979 resultados para optimization models


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Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

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This thesis considers optimization problems arising in printed circuit board assembly. Especially, the case in which the electronic components of a single circuit board are placed using a single placement machine is studied. Although there is a large number of different placement machines, the use of collect-and-place -type gantry machines is discussed because of their flexibility and increasing popularity in the industry. Instead of solving the entire control optimization problem of a collect-andplace machine with a single application, the problem is divided into multiple subproblems because of its hard combinatorial nature. This dividing technique is called hierarchical decomposition. All the subproblems of the one PCB - one machine -context are described, classified and reviewed. The derived subproblems are then either solved with exact methods or new heuristic algorithms are developed and applied. The exact methods include, for example, a greedy algorithm and a solution based on dynamic programming. Some of the proposed heuristics contain constructive parts while others utilize local search or are based on frequency calculations. For the heuristics, it is made sure with comprehensive experimental tests that they are applicable and feasible. A number of quality functions will be proposed for evaluation and applied to the subproblems. In the experimental tests, artificially generated data from Markov-models and data from real-world PCB production are used. The thesis consists of an introduction and of five publications where the developed and used solution methods are described in their full detail. For all the problems stated in this thesis, the methods proposed are efficient enough to be used in the PCB assembly production in practice and are readily applicable in the PCB manufacturing industry.

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This study aims to optimize an alternative method of extraction of carrageenan without previous alkaline treatment and ethanol precipitation using Response Surface Methodology (RSM). In order to introduce an innovation in the isolation step, atomization drying was used reducing the time for obtaining dry carrageenan powder. The effects of extraction time and temperature on yield, gel strength, and viscosity were evaluated. Furthermore, the extracted material was submitted to structural analysis, by infrared spectroscopy and nuclear magnetic resonance spectroscopy (¹H-NMR), and chemical composition analysis. Results showed that the generated regression models adequately explained the data variation. Carrageenan yield and gel viscosity were influenced only by the extraction temperature. However, gel strength was influenced by both, extraction time and extraction temperature. Optimal extraction conditions were 74 ºC and 4 hours. In these conditions, the carrageenan extract properties determined by the polynomial model were 31.17%, 158.27 g.cm-2, and 29.5 cP for yield, gel strength, and viscosity, respectively, while under the experimental conditions they were 35.8 ± 4.68%, 112.50 ± 4.96 g.cm-2, and 16.01 ± 1.03 cP, respectively. The chemical composition, nuclear magnetic resonance spectroscopy, and infrared spectroscopy analyses showed that the crude carrageenan extracted is composed mainly of κ-carrageenan.

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This study aimed to define the process conditions to obtain snacks from the by-products of rice and soybean with physical characteristics suitable for marketing. Therefore, the effects of moisture and extrusion temperature on the expansion and color of the products obtained experimentally obtained were evaluated, and the proximate composition of the by-products and that of the snack with greater desirability were determined. Response surface methodology and rotational central composite design were used, and desirability test based on the regression models adjusted was applied. The most desirable snack, with the highest expansion index (3.39), specific volume (13.5 mL.g-1), and the chromaticity coordinate a* (2.79), was obtained under 12 g.100 g-1 moisture and 85ºC of temperature in the third zone of the extruder. The snack produced under these conditions attained content of protein and lipid content 41 and 64% higher than that of the traditional corn snack. It can be concluded that producing extruded snack made form a mixture of broken grains, rice bran, and soybean okara (81:9:10) is technologically feasible, enabling the development of a new product with good nutritional value that can improve the diet of children, the main consumers of this type of food.

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AbstractOptimization of microwave drying conditions of Luvhele and Mabonde banana varieties were studied using response surface methodology. The drying was performed using a central composite rotatable design for two variables: microwave power level (100, 200 and 300 W) and drying time (40, 26, and 12 min.) for Luvhele; (100, 200 and 300 W) and (42, 27, and 12 min) for Mabonde. The colour and texture (hardness) data were analyzed using ANOVA and regression analysis. The fitness of the models obtained was good as the lack of fit for each of the models was not significant. The coefficient of determination R2 of the models was relatively high, hence the models obtained for the responses were adequate and acceptable. Drying conditions of 178.76 W, 12 min. drying time were found optimum for product quality at a desirability of 0.91 for Luvhele; while 127.67 W, 12 min. with a desirability of 0.86 was predicted for Mabonde. The result of this study could be used as a standard for microwave processing of Luvhele and Mabondebanana varieties.

