Telecommunication networks form an integral part of life. Avoiding failures on these networks is always not possible. Designing network structures that survive these failures have become important in ensuring the reliability of these network structures. With the introduction of SONET (Synchronous Optical Network) technology, rings have become the preferred survivable network structure. This network configuration has a set of disjoint rings (each node being a part of single ring), and these disjoint rings are connected via another main ring. In this research, we present a mathematical model for the design of such disjoint rings with node number balance criterion among the rings. When, given a set of nodes and distances between them, the Balanced Disjoint Rings (BDR) problem is the minimum total link length clustering of nodes into a given number of disjoint rings in such a way that there is almost the same number of nodes in each ring. The BDR problem is a class of the standard Traveling Salesman Problem (TSP). It is clear from this observation that the BDR problem becomes a TSP when the number of rings required is set to one. Hence BDR is NP-Hard, and we do not expect to obtain a polynomial time algorithm for its solution. To overcome this problem, we developed a set of construction heuristics (Break-MST, Distance Method, Hybrid Method, GRASP-Based Distance Method) and improvement heuristics (Multi-Exchange, Single Move). Different combinations of construction and improvement heuristics were implemented and the quality of solution thus obtained was compared to the standard Branch and Cut Technique. It was found that the algorithm with GRASP-Based Distance Method as the construction heuristic and multi-exchange - single-move combination as the improvement heuristic performed better than other combinations. All combinations performed better in general than the standard Branch and Cut technique in terms of solution time.

Acoustic horns are used in musical instruments and loudspeakers in order to provide an impedance match between an acoustic source and the surrounding air. The aim of this study is to develop numerical tools for the analysis and optimisation of such horns, with respect to their input impedance spectra. Important effects such as visco-thermal damping and modal conversion are shown to be localised to different parts of a typical brass instrument. This makes it possible to construct hybrid methods that apply different numerical techniques in different parts of the instrument. Narrow and slowly flaring parts are modelled using a one-dimensional transmission line analogy, and the rapidly flaring bell is modelled using a two-dimensional finite-difference method. The connection between the different regions is done by the aid of impedance boundary conditions. The use of such boundary conditions is investigated with respect to the required number of degrees of freedom. Numerical shape optimisation is employed in order to design horns with desired impedance characteristics throughout a design frequency band. A loudspeaker horn is optimised with respect to its sound power output, and a brass instrument is optimised with respect to its intonation. The horns are modelled using the finite-element method and a transmission line analogy. In order to achieve rapid convergence of the optimisation, gradient based minimisation algorithms are used. A prerequisite for success is the ability to accurately and inexpensively compute the gradient of the objective function. The gradient for the finite-element method is computed by an adjoint equation technique, whereas for the transmission line analogy, it is derived by formal differentiation of the model. In order to find smooth solutions, a smoothing technique is used, where optimisation is done with respect to the right hand side of a Poisson type equation.

