
Information Extraction from structured business documents by learning from similarity
Holeček, Martin ; Maršík, František (advisor) ; Liwicki, Marcus (referee) ; Mesiti, Marco (referee)
The automation of document processing is gaining recent attention due to the great potential to reduce manual work through improved methods and hardware. In this area, neural networks have been applied before  even though they have been trained only on relatively small datasets with hundreds of documents so far. To successfully explore deep learning techniques and improve the information ex traction results, a dataset with more than twentyfive thousand documents (pro forma invoices, invoices and debit note documents) has been compiled, anonymized and is published as a complement of this work. In the first part of the research, we will examine the documents from the point of view of table detection, present a survey on table detection methods and ultimately rephrase the table detection as a text box labelling problem to optimize micro F1 score of perword classification. We will show that we can extract specific information from structurally different tables or tablelike structures with one trainable model that features a comprehen sive representation of a page using graph over wordboxes, positional embeddings and trainable textual features. The first part is concluded with a novel neural network model that beats multiple baselines and achieves strong, practical results on the presented dataset....


The connection between the principle of the least action and the thermodynamic condition of stability
Maršík, František ; Trávníček, Zdeněk ; Antošová, Zuzana
The extended principle is formulated for a material point (M.P.) X, which has nonzero mass, temperature, and trajectory x(X,t). The Lagrangian of this variation principle is equal to the kinetic energy from which, the internal energy of the material point (which depends on the entropy) and the additional energy caused by the frictional force are subtracted. The relation between the inertial force and the entropy gradient is found and the gravitational force is completely replaced by the entropy gradient. Thanks to the mentioned properties of the total enthalpy, the Thermodynamic criterion of stability of the state of M.P., is formulated.


Analysis of spontaneous collapse in elastic tubes
Netušil, Marek ; Maršík, František (advisor) ; Horný, Lukáš (referee)
Interaction of fluid with elastic tube is complicated issue studied by many scientific departments around the world. Object of this thesis is to analyze simplified onedimensional model. At the beginning, used balance equations and basics of hyperelasticity are presented. Then we review three most common materials used for the description of blood vessels and other soft tissues. For these materials we introduce a method which we use to derive a relation between tube deformation and transmural pressure (i.e. difference between inner and outer pressure). In mathematical section we give brief review of theory of nonlinear hyperbolic equations and some relatively new results in the field of existence and uniqueness of a solution of onedimensional hyperbolic system. The "building stone" of these results is a solution of the socalled Riemann problem. We use a method for finding exact solutions to the Riemann problem to analyze studied model of fluidtube interaction and study dependence of the qualitative behavior of the solution on the material properties of the tube wall.


Suggestion of an optimal numerical method for solution of the RayleighPlesset equation with rebounding
Petrík, Peter ; Maršík, František (advisor) ; Zima, Patrik (referee)
Na/ev pram: X a v i l i opt.inia.lm niunericke metody pro le.^ loviuce s pmdkyini kavil acni'mi kolapsx Autor: Peter Peln'k Katedra (usl.av): Malemalickv uslav I ' K Vedouci bakalafske prace: Piol. hit!,. Marsik Fianlisek. UrSc. email vodouci'lio: marsik'nt .ras.c/ Abstrnkt: V praci si ndnicme presnost a casovou miioenosl jednokrokovvch ex plicit niVh I l i r t u d ( Klin;!,cl\UtT;i. BulirscllSt oer) s ;id;ipt a h i l l l l l l l klokem v Kayleijdl Plesselove lovnici, ktera popiMije vyvoj polomei n pi v nne l)iil)iiii\ \ kapalinr sc /nicnaini tln.ku. McUidv pndcriiujf lok/ilni chybii \ nn.stccli kdlapsu hiihlin. av^ik ^lobi'ilnf c!i\'l)a /usta"\;i \ nidu pou/itc tulcrancc, Bulii'scliSt.ocr inctdda \a ncjiiKMis] CMSOVOH nai'ociK)St. V pfi'padr [^ini^cKullii iiK'tnd /;i.\isi \ylicr oitiiiuil)ii nirtdd\ na pou/itr lolcranci. Pli slrcdnicli tnln ancich ur\'i lilujc \vpocc! i pnuxiti iT^ukiri/acr. (j. xavcdciii niA'f'1 jicx/ixihlr pmiiirnnr nii'slo rasu. ('MSOV'I ii/irocno^l poti/,it(' i)nMod\c tiicni' s ruxnynii pou/Jtyini vaiiatil a.nii rovtiicc (i/u(cnuick;i aproxi inacr/adialiat ick/i aproxiniacc plvniic sln/ky olisa.hu luililiiiy. si lacilt'lun./ nest a.rit.clna kapalina) I'l'i nekteryeh naslavcniYli \st ilpni'eli paranirl I'll \ i/,ol enilirkc vai'iatile io\"iiice doelii'txi k padu \'ypoelu...