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In the industry of the case company, transportation and warehousing costs account for more than 10% of the total cost which is more than on average. A Finnish company has an understanding that by sending larger shipments in parcels, they could save tens of thousands of euros annually in freight costs in Finland’s domestic shipments. To achieve these savings and optimize total logistics cost, company’s interest is to find out which is the cost efficient way of shipping road shipments of certain volumes; in parcel boxes or on pallets, and what should be the split volume determining the shipment type. Distribution center (DC) costs affect this decision and therefore they need to be also evaluated to determine the total logistics cost savings. Main results were achieved by executing activity-based costing-calculations including DC and road freight costs to determine the ideal split volume with which the total logistics cost is optimal. Calculations were done for Finland’s DC, separately for two main road freight destinations, Finland and Sweden, which cover 50% of road shipment spend. Data for calculations was collected both manually and automatically from various internal and external sources, such as the company ERP system and logistics service providers’ (LSP) reporting. DC processes were studied in practice and compared to model processes. Currently used freight rates were compared to existing pricing models and freight service tendering process was evaluated by participating in the process and comparing it to the models based on literature. The results show that the potential savings are not as significant as the company hoped for, mainly because of packing work increasing DC labor cost. Annual savings by setting ideal split volume per country would account for 0,4 % of the warehousing and transportation costs of shipments in scope of this thesis. Split volume should be set separately for each route, mainly because the pricing model for road freight is different in each country. For some routes bigger parcels should be sent but for some routes pallets should be used more. Next step is to do these calculations for remaining routes to determine total savings potential. Other findings show that the processes in the DC are designed well and the company could achieve savings by executing tenders more efficiently. Company should also pay more attention to parcel pricing and packing the shipments accordingly.

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Liberalization of electricity markets has resulted in a competed Nordic electricity market, in which electricity retailers play a key role as electricity suppliers, market intermediaries, and service providers. Although these roles may remain unchanged in the near future, the retailers’ operation may change fundamentally as a result of the emerging smart grid environment. Especially the increasing amount of distributed energy resources (DER), and improving opportunities for their control, are reshaping the operating environment of the retailers. This requires that the retailers’ operation models are developed to match the operating environment, in which the active use of DER plays a major role. Electricity retailers have a clientele, and they operate actively in the electricity markets, which makes them a natural market party to offer new services for end-users aiming at an efficient and market-based use of DER. From the retailer’s point of view, the active use of DER can provide means to adapt the operation to meet the challenges posed by the smart grid environment, and to pursue the ultimate objective of the retailer, which is to maximize the profit of operation. This doctoral dissertation introduces a methodology for the comprehensive use of DER in an electricity retailer’s short-term profit optimization that covers operation in a variety of marketplaces including day-ahead, intra-day, and reserve markets. The analysis results provide data of the key profit-making opportunities and the risks associated with different types of DER use. Therefore, the methodology may serve as an efficient tool for an experienced operator in the planning of the optimal market-based DER use. The key contributions of this doctoral dissertation lie in the analysis and development of the model that allows the retailer to benefit from profit-making opportunities brought by the use of DER in different marketplaces, but also to manage the major risks involved in the active use of DER. In addition, the dissertation introduces an analysis of the economic potential of DER control actions in different marketplaces including the day-ahead Elspot market, balancing power market, and the hourly market of Frequency Containment Reserve for Disturbances (FCR-D).

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This paper aims at reconciling the evidence that sophisticated valuation models are increasingly used by companies in their investment appraisal with the literature of bounded rationality, according to which objective optimization is impracticable in the real world because it would demand an immense level of sophistication of the analytical and computational processes of human beings. We show how normative valuation models should rather be viewed as forms of reality representation, frameworks according to which the real world is perceived, fragmented for a better understanding, and recomposed, providing an orderly method for undertaking a task as complex as the investment decision.

