Optimization problems with chance constraints

Autor se v diplomové práci zabývá optimalizačními úlohami s pravděpodob- nostními omezeními. Konkrétně pak situacemi, kdy není známo pravděpo- dobnostní rozdělení přítomného náhodného efektu. K řešení těchto problém· lze přistoupit metodami optimistických a pesimistických scénář·, kdy z dané rodiny možných pravděpodobnostních rozdělení vybíráme bu¤ nejpříznivější možnou variantu, nebo naopak tu nejméně výhodnou. Optimalizační úlohy s pravděpodobnostními omezeními formulovanými pomocí výše zmíněných přístup· byly za učinění jistých předpoklad· transformovány do jednoduš- ších a řešitelných optimalizačních úloh. Dosažené výsledky byly aplikovány na reálná data z oblastí optimalizace portfolia a zpracování obrazu. 1Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Extrakce informací z modelovacích nástrojů pro databáze

Data lineage je zobrazením toku informácií v komplikovaných systémoch. V prípade, že takýmto systémom je databáza, ukazuje tabuľky a stĺpce, spolu s transformáciami, ktoré modifikujú dáta v nej uložené. Takýto pohľad však môže byť ťažko pochopiteľný pre ľudí, ktorí sú menej zbehlí v technickom prostredí, keďže databázové objekty väčšinou podliehajú menným konvenciám a častokrát reprezentujú implementačné detaily. Pre jednoduchšie pochopenie dátových tokov sme vypracovali softvér Metadata Extractor. Ten na jednej strane získava podrobný popis databázových objektov a zároveň prináša novú perspektívu na tok dát pomocou business lineage, ktorá je pochopiteľná pre širší okruh ľudí. Informácie potrebné na vytvorenie takejto funkcionality získavame z mode- lovacích nástrojov, akými sú napríklad ER/Studio a PowerDesigner, ktoré sa využívajú pri navrhovaní databáz. Naše riešenie využíva a zároveň rozširuje Manta Flow, čo je softérový nástroj na vytváranie dátových tokov. 1Data lineage is a way of showing how information flows through complicated software systems. If the given system is a database, tables and columns are visualized along with transformations of the stored data. However, this picture may be difficult to understand for people with weaker technical background, as database objects usually obey naming conventions and do not necessarily represent something tangible. To improve lineage comprehension, we developed a software called Metadata Extractor that on one hand brings the further description of the database objects, as well as introduces a whole new perspective on data in a system through business lineage aimed for non-technical users. The additional metadata enriching data lineage is extracted from data modeling tools, such as ER/Studio and PowerDesigner, that are widely used in the database design process. The solution extends the Manta Flow lineage tool while taking advantage of its features at the same time. 1Department of Distributed and Dependable SystemsKatedra distribuovaných a spolehlivých systémůMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Quantum synthesis of arbitrary unitary operators

Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for realization of any unitary operator which acts on a (truncated) Hilbert space of a single bosonic mode. In particular, we consider a physical implementation of unitary transformations acting on 1-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the discrete Fourier transform.Comment: 6 RevTeX pages with 3 figures, submitted to Phys.Rev.A, see also http://nic.savba.sk/sav/inst/fyzi/qo

Mimicking a Kerrlike medium in the dispersive regime of second-harmonic generation

We find an effective Hamiltonian describing the process of second-harmonic generation in the far-off resonant limit. We show that the dynamics of the fundamental mode is governed by a Kerrlike Hamiltonian. Some dynamical consequences are examined.Comment: 12 pages, 4 figures Submitted to Optics Communication

Pfaffian pairing wave functions in electronic structure quantum Monte Carlo

We investigate the accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-pfaffian pairing wave functions. We show that a small number of pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.Comment: 4 pages, 2 figures, 2 tables, submitted to PR

High-order nonlinearities in the motion of a trapped atom

Published versio

Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies

A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions.Comment: 7 pages, 7 figure

Testiranje na antineuronska protutijela u neuobičajenom slučaju ponovljene Bellove paralize

The term Bell\u27s palsy (BP) is nowadays reserved for peripheral facial nerve paralysis without well-defined etiology and pathogenesis. BP is not a life threatening condition but it has a potential cosmetic mutilatory effect, and there is also a possibility of serious ophthalmologic complications (corneal ulcers). Recurrent paralyses are noted in 7% - 8% of BP cases. Only two patients with four BP episodes out of 170 patients, and only one patient with more than four BP episodes out of 2414 BP cases have been reported in the literature. The highest number of BP recurrences found in the available literature is nine. A brief review of the epidemiology and etiopathogenesis of BP is presented, a case of unusual recurrent BP is reported, and the immune pathomechanisms are discussed.Pojam Bellove paralize (BP) danas označava perifernu paralizu ličnoga živca nejasne etiologije i patogeneze. BP nije stanje koje bi ugrozilo život bolesnika, ali može imati znatne estetske posljedice te izazvati ozbiljne oftalmološke komplikacije (ulceracije rožnice). Ponovljene paralize javljaju se u 7% - 8% slučajeva BP. U literaturi je opisano samo dvoje bolesnika s četiri epizode BP od ukupno 1700 bolesnika, te samo jedan bolesnik s više od četiri epizode BP od ukupno 2414 slučajeva BP. U dostupnoj literaturi, najveći broj ponovljenih BP je devet. U radu se daje kratak pregled epidemiologije i etiopatogeneze BP, uz prikaz neuobičajenog slučaja ponovljene BP, uključujući raspravu o imunološkim patomehanizmima

N-Photon wave packets interacting with an arbitrary quantum system

We present a theoretical framework that describes a wave packet of light prepared in a state of definite photon number interacting with an arbitrary quantum system (e.g. a quantum harmonic oscillator or a multi-level atom). Within this framework we derive master equations for the system as well as for output field quantities such as quadratures and photon flux. These results are then generalized to wave packets with arbitrary spectral distribution functions. Finally, we obtain master equations and output field quantities for systems interacting with wave packets in multiple spatial and/or polarization modes.Comment: 20 pages, 8 figures. Published versio

Quantum versus classical descriptions of sub-Poissonian light generation in three-wave mixing

Sub-Poissonian light generation in the non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q-functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behavior are obtained analytically by applying the classical trajectories. Scaling laws for the maximum sub-Poissonian behavior are found. Noise suppression levels in the non-degenerate vs degenerate three-wave mixing are discussed on different time scales compared to the revival times. It is shown that the non-degenerate conversion offers much better stabilization of the suppressed noise in comparison to that of degenerate process.Comment: 9 pages, 12 figures, to be published in J. Optics