The objective of this study was to analyse the central concepts of radiography and connections between them, assumed to define the focus of the radiography science. The objective was also to define these concepts theoretically, and to formulate a model defining the focus of radiography science. Radiography refers here to radiographers' professional work, education and radiography science. The concepts of nursing, environment, health and human being were used as starting point for the study, as they are commonly applied, but not clearly defined in radiography. The study was conducted in three phases in accordance with the hybrid method of concept analysis. During the theoretical phase, the theoretical phase model and tentative definitions were developed on the grounds of literature. These were further developed during the empirical phase, as the empirical phase model was formulated on the grounds of empirical data. Data were collected in the form of interviews and written material from selected experts (n = 8). In the analytical phase, theoretical definitions and the model of the focus of radiography science were formulated as a synthesis of the results of former phases. The total number of data was 1,147 pages, and it was analysed with the method of qualitative content analysis. Based on the results, the concept of nursing was substituted with the concept of clinical radiography and radiotherapy, which was defined as radiographer's work within health care. Seamless combination of patient care and service as well as technical usage of radiation and radiation protection was found to be the core of a radiographer's work, aimed at serving the health care field as part of a multiprofessional teamwork. Essential characteristics of the work were found to be theoretical and practical-technical expertise, guiding elements, implementation as a process, and responsibility for safety as well as optimizing decision-making. Environment was defined as the physical and functional environment in health care, cultural environment, cognitive environment, and context of a radiographer's expertise. The concept of health was substituted with the concept of health and illness, which was defined as a holistic and variable state of being that is indirectly affected by radiation. A human being was defined as a dignified individual or community, which is also a holistic and variable being. Connections were found to be positive, negative, characterizing, directing, functional and experimental by nature. On the basis of the results, radiography science could be named the clinical science of radiography and radiotherapy. The model formulated in this study describes the focus of the clinical science of radiography and radiotherapy on a general level. The results may be exploited in the development of the clinical science of radiography and radiotherapy, in theory development and in education within radiography. They may also clarify the identity of this science and understanding regarding it. / Tiivistelmä Tutkimuksen tarkoituksena oli analysoida radiografian keskeisiä käsitteitä ja niiden välisiä yhteyksiä, joiden voidaan olettaa määrittävän radiografiatieteen tutkimuskohdetta. Tarkoituksena oli määritellä käsitteet teoreettisesti sekä muodostaa käsitteiden ja niiden välisten yhteyksien perusteella malli radiografiatieteen tutkimuskohteesta. Radiografialla tarkoitetaan tässä tutkimuksessa röntgenhoitajan työtä ja koulutusta sekä radiografiatiedettä. Lähtökohtana käytettiin hoitotieteen käsitteitä hoitotyö, ympäristö, terveys ja ihminen, joita on radiografiassa käytetty ja sovellettu, mutta ei täsmällisesti määritelty. Tutkimus toteutettiin kolmivaiheisesti hybridisen käsiteanalyysimenetelmän mukaan. Teoreettisessa vaiheessa muodostettiin kirjallisuuden perusteella käsitteiden työmääritelmät ja teoreettisen vaiheen malli. Empiirisessä vaiheessa muodostettiin empiirisen vaiheen malli asiantuntijoilta (n = 8) kerätyn kirjallisen ja haastatteluaineiston perusteella. Analyyttisessä vaiheessa muodostettiin tulosten systemaattiseen vertailuun perustuvana synteesinä käsitteiden teoreettiset määritelmät ja malli radiografiatieteen tutkimuskohteesta. Aineiston kokonaismäärä oli 1147 sivua, ja se analysoitiin laadullisella sisällönanalyysillä. Tutkimuksen tuloksena hoitotyö-käsite korvattiin käsitteellä kliininen röntgenhoitajan työ. Se määriteltiin röntgenhoitajan terveydenhuollossa toteuttamaksi työksi, jonka ydin on teknisen säteilynkäytön ja säteilysuojelun sekä potilaan hoidon ja palvelun saumaton yhdistäminen. Ytimen avulla työ palvelee terveydenhuollon toimintaympäristöä osana moniammatillista tiimityötä. Työn keskeiset ominaisuudet ovat teoreettinen ja käytännöllis-tekninen asiantuntijuus, ohjaavat tekijät, prosessimaisuus sekä turvallisuusvastuu ja optimoiva päätöksenteko. Ympäristö määriteltiin fyysiseksi terveydenhuollon toimintaympäristöksi, kulttuuriympäristöksi, kognitiiviseksi ympäristöksi ja röntgenhoitajan asiantuntijuuden muodostamaksi ympäristöksi. Terveys-käsite korvattiin käsitteellä terveys ja sairaus, joka määriteltiin kokonaisvaltaiseksi ilmiöksi ja muuttuvaksi tilaksi, jonka kannalta keskeisiä ovat säteilyn välilliset vaikutukset. Ihminen määriteltiin arvokkaaksi yksilöksi tai yhteisöksi, joka on kokonaisvaltainen ja muuttuva olento. Käsitteiden väliset yhteydet voivat olla positiivisia, negatiivisia, luonnehtivia ja ohjaavia yhteyksiä sekä tekemis- ja kokemisyhteyksiä. Tulosten perusteella radiografiatieteen nimeksi sopisi kliininen radiografiatiede. Tutkimuksessa tuotettu malli määrittää kliinisen radiografiatieteen tutkimuskohdetta yleisluontoisesti. Tuloksia voidaan hyödyntää lähinnä kliinisen radiografiatieteen kehittämisessä, teorianmuodostuksessa ja radiografian koulutuksessa. Tulokset voivat myös auttaa selkeyttämään kliinisen radiografiatieteen identiteettiä ja lisäämään sitä koskevaa ymmärrystä.

