**838**

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**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, ...

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**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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**Bivariate Geometric Distribution and Competing Risks: Statistical Analysis and Application**

Volf, Petr

2020 - English
The contribution studies the statistical model for discrete time two-variate duration (time-to-event) data. The analysis is complicated by partial data observation caused either by the right-side censoring or by the presence of dependent competing events. The case is modeled and analyzed with the aid of a two-variate geometric distribution. The model identifiability is discussed and it is shown that the model is not identifiable without proper additional assumptions. The method of analysis is illustrated both on artificially generated\nexample and on real unemployment data.
Keywords:
*bivariate geometric distribution; competing risks; unemployment data*
Fulltext is available at external website.
Bivariate Geometric Distribution and Competing Risks: Statistical Analysis and Application

The contribution studies the statistical model for discrete time two-variate duration (time-to-event) data. The analysis is complicated by partial data observation caused either by the right-side ...

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**Use of the BCC and Range Directional DEA Models within an Efficiency Evaluation**

Houda, Michal

2020 - English
The contribution deals with two data envelopment analysis (DEA) models, in particular the BCC model (radial DEA model with variable returns to scale), and the range directional model. The mathematical description of the models are provided and several properties reported. A numerical comparison of the two models on real industrial data is provided with discussion about possible drawbacks of simplifying modeling procedures.
Keywords:
*Data Envelopment Analysis; BCC Model; Range Directional Model*
Fulltext is available at external website.
Use of the BCC and Range Directional DEA Models within an Efficiency Evaluation

The contribution deals with two data envelopment analysis (DEA) models, in particular the BCC model (radial DEA model with variable returns to scale), and the range directional model. The mathematical ...

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**A Note on Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure**

Kaňková, Vlasta

2020 - English
Nonlinear dependence on a probability measure begins to appear (last time) in a stochastic optimization rather often. Namely, the corresponding type of problems corresponds to many situations in applications. The nonlinear dependence can appear as in the objective functions so in a constraints set. We plan to consider the case of static (one-objective) problems in which nonlinear dependence appears in the objective function with a few types of constraints sets. In details we consider constraints sets “deterministic”, depending nonlinearly on the probability measure, constraints set determined by second order stochastic dominance and the sets given by mean-risk problems. The last case means that the constraints set corresponds to solutions those guarantee an acceptable value in both criteria. To introduce corresponding assertions we employ the stability results based on the Wasserstein metric and L1 norm. Moreover, we try to deal also with the case when all results have to be obtained (estimated) on the data base.
Keywords:
*Stochastic optimization problem; Nonlinear dependence; Empirical estimates; Static problems*
Fulltext is available at external website.
A Note on Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure

Nonlinear dependence on a probability measure begins to appear (last time) in a stochastic optimization rather often. Namely, the corresponding type of problems corresponds to many situations in ...

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**Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes**

Sladký, Karel

2020 - English
This contribution is devoted to risk-sensitivity in long-run average optimality of Markov and semi-Markov reward processes. Since the traditional average optimality criteria cannot reflect the variability-risk features of the problem, we are interested in more sophisticated approaches where the stream of rewards generated by the Markov chain that is evaluated by an exponential utility function with a given risk sensitivity coefficient. Recall that for the risk sensitivity coefficient equal to zero (i.e. the so called risk-neutral case) we arrive at traditional optimality criteria, if the risk sensitivity coefficient is close to zero the Taylor expansion enables to evaluate variability of the generated total reward. Observe that the first moment of the total reward corresponds to expectation of total reward and the second central moment to the reward variance. In this note we present necessary and sufficient risk-sensitivity and risk-neutral optimality conditions for long run risk-sensitive average optimality criterion of unichain Markov and semi-Markov reward processes.
Keywords:
*Markov and semi-Markov reward processes; exponential utility function; risk sensitivity*
Fulltext is available at external website.
Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes

This contribution is devoted to risk-sensitivity in long-run average optimality of Markov and semi-Markov reward processes. Since the traditional average optimality criteria cannot reflect the ...

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**A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts**

Daniel, M.; Kratochvíl, Václav

2019 - English
This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In general, we make an effort to reach a simple upper bound function for $Conf$. (Nevertheless, the maximal value of conflict is, of course, equal to 1 for fully conflicting belief functions). We apply both theoretical research using the recent results on belief functions and also experimental computational approach here.
Keywords:
*Belief functions; Dempster-Shafer theory; Uncertainty; Conflict-ing belief masses; Conflict between belief functions; Hidden conflict*
Fulltext is available at external website.
A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts

This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In ...

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**Second Order Optimality in Markov and Semi-Markov Decision Processes**

Sladký, Karel

2019 - English
Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per time may be quite insufficient to characterize the problem from the point of a decision maker. To this end it may be preferable if not necessary to select more sophisticated criteria that also reflect variability-risk features of the problem. Perhaps the best known approaches stem from the classical work of Markowitz on mean-variance selection rules, i.e. we optimize the weighted sum of average or total reward and its variance. Such approach has been already studied for very special classes of semi-Markov decision processes, in particular, for Markov decision processes in discrete - and continuous-time setting. In this note these approaches are summarized and possible extensions to the wider class of semi-Markov decision processes is discussed. Attention is mostly restricted to uncontrolled models in which the chain is aperiodic and contains a single class of recurrent states. Considering finite time horizons, explicit formulas for the first and second moments of total reward as well as for the corresponding variance are produced.
Keywords:
*semi-Markov processes with rewards; discrete and continuous-time Markov reward chains; risk-sensitive optimality; average reward and variance over time*
Fulltext is available at external website.
Second Order Optimality in Markov and Semi-Markov Decision Processes

Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per ...

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**Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates**

Kaňková, Vlasta

2019 - English
Many economic and financial situations depend simultaneously on a random element and on a decision parameter. Mostly it is possible to influence the above mentioned situation by an optimization model depending on a probability measure. We focus on a special case of one-stage two objective stochastic “Mean-Risk problem”. Of course to determine optimal solution simultaneously with respect to the both criteria is mostly impossible. Consequently, it is necessary to employ some approaches. A few of them are known (from the literature), however two of them are very important: first of them is based on a scalarizing technique and the second one is based on the stochastic dominance. First approach has been suggested (in special case) by Markowitz, the second approach is based on the second order stochastic dominance. The last approach corresponds (under some assumptions) to partial order in the set of the utility functions.\nThe aim of the contribution is to deal with the both main above mentioned approaches. First, we repeat their properties and further we try to suggest possibility to improve the both values simultaneously with respect to the both criteria. However, we focus mainly on the case when probability characteristics has to be estimated on the data base.
Keywords:
*Two-objective stochastic optimization problems; scalarization; stochastic dominance; empirical estimates*
Fulltext is available at external website.
Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates

Many economic and financial situations depend simultaneously on a random element and on a decision parameter. Mostly it is possible to influence the above mentioned situation by an optimization model ...

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**Theory of SSB Representation of Preferences Revised**

Pištěk, Miroslav

2019 - English
A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the classical (algebraic) case. Equipping a linear vector space with the so-called inductive linear topology, we derive the algebraic SSB representation on a topological basis, thus weakening\nthe convexity assumption. Such a unifying approach to SSB representation permits also to fully discuss the relationship of topological and algebraic axioms of continuity, and leads to a stronger existence result for a maximal element. By applying this theory to probability measures we show the existence of a maximal preferred measure for an infinite set of pure outcomes, thus generalizing all available existence theorems in this context.
Keywords:
*probability measures; inductive linear topology; topological vector space*
Fulltext is available at external website.
Theory of SSB Representation of Preferences Revised

A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the ...

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