLD ICs when spatio-temporally comparing them. Finally, we report several the most stable source space EEG-fMRI patterns together with their interpretation and comparison to the electrode space patterns.
Keywords:
*EEG-fMRI Integration; EEG-informed fMRI; Spatio-spectral Decomposition; Electrical Source Imaging; Independent Component Analysis; Resting State Networks*
Available in digital repository of the ASCR
Spatio-Spectral EEG Patterns in the Source-Reconstructed Space and Relation to Resting-State Networks: An EEG-fMRI Study

In this work, we present and evaluate a novel EEG-fMRI integration approach combining a spatio-spectral decomposition method and a reliable source localization technique. On the large 72 subjects ...

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**Scalar-Valued Score Functions and their use in Parametric Estimation**

Fabián, Zdeněk

2022 - English
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic properties of score functions of standard distributions, generalize the approach for parametric families and show how to use them for solutions of problems of parametric statistics.
Keywords:
*core random variable; score mean; score variance; score distance; score correlation*
Available in a digital repository NRGL
Scalar-Valued Score Functions and their use in Parametric Estimation

In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic ...

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**A Measure of Variability WIthin Parametric Families of Continuous Distributions**

Fabián, Zdeněk

2022 - English
A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified a score variance as a finite measure of variability of distributions with respect to the typical value and discussed its properties and methods of estimation. Itroducing a generalized Rao distance in the sample space one can appraise the precision of the estimate of the typical value.
Keywords:
*scalar-valued score; score mean; score variance; distance in the sample space*
Available at various institutes of the ASCR
A Measure of Variability WIthin Parametric Families of Continuous Distributions

A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified ...

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**Score correlation for skewed distributions**

Fabián, Zdeněk

2022 - English
Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coeﬃcient ”tai-lored” to the assumed probabilistic model and study its properties by means of simulation experiments. It appeared that the new correlation method is useful for enormously skewed distributions.
Keywords:
*Scalar-valued score; score coeﬃcient of variation; Monte Carlo*
Available at various institutes of the ASCR
Score correlation for skewed distributions

Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coeﬃcient ”tai-lored” to the assumed probabilistic model and study its ...

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**Introduction to statistical inference based on scalar-valued scores**

Fabián, Zdeněk

2022 - English
In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, but their ”treated forms”,the values of the scalar-valued score function corresponding to the model. Based on this modiﬁed concept of the score function, we develop theory of score random variables, study their geometry and deﬁne their new characteristics, ﬁnite even in cases of heavy-tailed models. A generalization for parametric families provides a new approach to parametric point estimation.
Keywords:
*continuous distributions; score mean; score variance; score moment estimation method; score distance*
Available at various institutes of the ASCR
Introduction to statistical inference based on scalar-valued scores

In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, ...

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**A New Look to Information and Uncertainty of Continuous Distributions**

Fabián, Zdeněk

2022 - English
We deﬁne information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their mean values are the generalized Fisher information and a new measure of variability, the score variance. In a series of examples we show why to use new concepts instead of the diﬀerential entropy.
Keywords:
*Diﬀerential entropy; information function; uncertainty function; mean information of distribution*
Available at various institutes of the ASCR
A New Look to Information and Uncertainty of Continuous Distributions

We deﬁne information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their ...

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**Large Perimeter Objects Surrounded by a 1.5D Terrain**

Keikha, Vahideh

2022 - English
Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k > 0, we design an FPTAS that efficiently approximates such polygons within a factor (1 − ǫ). For the special case of the´largest-perimeter contained triangle in T , we design an O(n log n) time exact algorithm that matches the same result for the area measure.
Available in digital repository of the ASCR
Large Perimeter Objects Surrounded by a 1.5D Terrain

Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k ...

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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 at various institutes 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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