In this thesis we study stochastic modeling and simulation methods for biochemical systems. The thesis is focused on systems with multi-state and multi-scale features and divided into two parts. In the first part, we propose new algorithms that improve existing multi-state simulation methods. We first compare the well known Gillespie\\\'s stochastic simulation algorithm (SSA) with the StochSim, an agent-based simulation method. Based on the analysis, we propose a hybrid method that possesses the advantages of both methods. Then we propose two new methods that extend the Network-Free Algorithm (NFA) for rule-based models. Numerical results are provided to show the performance improvement by our new methods. In the second part, we investigate two simulation schemes for the multi-scale feature: Haseltine and Rawlings\\\' hybrid method and the quasi-steady-state stochastic simulation method. We first propose an efficient partitioning strategy for the hybrid method and an efficient way of building stochastic cell cycle models with this new partitioning strategy. Then, to understand conditions where the two simulation methods can be applied, we develop a way to estimate the relaxation time of the fast sub-network, and compare it with the firing interval of the slow sub-network. Our analysis are verified by numerical experiments on different realistic biochemical models. / Ph. D.

In this thesis we study modeling and simulation approaches for multiscale biochemical systems. The thesis addresses both modeling methods and simulation strategies. In the first part, we propose modeling methods to study the behavior of the insulin secretion pathway. We first expand the single cell model proposed by Bertram et. al. to model multiple cells. Synchronization among multiple cells is observed. Then an unhealthy cell model is proposed to study the insulin secretion failure caused by weakening of mitochondria function. By studying the interaction between the healthy and unhealthy cells, we find that the insulin secretion can be reinstated by increasing the glucokinase level. This new discovery sheds light on antidiabetic medication. In order to study the stochastic dynamics of the insulin secretion pathway, we first apply the hybrid method to model the discrete events in the insulin secretion pathway. Based on the hybrid model, a probability based measurement is proposed and applied to test the new antidiabetic remedy. In the second part, we focus on different simulation schemes for multiscale biochemical systems. We first propose a partitioning strategy for the hybrid method which leads to an efficient way of building stochastic cell cycle models. Then different implementation methods for the hybrid method are studied. A root finding method based on inverse interpolation is introduced to implement the hybrid method with three different ODE solvers. A detailed discussion of the performance of these three ODE solvers is presented. Last, we propose a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. The efficiency is demonstrated by applying this new strategy on a stiff decaying dimerization model and a heat shock protein regulation model. / Ph. D.

Gillespie's stochastic simulation algorithm (SSA) has been a conventional method for stochastic modeling and simulation of biochemical systems. However, its population-based scheme faces the challenge from multi-state situations in many biochemical models. To tackle this problem, Morton-Firth and Bray's stochastic simulator (StochSim) was proposed with a particle-based scheme. The thesis first provides a detailed comparison between these two methods, and then proposes improvements on StochSim and a hybrid method to combine the advantages of the two methods. Analysis and numerical experiment results demonstrate that the hybrid method exhibits extraordinary performance for systems with both the multi-state feature and a high total population. In order to deal with the combinatorial complexity caused by the multi-state situation, the rules-based modeling was proposed by Hlavacek's group and the particle-based Network-Free Algorithm (NFA) has been used for its simulation. In this thesis, we improve the NFA so that it has both the population-based and particle-based features. We also propose a population-based method for simulation of the rule-based models. The bacterial chemotaxis model has served as a good biological example involving multi-state species. We implemented different simulation methods on this model. Then we constructed a graphical interface and compared the behaviors of the bacterium under different mechanisms, including simplified mathematical models and chemically reacting networks which are simulated stochastically. / Master of Science

