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Computing the Decomposable Entropy of Graphical Belief Function Models
Jiroušek, Radim; Kratochvíl, Václav; Shenoy, P. P.
2022 - English
In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy. Here, we provide an algorithm for computing the decomposable entropy of directed graphical D-S belief function models. For undirected graphical belief function models, assuming that each belief function in the model is non-informative to the others, no algorithm is necessary. We compute the entropy of each belief function and add them together to get the decomposable entropy of the model. Finally, the decomposable entropy generalizes Shannon’s entropy not only for the probability of a single random variable but also for multinomial distributions expressed as directed acyclic graphical models called Bayesian networks.
Keywords:
Decomposable Entropy; DempsterShafer belief functions; Bayesian networks
Fulltext is available at external website.
Computing the Decomposable Entropy of Graphical Belief Function Models
In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy. Here, we provide an algorithm for computing the decomposable ...
Classes of Conflictness / Non-Conflictness of Belief Functions
Daniel, Milan; Kratochvíl, Václav
2022 - English
Theoretic, descriptive and experimental analysis and description of classes of conflictness, non-conflictness and of conflict hiddeness of belief functions. Theoretic extension of theory of hidden conflicts. Idea of catalogue of belief structures.
Keywords:
belief functions; theory of hidden conflicts; classes of conflictness
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Classes of Conflictness / Non-Conflictness of Belief Functions
Theoretic, descriptive and experimental analysis and description of classes of conflictness, non-conflictness and of conflict hiddeness of belief functions. Theoretic extension of theory of hidden ...
Central Moments and Risk-Sensitive Optimality in Markov Reward Processes
Sladký, Karel
2021 - English
In this note we consider discrete- and continuous-time Markov decision processes with finite state space. There is no doubt that usual optimality criteria examined in the literature on optimization of Markov reward processes, e.g. total discounted or mean reward, may be quite insufficient to select more sophisticated criteria that reflect also the variability-risk features of the problem. In this note we focus on models where the stream of rewards generated by the Markov process is evaluated by an exponential utility function with a given risk sensitivity coefficient (so-called risk-sensitive models).For the risk sensitive case, i.e. if the considered risk-sensitivity coefficient is non-zero, we establish explicit formulas for growth rate of expectation of the exponential utility function. Recall that in this case along with the total reward also it higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulas for calculating variance a higher central moments of the total reward generated by the |Markov reward process along with its asymptotic behaviour.
Keywords:
discrete- and continuous-time Markov reward chains; exponential utility; moment generating functions
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Central Moments and Risk-Sensitive Optimality in Markov Reward Processes
In this note we consider discrete- and continuous-time Markov decision processes with finite state space. There is no doubt that usual optimality criteria examined in the literature on optimization of ...
Mathematics and Optimal control theory meet Pharmacy: Towards application of special techniques in modeling, control and optimization of biochemical networks
Papáček, Štěpán; Matonoha, Ctirad; Duintjer Tebbens, Jurjen
2021 - English
Similarly to other scienti c domains, the expenses related to in silico modeling in pharmacology need not be extensively apologized. Vis a vis both in vitro and in vivo experiments, physiologically-based pharmacokinetic (PBPK) and pharmacodynamic models represent an important tool for the assessment of drug safety before its approval, as well as a viable option in designing dosing regimens. In this contribution, some special techniques related to the mathematical modeling, control and optimization of biochemical networks are presented on a paradigmatic example of enzyme kinetics.
Keywords:
Dynamical system; Systems pharmacology; Biochemical network; Input-output regulation; Optimization
Fulltext is available at external website.
Mathematics and Optimal control theory meet Pharmacy: Towards application of special techniques in modeling, control and optimization of biochemical networks
Similarly to other scienti c domains, the expenses related to in silico modeling in pharmacology need not be extensively apologized. Vis a vis both in vitro and in vivo experiments, ...
Multimodal data fusion in remote sensing
Greško, Šimon; Zitová, Barbara
2021 - English
With fast development of remote sensing technologies, demand for remote sensing data started to be increasing. Providing space resolution of these data may not be sufficient for target application. For that reason the methods for fusing remote sensing images were developed. This issue appears in the question of demand for high resolution thermal data. Sentinel-3 provides free remote sensing thermal data with space resolution 1000x1000 m, which may be insufficient for some specialized applications. In this thesis, standard methods of image fusion are presented as well as specialized methods for thermal sharpening, their modifications, implementation and results including validation and comparison.
Keywords:
remote sensing; thermal sharpening; sentinel
Fulltext is available at external website.
