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Robot Control in Terms of Hamiltonian Mechanics
Záda, V.; Belda, Květoslav
2016 - English
The paper deals with a mathematical modeling of robot motion and control. Instead of frequently used Lagrangian formulation of robot dynamics, this paper presents robot dynamics by Hamiltonian formulation. This formulation leads to different physical descriptive quantities considered for control design. In the paper, as a comparative control approach, PD control with gravity compensation is considered. The control approach considering Hamiltonian formulation is demonstrated for simplicity on two-mass robot-arm system. However, the explained modeling approach is general and it can be applied, e.g., to usual industrial articulated robots-manipulators with multiple degrees of freedom.
Keywords:
Robot-manipulator; Hamiltonian formalism; Modeling; Robot control; PD control
Fulltext is available at external website.
Robot Control in Terms of Hamiltonian Mechanics
The paper deals with a mathematical modeling of robot motion and control. Instead of frequently used Lagrangian formulation of robot dynamics, this paper presents robot dynamics by Hamiltonian ...
Transient and Average Markov Reward Chains with Applications to Finance
Sladký, Karel
2016 - English
The article is devoted to Markov reward chains, in particular, attention is primarily focused on the reward variance arising by summation of generated rewards. Explicit formulae for calculating the variances for transient and average models are reported along with sketches of algorithmic procedures for finding policies guaranteeing minimal variance in the class of policies with a given transient or average reward. Application of the obtained results to financial models is indicated.
Keywords:
dynamic programming; transient and average Markov reward chains; reward-variance optimality; optimality in financial models
Fulltext is available at external website.
Transient and Average Markov Reward Chains with Applications to Finance
The article is devoted to Markov reward chains, in particular, attention is primarily focused on the reward variance arising by summation of generated rewards. Explicit formulae for calculating the ...
Capital market efficiency in the Ising model environment: Local and global effects
Krištoufek, Ladislav; Vošvrda, Miloslav
2016 - English
Financial Ising model is one of the simplest agent-based models (building on a parallel between capital markets and the Ising model of ferromag- netism) mimicking the most important stylized facts of financial returns such as no serial correlation, fat tails, volatility clustering and volatility persistence on the verge of non-stationarity. We present results of Monte Carlo simulation study investigating the relationship between parameters of the model (related to herding and minority game behaviors) and crucial characteristics of capital market e ciency (with respect to the e cient market hypothesis). We find a strongly non-linear relationship between these which opens possibilities for further research. Specifically, the existence of both herding and minority game behavior of market participants are necessary for attaining the e cient market in the sense of the e cient market hypothesis.
Keywords:
Ising model; efficient market hypothesis; Monte Carlo simulation
Fulltext is available at external website.
Capital market efficiency in the Ising model environment: Local and global effects
Financial Ising model is one of the simplest agent-based models (building on a parallel between capital markets and the Ising model of ferromag- netism) mimicking the most important stylized facts of ...
A Note on Optimal Value of Loans
Kaňková, Vlasta
2016 - English
People try to gain (in the last decades) own residence (a flat or a little house). Since young people do not posses necessary financial resources, bank sector offers them a mortgage. Of course, the aim of any bank is to profit from such a transaction. Therefore, according to their possibilities, the banks employ excellent experts to analyze the financial situation of potenitial clients. Consequently, the banks know what could be a maximal size of the loan (in dependence on the debtor's position, salary and age) and what is reasonable size of installments. The aim of this contribution is to analyze the situation from the second size. In particular, the aim is to investgate the possibilities of the debtors not only on the dependence on their present - day situation, but also on their future private and subjective decisions and on possible “unpleasant” events. Moreover, consequently according to these indexes, the aim of this contribution is to suggest a method for a recognition of a “safe” loan and simultaneously to offer tactics to state a suitable environment for future time.The stochastic programming theory will be employed to it.
Keywords:
Loan; debtor; installments; multistage stochastic programming
Fulltext is available at external website.
A Note on Optimal Value of Loans
People try to gain (in the last decades) own residence (a flat or a little house). Since young people do not posses necessary financial resources, bank sector offers them a mortgage. Of course, the ...
Discrete Dynamic Endogenous Growth Model: Derivation, Calibration and Simulation
Kodera, J.; Van Tran, Q.; Vošvrda, Miloslav
2016 - English
Endogenous economic growth model were developed to improve traditional growth models with exogenous technological changes. There are several approaches how to incorporate technological progress into a growth model. Romer was the first author who has introduced it by expanding the variety of intermediate goods. Overall, the growth models are often continuous. In our paper we formulate a discrete version of Romer's model with endogenous technological change based on expanding variety of intermediates, both in the final good sector and in the research-development sector, where the target is to maximize present value of the returns from discovering of intermediate goods which should prevail introducing costs. These discrete version then will be calibrated by a numerical example. Our aim is to find the solution and analyse the development of economic variables with respect to external changes.
Keywords:
growth model; endogenous technological progress; Romer's model; discrete optimization problem
Fulltext is available at external website.
