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The scalar-valued score functions of continuous probability distribution
Fabián, Zdeněk
2019 - anglický
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. Klíčová slova: Shortcomings of probability theory; Scalar-valued score functions; Characteristics of continous random variables; Parametric estimation; Transformed distributions; Skew-symmetric distributions Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
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 ...

Fabián, Zdeněk
Ústav informatiky, 2019

Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
2019 - anglický
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions. Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator

This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of ...

Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
Ústav informatiky, 2019

A Logical Characteristic of Read-Once Branching Programs
Žák, Stanislav
2019 - anglický
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? Klíčová slova: branching programs; computational complexity; logic Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
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 ...

Žák, Stanislav
Ústav informatiky, 2019

Absolute Value Mapping
Rohn, Jiří
2019 - anglický
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. Klíčová slova: absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability Plné texty jsou dostupné v digitálním repozitáři NUŠL
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 ...

Rohn, Jiří
Ústav informatiky, 2019

Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství
Rohn, Jiří
2019 - český
V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. Bouška, J. Rohn a B. Kalendovský). Klíčová slova: Leontěvův model; intervalová data; zaručené řešení; neexistence; matice 28 x 28 Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství

V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. ...

Rohn, Jiří
Ústav informatiky, 2019

On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle
Matonoha, Ctirad; Papáček, Š.
2019 - anglický
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions. Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle

This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of ...

Matonoha, Ctirad; Papáček, Š.
Ústav informatiky, 2019

Overdetermined Absolute Value Equations
Rohn, Jiří
2019 - anglický
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case. Klíčová slova: absolute value equations; overdetermined system Plné texty jsou dostupné v digitálním repozitáři NUŠL
Overdetermined Absolute Value Equations

We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.

Rohn, Jiří
Ústav informatiky, 2019

A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
Lukšan, Ladislav; Vlček, Jan
2019 - anglický
In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method. Klíčová slova: nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix

In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, ...

Lukšan, Ladislav; Vlček, Jan
Ústav informatiky, 2019

Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - anglický
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real. Klíčová slova: symmetric matrix; positive semide nite matrix; real spectrum Plné texty jsou dostupné v digitálním repozitáři NUŠL
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.

Rohn, Jiří
Ústav informatiky, 2019

Hybrid Methods for Nonlinear Least Squares Problems
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2019 - anglický
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). Klíčová slova: numerical optimization; nonlinear least squares; trust region methods; hybrid methods; sparse problems; partially separable problems; numerical experiments Plné texty jsou dostupné v digitálním repozitáři NUŠL
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 ...

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
Ústav informatiky, 2019

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