Metoda vrstevnic a modelování proudění nemísitelných nestlačitelných tekutin
Čapek, Marek ; Hron, Jaroslav (advisor) ; Maršík, František (referee)
The focus of this thesis are threedimensional simulations of flow of two immiscible incompressible viscous fluids and distribution of concentration transported by the flow where the free interface between the fluids is realized by levelset method. It is applied to blood flow and coagulation. The blood flow is described using NavierStokes equations for incompressible fluids, numerical method is done by finite element method with Q2  Q1 elements and the problem is solved as coupled. The distribution of concentration is described using transport equation, discretization is done using Q1 elements.

 
 
 

Matematická analýza a výpočtový algoritmus RayleighovyPlessetovy rovnice v okolí prudkého kolapsu bublinky.
Petrík, Peter ; Maršík, František (advisor) ; Rudolf, Pavel (referee)
The RayleighPlesset equation is commonly used to describe the dynamics of spherical bubbles in water. However, as highspeed observations show, the bubble looses its spherical shape during the violent collapse and often ssions into a number of smaller bubbles before it rebounds again or dissolves completely. The objective of the work is to bridge the gap between the \spherical\ RayleighPlesset approach and the \nonspherical\ behavior of the collapsing bubble in conditions when the RayleighPlesset equation is no longer valid. The objective is achieved in 3 steps. First, the new criterion for the assessment of the reliability of the RayleighPlesset equation is proposed. Second, the analysis of the shape stability of the spherical surface of the bubble during the collapse lead to the development of a physical model, which incorporates the loss of shape stability, surface energy dissipation and the ssion process. Moreover it estimates the number of bubble fragments as well as conditions when the ssion occurs. Finally, theoretical results are incorporated into the complex numerical code, with the focus on error estimation, specially propagation of rounding error. The sample numerical results for typical hydrodynamic cavitation situations were calculated. The results of this work have to be further con rmed...


Generace vířivosti rychlostního pole gradientem entropie
Novák, Martin ; Maršík, František (advisor) ; Grmela, Miroslav (referee)
The master thesis studies the impact of the entropy gradient on the vorticity of ve locity field, particularly by applying the linear momentum balances. These balances are formulated for Thermoviscous fluids (later fluids) and Thermoviscouselastic ma terial (later solids) with the other balances (energy, mass, etc.). In order to derive these balances, the Classical continuum mechanics approach is used along with the respec tive Variational principles. The thesis emphasizes the Variational principles applica tion representing the modification of the Bateman principle [Bat29] and its comparison with the Classical approach, linked to the L. Crocco work [Cro37], particularly in the case of vorticity generation. It is pointed that by the definition of the dissipative en tropy sdis a harmony of both approaches can be achieved and that, in the case of an appropriate limit, the direct effect of the entropy gradient on the vorticity of velocity field can be demonstrated. By applying this conclusion the relationship between the change of circulation among a closed curve and released heat on the given geometry is indicated.