Multimodal data fusion in remote sensing
With fast development of remote sensing technologies, demand for remote sensing data started to be increasing. Providing space resolution of these data may not be sufficient for target application. ...
REGULATORY NETWORK OF DRUG-INDUCED ENZYME PRODUCTION: PARAMETER ESTIMATION BASED ON THE PERIODIC DOSING RESPONSE MEASUREMENT
Papáček, Štěpán; Lynnyk, Volodymyr; Rehák, Branislav
2021 - English
The common goal of systems pharmacology, i.e. systems biology applied to the eld of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system is controlled (or periodically forced) by an input signal being a drug intake. Our aim is to test the model features under both periodic and nonrecurring dosing, and eventually to provide an innovative method for a parameter estimation based on the periodic dosing response measurement.
Keywords:
Dynamical system; Regulatory network; Input-output; Regulation; Parameter estimation; FFT
Fulltext is available at external website.
REGULATORY NETWORK OF DRUG-INDUCED ENZYME PRODUCTION: PARAMETER ESTIMATION BASED ON THE PERIODIC DOSING RESPONSE MEASUREMENT
The common goal of systems pharmacology, i.e. systems biology applied to the eld of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. ...
Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election
Kalina, Jan; Vidnerová, P.
2021 - English
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however vulnerable to leverage points in the regression model, an alternative approach denoted as implicitly weighted regression quantiles have been proposed. The aim of current work is to apply them to the results of the second round of the 2018 presidential election in the Czech Republic. The election results are modeled as a response of 4 demographic or economic predictors over the 77 Czech counties. The analysis represents the first application of the implicitly weighted regression quantiles to data with more than one regressor. The results reveal the implicitly weighted regression quantiles to be indeed more robust with respect to leverage points compared to standard regression quantiles. If however the model does not contain leverage points, both versions of the regression quantiles yield very similar results. Thus, the election dataset serves here as an illustration of the usefulness of the implicitly weighted regression quantiles.
Keywords:
linear regression; quantile regression; robustness, outliers; elections results
Fulltext is available at external website.
Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however ...
A NUMERICAL METHOD FOR THE SOLUTION OF THE NONLINEAR OBSERVER PROBLEM
Rehák, Branislav
2021 - English
The central part in the process of solving the observer problem for nonlinear systems is to nd a solution of a partial differential equation of first order. The original method proposed to solve this equation used expansions into Taylor polynomials, however, it suffers from rather restrictive assumptions while the approach proposed here allows to generalize these requirements. Its characteristic feature is that it is based on the application of the Finite Element\nMethod. An illustrating example is provided.
Keywords:
Finite element method; Observer; Partial differential equation
Fulltext is available at external website.
A NUMERICAL METHOD FOR THE SOLUTION OF THE NONLINEAR OBSERVER PROBLEM
The central part in the process of solving the observer problem for nonlinear systems is to nd a solution of a partial differential equation of first order. The original method proposed to solve ...
On kernel-based nonlinear regression estimation
Kalina, Jan; Vidnerová, P.
2021 - English
This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric applications, and regularization networks, which represent machine learning tools very rarely used in econometric modeling. This paper recalls both approaches and describes their common features as well as differences. For the Nadaraya-Watsonestimator, we explain its connection to the conditional expectation of the response variable. Our main contribution is numerical analysis of suitable data with an economic motivation and a comparison of the two nonlinear regression tools. Our computations reveal some tools for the Nadaraya-Watson in R software to be unreliable, others not prepared for a routine usage. On the other hand, the regression modeling by means of regularization networks is much simpler and also turns out to be more reliable in our examples. These also bring unique evidence revealing the need for a careful choice of the parameters of regularization networks
Keywords:
Nonlinear regression; machine learning; kernel smoothing; regularization; regularization networks
Fulltext is available at external website.
On kernel-based nonlinear regression estimation
This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric ...
Systems biology analysis of a drug metabolism (with slow-fast. . . )
Papáček, Štěpán; Lynnyk, Volodymyr; Rehák, Branislav
2020 - English
In the systems biology literature, complex systems of biochemical reactions (in form of ODEs) have become increasingly common. This issue of complexity is often making the modelled processes (e.g. drug metabolism, XME induction, DDI) difficult to intuit or to be computationally tractable, discouraging their practical use.
Keywords:
Dynamical system; Complex system; Optimization
Fulltext is available at external website.
Systems biology analysis of a drug metabolism (with slow-fast. . . )
In the systems biology literature, complex systems of biochemical reactions (in form of ODEs) have become increasingly common. This issue of complexity is often making the modelled processes (e.g. ...
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