Discrete Dynamic Endogenous Growth Model: Derivation, Calibration and Simulation
Endogenous economic growth model were developed to improve traditional growth models with exogenous technological changes. There are several approaches how to incorporate technological progress into a ...
Approximate Transition Density Estimation of the Stochastic Cusp Model
Voříšek, Jan
2016 - English
Stochastic cusp model is defined by stochastic differential equation with cubic drift. Its stationary density allows for skewness, different tail shapes and bimodality. There are two stable equilibria in bimodality case and movement from one equilibrium to another is interpreted as a crash. Qualitative properties of the cusp model were employed to model crashes on financial markets, however, practical applications of the model employed the stationary distribution, which does not take into account the serial dependence between observations. Because closed-form solution of the transition density is not known, one has to use approximate technique to estimate transition density. This paper extends approximate maximum likelihood method, which relies on the closed-form expansion of the transition density, to incorporate time-varying parameters of the drift function to be driven by market fundamentals. A measure to predict endogenous crashes of the model is proposed using transition density estimates. Empirical example estimates Iceland Krona depreciation with respect to the British Pound in the year 2001 using differential of interbank interest rates as a market fundamental.
Keywords:
multimodal distributions; stochastic cusp model; approximate transition density
Fulltext is available at external website.
Approximate Transition Density Estimation of the Stochastic Cusp Model
Stochastic cusp model is defined by stochastic differential equation with cubic drift. Its stationary density allows for skewness, different tail shapes and bimodality. There are two stable equilibria ...
Lazy Learning of Environment Model from the Past
Štěch, J.; Guy, Tatiana Valentine; Pálková, B.; Kárný, Miroslav
2015 - English
The paper addresses a lazy learning (LL) approach to decision making (DM) problem described in fully probabilistic way. The key idea of LL is to simplify the actual DM problem by using past DM problems similar to the current one. The approach can decrease computation complexity and increase quality of learning when no rich alternative information available. The proposed LL approach helps to learn the environment model based on a proximity of the past and current DM problem with Kullback-Leibler divergence serving as a proximity measure. The implemented algorithm is verified on the real data. The results show that the proposed approach improves prediction quality.
Keywords:
Lazy learning; local modelling; prediction for optimisation
Fulltext is available at external website.
Lazy Learning of Environment Model from the Past
The paper addresses a lazy learning (LL) approach to decision making (DM) problem described in fully probabilistic way. The key idea of LL is to simplify the actual DM problem by using past DM ...
Extended Bidirectional Texture Function Moving Average Model
Havlíček, Michal
2015 - English
The bidirectional texture function (BTF) is the recent most advanced representation of visual properties of material surface. It specifies its appearance due to varying spatial, illumination, and viewing conditions. Corresponding enormous BTF measurements require compact mathematical representation for visual fidelity preserving compression. We present a novel BTF model based on a set of underlying three dimensional moving average random field (3D MA RF) models. 3D MA assumes the texture considered as a product of a convolution of an uncorrelated three dimensional random field with a three dimensional filter which completely characterizes the texture. The BTF model combines several spatial factors, subsequently factorized into a set of 3D MA representations, and range map to produce the required BTF texture. This enables high BTF space compression ratio, unrestricted texture enlargement, and reconstruction of unmeasured parts of the BTF space. We also compare proposed model with its simpler two dimensional variant in terms of colour distribution fidelity.
Keywords:
Bidirectional texture function; moving average random field model
Fulltext is available at external website.
Extended Bidirectional Texture Function Moving Average Model
The bidirectional texture function (BTF) is the recent most advanced representation of visual properties of material surface. It specifies its appearance due to varying spatial, illumination, and ...
Estimation of Hopping Rates From Real Traffic Trajectories
Fajfrová, Lucie; Hrabák, Pavel
2015 - English
Variety of hopping particle systems (ZRP, TASEP, MTP) have been investigated from the point of view of the traffic flow modelling. Such models are characterized by the local hopping rates determining the model dynamics. Several techniques of estimating appropriately the hopping rates from real traffic trajectories are introduced. Properties of corresponding models are discussed.
Keywords:
Hopping particle systems; Estimation of hopping rates; Intelligent Driver Model
Fulltext is available at external website.
Estimation of Hopping Rates From Real Traffic Trajectories
Variety of hopping particle systems (ZRP, TASEP, MTP) have been investigated from the point of view of the traffic flow modelling. Such models are characterized by the local hopping rates determining ...
Statistical analysis of competing risks in an unemployment study
Volf, Petr
2015 - English
This study is concerned with the analysis of dependence of random variables - latent times to events, in a competing risks case. We discuss first the problem of identifiability of marginal and joint distributions of competing random variables. Then, the copula models are utilized in order to express the dependence. Finally, the Gauss copula is used to solution of a real example with unemployment data.
Keywords:
statistics; competing risks,; copula; unemployment study
Fulltext is available at external website.
Statistical analysis of competing risks in an unemployment study
This study is concerned with the analysis of dependence of random variables - latent times to events, in a competing risks case. We discuss first the problem of identifiability of marginal and joint ...
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