Modeling the single-scattering properties of nonspherical particles in the atmo¬sphere (in particular, ice crystals and dust aerosols) has important applications to climate and remote sensing studies. The first part of the dissertation (Chapters II¬V) reports a combination of exact numerical methods, including the finite-difference time-domain (FDTD), the discrete-dipole-approximation (DDA), and the T-matrix methods, and an approximate method-the physical-geometric optics hybrid (PGOH) method-in the computation of the optical properties of the non-spherical particles in a complete range of size parameters. The major advancements are made on the modeling capabilities of the PGOH method, and the knowledge of the electromag¬netic tunneling effect – a semi-classical scattering effect. This research is important to obtain reliable optical properties of nonspherical particles in a complete range of size parameters with satisfactory accuracy and computational efficiency. The second part (Chapters VI-VII) of the dissertation is to investigate the de¬pendence of the optical properties of ice crystals and mineral dust aerosols in the atmosphere on the spectrum, the particle size and the morphology based on compu¬tational models. Ice crystals in the atmosphere can be classified to be simple regular faceted particles (such as hexagon columns, plates, etc.) and imperfect ice crystals. Modeling of the scattering by regular ice crystals is straightforward, as their morphologies can be easily defined. For imperfect ice crystals, the morphology is quite diverse, which complicates the modeling process. We present an effective approach of using irregular faceted particle to characterize the imperfectness of ice crystals. As an example of application, less-than-unity backscattering color ratio of cirrus clouds is demonstrated and explained theoretically, which provides guidance in the calibra¬tion algorithm for 1.064-µm channel on the Calipso lidar. Dust aerosols have no particular morphology. To develop an approach to modeling the optical properties of realistic dust particles, the principle of using simple shapes (triaxial ellipsoids and nonsymmetric hexahedra) to represent irregular dust particles is explored. Simulated results have been compared with those measured in laboratory for several realistic aerosol samples. Agreement between simulated results and measurement suggests the potential applicability of the two aforementioned aerosol models. We also show the potential impact of the present study to passive and active atmospheric remote sensing and future research works.

A new whole-core transport method is described for 3-D hexagonal geometry. This is an extension of a stochastic-deterministic hybrid method which has previously been shown highly accurate and efficient for eigenvalue problems. Via Monte Carlo, it determines the solution to the transport equation in sub-regions of reactor cores, such as individual fuel elements or sections thereof, and uses those solutions to compose a library of response expansion coefficients. The information acquired allows the deterministic solution procedure to arrive at the whole core solution for the eigenvalue and the explicit fuel pin fission density distribution more quickly than other transport methods. Because it solves the transport equation stochastically, complicated geometry may be modeled exactly and therefore heterogeneity even at the most detailed level does not challenge the method. In this dissertation, the method is evaluated using comparisons with full core Monte Carlo reference solutions of benchmark problems based on gas-cooled, graphite-moderated reactor core designs. Solutions are given for core eigenvalue problems, the calculation of fuel pin fission densities throughout the core, and the determination of incremental control rod worth. Using a single processor, results are found in minutes for small cores, and in no more than a few hours for a realistically large core. Typical eigenvalues calculated by the method differ from reference solutions by less than 0.1%, and pin fission density calculations have average accuracy of well within 1%, even for unrealistically challenging core configuration problems. This new method enables the accurate determination of core eigenvalues and flux shapes in hexagonal cores with efficiency far exceeding that of other transport methods.

