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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 ...
Inspection of endangered cultural heritage assets in Iran
Drdácký, Miloš
2019 - English
Findings and comments based on visual inspection of damaged historical buildings – cultural heritage monuments - by Professor Miloš Drdácký. lt seems that there is a lack of an advanced documentation and especially diagnostics of condition of historical buildings and monuments. Namely, long term monitoring of defects in their relation to loadings is missing. Further, laboratories and know how for determination of material characteristics has a potential for improvement.
Keywords:
cultural heritage; Iran; visual inspection; ICOMOS ISCARSAH mission
Available at various institutes of the ASCR
Inspection of endangered cultural heritage assets in Iran
Findings and comments based on visual inspection of damaged historical buildings – cultural heritage monuments - by Professor Miloš Drdácký. lt seems that there is a lack of an advanced documentation ...
A Logical Characteristic of Read-Once Branching Programs
Žák, Stanislav
2019 - English
We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two appropriate properties: i) The ”knowledge” arising at a stage of computation in question is derivable from the ”knowledge” arising at the previous stage according to the rules of the model and according to the local arrangement of the b.p. ii) The model confirms the intuitively well-known fact that the knowledge arising at a node of a computation depends not only on it but in some cases also on a ”mystery” information. (I. e. different computations reaching the same node may have different knowledge(s) arisen at it.) We prove that with respect to our model no such information exists in read-once b.p.‘s but on the other hand in b. p.‘s which are not read-once such information must be present. The read-once property forms a frontier. More concretely, we may see the instances of our models as a systems S = (U,D) where U is a universe of knowledge and D are derivation rules. We say that a b.p. P is compatible with a system S iff along each computation in P S derives F (false) or T (true) at the end correctly according to the label of the reached sink. This key notion modifies the classic paradigm which takes the computational complexity with respect to different classes of restricted b.p.‘s (e.g. read-once b.p.‘s, k-b.p.‘s, b.p.‘s computing in limited time etc.). Now, the restriction is defined by a subset of systems and only these programs are taken into account which are compatible with at least one of the chosen systems. Further we understand the sets U of knowledge(s) as a sets of admissible logical formulae. It is clear that more rich sets U‘s imply the large restrictions on b.p.‘s and consequently the smaller complexities of Boolean functions are detected. More rich logical equipment implies stronger computational effectiveness. Another question arises: given a set of Boolean functions (e.g. codes of some graphs) what logical equipment is optimal from the point of complexity?
Keywords:
branching programs; computational complexity; logic
Available in digital repository of the ASCR
A Logical Characteristic of Read-Once Branching Programs
We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two ...
Report on the reference densities of water and air employed for the adjustment of vibrating tube density meter
Vinš, Václav; Prokopová, Olga
2019 - English
Zpráva představuje souhrn několika modelů pro určení referenčních hustot čisté vody a vlhkého vzduchu při atmosférickém tlaku, které jsou potřebné k teplotní kalibraci hustoměru s vibrační trubicí Anton Paar DMA 5000 M. Při nastavení přístroje využívaného v Laboratoři termofyzikálních vlastností vzešla řada technických otázek ohledně kalibrace přístroje. Tato zpráva slouží zejména jako podklad k diskuzi se zástupci společnosti Anton Paar. S použitím softwaru pro technické výpočty Matlab byly vytvořeny programy pro výpočet hustoty vody pomocí stavové rovnice IAPWS-95 od Wagnera a Pruße (2002), CIPM standardu od Tanaky a kol. (2001) a vztahu od Spiewecka a Bettina (1992). Pro vlhký vzduch byl sestaven model na základě IAPWS Guideline G8-10 (2010) založeném na stavové rovnici pro suchý vzduch od Lemmona a kol. (2000) a stavové rovnici pro vodu IAPWS-95. Výsledky byly porovnány s CIPM standardem od Picarda a kol. (2008) a zjednodušeným vztahem od Spiewecka a Bettina (1992). V závěrečné části jsou prezentována data naměřená v Laboratoři termofyzikálních vlastností pro čistou vodu v teplotním rozsahu 2 až 50 °C pro různá nastavení referenčních vztahů pro hustoty vody a vlhkého vzduchu použité při kalibraci přístroje.\n
Available at various institutes of the ASCR
Report on the reference densities of water and air employed for the adjustment of vibrating tube density meter
Zpráva představuje souhrn několika modelů pro určení referenčních hustot čisté vody a vlhkého vzduchu při atmosférickém tlaku, které jsou potřebné k teplotní kalibraci hustoměru s vibrační trubicí ...
Approximate Bayesian state estimation and output prediction using state-space model with uniform noise
Lainová, Eva; Kuklišová Pavelková, Lenka; Jirsa, Ladislav
2019 - English
This paper contributes to the problem of approximate Bayesian state estimation and output prediction using state space model with uniformly distributed noise. Algorithms for Bayesian filtering and output prediction for states uniformly distributed on an orthotopic support and Bayesian filtering and output prediction for states uniformly distributed on a parallelotopic support are presented and compared.
Keywords:
Bayesian filtering; state estimation; output prediction; uniform noise; parallelotopic support; orthotopic support
Fulltext is available at external website.
Approximate Bayesian state estimation and output prediction using state-space model with uniform noise
This paper contributes to the problem of approximate Bayesian state estimation and output prediction using state space model with uniformly distributed noise. Algorithms for Bayesian filtering and ...
Absolute Value Mapping
Rohn, Jiří
2019 - English
We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for each right-hand side.
Keywords:
absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability
Available in a digital repository NRGL
Absolute Value Mapping
We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for ...
Overdetermined Absolute Value Equations
Rohn, Jiří
2019 - English
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.
Keywords:
absolute value equations; overdetermined system
Available in a digital repository NRGL
Overdetermined Absolute Value Equations
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.
Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - English
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.
Keywords:
symmetric matrix; positive semide nite matrix; real spectrum
Available in a digital repository NRGL
Generalization of a Theorem on Eigenvalues of Symmetric Matrices
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.
Hybrid Methods for Nonlinear Least Squares Problems
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2019 - English
This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved in a unified way. Some proofs concerning trust region methods, which are difficult to find in the literature, are also added. In particular, the report contains an analysis of a new simple hybrid method with Jacobian corrections (Section 8) and an investigation of the simple hybrid method for sparse least squares problems proposed previously in [33] (Section 14).
Keywords:
numerical optimization; nonlinear least squares; trust region methods; hybrid methods; sparse problems; partially separable problems; numerical experiments
Available in a digital repository NRGL
Hybrid Methods for Nonlinear Least Squares Problems
This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with ...
Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
Rohn, Jiří
2019 - English
We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is generally not valid, and we prove that it becomes true under an additional assumption of positive semide niteness of the midpoint matrix. The proof is constructive.
Keywords:
symmetric interval matrix; singularity; positive semide niteness
Available in a digital repository NRGL
Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is ...
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