Stochastic variability of output levels in a pulp mill

Quite often, in the construction of a pulp mill involves establishing the size of tanks which will accommodate the material from the various processes in which case estimating the right tank size a priori would be vital. Hence, simulation of the whole production process would be worthwhile. Therefore, there is need to develop mathematical models that would mimic the behavior of the output from the various production units of the pulp mill to work as simulators. Markov chain models, Autoregressive moving average (ARMA) model, Mean reversion models with ensemble interaction together with Markov regime switching models are proposed for that purpose.

Applying Qt to programming courses

Työn tavoitteena on sovittaa Qt opetussuunnitelmaan. Työ sisältää Qt:n lyhyen historian sekä katsauksen sen nykytilaan. Nykytilakatsaus sisältää kolme näkökulmaa: miten ja missä Qt:ta voidaan käyttää, sekä sen käyttötarkoitukset teollisuudessa ja opetuksessa. Työn tuloksena syntyy luentodemonstraatiota varten pieni ohjelma, joka on luotu C++:n ja Qt Designerin avulla ja käyttää olennaisia käyttöliittymäkirjaston olioita. Toisena tuotteena työssä syntyy luonnos Lappeenrannan Teknillisen Yliopiston ohjelmointikursseista, joissa Qt:ta voitaisiin käyttää avustamaan opiskelijoita näkemään, miten graafinen ohjelma luodaan sekä valmentaa heitä ymmärtämään viitekehyksien ja graafisten kirjastojen tuomat edut.

Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Developing an introductory object-oriented programming course

The state of the object-oriented programming course in Lappeenranta University of Technology had reached the point, where it required changes to provide better learning opportunities and thus the learning outcomes. Based on the student feedback the course was partially dated and ineffective. The components of the course were analysed and the ineffective elements were removed and new methods were introduced to improve the course. The major changes included the change from traditional teaching methods to reverse classroom method and the use of Java as the programming language. The changes were measured by the student feedback, lecturer’s observations and comparison to previous years. The feedback suggested that the changes were successful; the course received higher overall grade than before.

Open source solutions for multiplatform graphics programming

New emerging technologies in the recent decade have brought new options to cross platform computer graphics development. This master thesis took a look for cross platform 3D graphics development possibilities. All platform dependent and non real time solutions were excluded. WebGL and two different OpenGL based solutions were assessed via demo application by using most recent development tools. In the results pros and cons of the each solutions were noted.

Parameter estimation for Chaotic or Stochastic Dynamics

Since its discovery, chaos has been a very interesting and challenging topic of research. Many great minds spent their entire lives trying to give some rules to it. Nowadays, thanks to the research of last century and the advent of computers, it is possible to predict chaotic phenomena of nature for a certain limited amount of time. The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood, and give some hints for a more optimized use of it, together with a possible application to the industry. The main part of our study concerned two chaotic attractors whose general behaviour is diff erent, in order to capture eventual di fferences in the results. In the various simulations that we performed, the initial conditions have been changed in a quite exhaustive way. The results obtained show that, under certain conditions, this method works very well in all the case. In particular, it came out that the most important aspect is to be very careful while creating the training set and the empirical likelihood, since a lack of information in this part of the procedure leads to low quality results.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.