Um método híbrido aplicado é proposto para um problema inverso que trata de uma cavidade tridimensional preenchida com meio transparente. As paredes são assumidas cinza e difusas, e o único mecanismo de transferência de calor presente é a radiação térmica. É um caso idealizado, mas que encontra ampla aplicação em sistemas de engenharia. Prescrevem-se duas condições de contorno na base da cavidade – temperatura e fluxo de calor – e, para satisfazêlas, buscam-se o fluxo de calor e a distribuição espacial dos aquecedores. Na superfície superior, que contêm os aquecedores, nenhuma condição de contorno é imposta. Este tipo de problema, quando solucionado através de técnicas convencionais, envolve um procedimento de tentativa e erro, que, além de demandar um elevado tempo computacional, conduz a resultados pouco precisos. Na análise inversa, opta-se por otimização ou pela aplicação de um método de regularização, pois o problema resultante é mal condicionado por envolver a equação integral de Fredholm de primeira espécie. Neste trabalho, optou-se por acoplar otimização e regularização como uma alternativa baseada no emprego distinto dessas duas formas de abordagem. A tarefa de busca por posições para os aquecedores ficou por conta do método da Otimização Extrema Generalizada, enquanto o método de regularização da Decomposição em Valores Singulares Truncada calcula o fluxo de calor dos aquecedores para cada configuração gerada pelo processo de otimização. A aplicação da técnica híbrida conduziu a resultados mais precisos do que aqueles que normalmente se obtêm apenas com regularização, reduzindo consideravelmente o tempo computacional da solução baseada apenas na otimização. / This work considers the inverse analysis in a three-dimensional rectangular enclosure with diffuse-gray surfaces. The locations and powers of the heaters sources are left unconstrained and two conditions are imposed on the design surface – uniform heat flux and temperature distributions. The solution to this kind of problem by conventional techniques is possible only with trial-and-error procedure and in this case, the forward solution will be run oftentimes without guarantee to find out a good answer. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A new solution procedure – termed hybrid solution – which couples two methods, the Generalized Extremal Optimization (GEO) and the Truncated Singular Value Decomposition (TSVD) is proposed. The search of locations is treated as an optimization problem, by GEO algorithm, whereas the solution of the system equation, that embodies the Fredholm integral equation of first kind and, therefore, is expected to be ill-conditioned, is build up through a TSVD regularization method. The hybrid method provides better results than TSVD and, when compared with GEO, reduces the computational time substantially.

Um método híbrido aplicado é proposto para um problema inverso que trata de uma cavidade tridimensional preenchida com meio transparente. As paredes são assumidas cinza e difusas, e o único mecanismo de transferência de calor presente é a radiação térmica. É um caso idealizado, mas que encontra ampla aplicação em sistemas de engenharia. Prescrevem-se duas condições de contorno na base da cavidade – temperatura e fluxo de calor – e, para satisfazêlas, buscam-se o fluxo de calor e a distribuição espacial dos aquecedores. Na superfície superior, que contêm os aquecedores, nenhuma condição de contorno é imposta. Este tipo de problema, quando solucionado através de técnicas convencionais, envolve um procedimento de tentativa e erro, que, além de demandar um elevado tempo computacional, conduz a resultados pouco precisos. Na análise inversa, opta-se por otimização ou pela aplicação de um método de regularização, pois o problema resultante é mal condicionado por envolver a equação integral de Fredholm de primeira espécie. Neste trabalho, optou-se por acoplar otimização e regularização como uma alternativa baseada no emprego distinto dessas duas formas de abordagem. A tarefa de busca por posições para os aquecedores ficou por conta do método da Otimização Extrema Generalizada, enquanto o método de regularização da Decomposição em Valores Singulares Truncada calcula o fluxo de calor dos aquecedores para cada configuração gerada pelo processo de otimização. A aplicação da técnica híbrida conduziu a resultados mais precisos do que aqueles que normalmente se obtêm apenas com regularização, reduzindo consideravelmente o tempo computacional da solução baseada apenas na otimização. / This work considers the inverse analysis in a three-dimensional rectangular enclosure with diffuse-gray surfaces. The locations and powers of the heaters sources are left unconstrained and two conditions are imposed on the design surface – uniform heat flux and temperature distributions. The solution to this kind of problem by conventional techniques is possible only with trial-and-error procedure and in this case, the forward solution will be run oftentimes without guarantee to find out a good answer. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A new solution procedure – termed hybrid solution – which couples two methods, the Generalized Extremal Optimization (GEO) and the Truncated Singular Value Decomposition (TSVD) is proposed. The search of locations is treated as an optimization problem, by GEO algorithm, whereas the solution of the system equation, that embodies the Fredholm integral equation of first kind and, therefore, is expected to be ill-conditioned, is build up through a TSVD regularization method. The hybrid method provides better results than TSVD and, when compared with GEO, reduces the computational time substantially.