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La survie des réseaux est un domaine d'étude technique très intéressant ainsi qu'une préoccupation critique dans la conception des réseaux. Compte tenu du fait que de plus en plus de données sont transportées à travers des réseaux de communication, une simple panne peut interrompre des millions d'utilisateurs et engendrer des millions de dollars de pertes de revenu. Les techniques de protection des réseaux consistent à fournir une capacité supplémentaire dans un réseau et à réacheminer les flux automatiquement autour de la panne en utilisant cette disponibilité de capacité. Cette thèse porte sur la conception de réseaux optiques intégrant des techniques de survie qui utilisent des schémas de protection basés sur les p-cycles. Plus précisément, les p-cycles de protection par chemin sont exploités dans le contexte de pannes sur les liens. Notre étude se concentre sur la mise en place de structures de protection par p-cycles, et ce, en supposant que les chemins d'opération pour l'ensemble des requêtes sont définis a priori. La majorité des travaux existants utilisent des heuristiques ou des méthodes de résolution ayant de la difficulté à résoudre des instances de grande taille. L'objectif de cette thèse est double. D'une part, nous proposons des modèles et des méthodes de résolution capables d'aborder des problèmes de plus grande taille que ceux déjà présentés dans la littérature. D'autre part, grâce aux nouveaux algorithmes, nous sommes en mesure de produire des solutions optimales ou quasi-optimales. Pour ce faire, nous nous appuyons sur la technique de génération de colonnes, celle-ci étant adéquate pour résoudre des problèmes de programmation linéaire de grande taille. Dans ce projet, la génération de colonnes est utilisée comme une façon intelligente d'énumérer implicitement des cycles prometteurs. Nous proposons d'abord des formulations pour le problème maître et le problème auxiliaire ainsi qu'un premier algorithme de génération de colonnes pour la conception de réseaux protegées par des p-cycles de la protection par chemin. L'algorithme obtient de meilleures solutions, dans un temps raisonnable, que celles obtenues par les méthodes existantes. Par la suite, une formulation plus compacte est proposée pour le problème auxiliaire. De plus, nous présentons une nouvelle méthode de décomposition hiérarchique qui apporte une grande amélioration de l'efficacité globale de l'algorithme. En ce qui concerne les solutions en nombres entiers, nous proposons deux méthodes heurisiques qui arrivent à trouver des bonnes solutions. Nous nous attardons aussi à une comparaison systématique entre les p-cycles et les schémas classiques de protection partagée. Nous effectuons donc une comparaison précise en utilisant des formulations unifiées et basées sur la génération de colonnes pour obtenir des résultats de bonne qualité. Par la suite, nous évaluons empiriquement les versions orientée et non-orientée des p-cycles pour la protection par lien ainsi que pour la protection par chemin, dans des scénarios de trafic asymétrique. Nous montrons quel est le coût de protection additionnel engendré lorsque des systèmes bidirectionnels sont employés dans de tels scénarios. Finalement, nous étudions une formulation de génération de colonnes pour la conception de réseaux avec des p-cycles en présence d'exigences de disponibilité et nous obtenons des premières bornes inférieures pour ce problème.

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Parmi les méthodes d’estimation de paramètres de loi de probabilité en statistique, le maximum de vraisemblance est une des techniques les plus populaires, comme, sous des conditions l´egères, les estimateurs ainsi produits sont consistants et asymptotiquement efficaces. Les problèmes de maximum de vraisemblance peuvent être traités comme des problèmes de programmation non linéaires, éventuellement non convexe, pour lesquels deux grandes classes de méthodes de résolution sont les techniques de région de confiance et les méthodes de recherche linéaire. En outre, il est possible d’exploiter la structure de ces problèmes pour tenter d’accélerer la convergence de ces méthodes, sous certaines hypothèses. Dans ce travail, nous revisitons certaines approches classiques ou récemment d´eveloppées en optimisation non linéaire, dans le contexte particulier de l’estimation de maximum de vraisemblance. Nous développons également de nouveaux algorithmes pour résoudre ce problème, reconsidérant différentes techniques d’approximation de hessiens, et proposons de nouvelles méthodes de calcul de pas, en particulier dans le cadre des algorithmes de recherche linéaire. Il s’agit notamment d’algorithmes nous permettant de changer d’approximation de hessien et d’adapter la longueur du pas dans une direction de recherche fixée. Finalement, nous évaluons l’efficacité numérique des méthodes proposées dans le cadre de l’estimation de modèles de choix discrets, en particulier les modèles logit mélangés.

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Les centres d’appels sont des éléments clés de presque n’importe quelle grande organisation. Le problème de gestion du travail a reçu beaucoup d’attention dans la littérature. Une formulation typique se base sur des mesures de performance sur un horizon infini, et le problème d’affectation d’agents est habituellement résolu en combinant des méthodes d’optimisation et de simulation. Dans cette thèse, nous considérons un problème d’affection d’agents pour des centres d’appels soumis a des contraintes en probabilité. Nous introduisons une formulation qui exige que les contraintes de qualité de service (QoS) soient satisfaites avec une forte probabilité, et définissons une approximation de ce problème par moyenne échantillonnale dans un cadre de compétences multiples. Nous établissons la convergence de la solution du problème approximatif vers celle du problème initial quand la taille de l’échantillon croit. Pour le cas particulier où tous les agents ont toutes les compétences (un seul groupe d’agents), nous concevons trois méthodes d’optimisation basées sur la simulation pour le problème de moyenne échantillonnale. Étant donné un niveau initial de personnel, nous augmentons le nombre d’agents pour les périodes où les contraintes sont violées, et nous diminuons le nombre d’agents pour les périodes telles que les contraintes soient toujours satisfaites après cette réduction. Des expériences numériques sont menées sur plusieurs modèles de centre d’appels à faible occupation, au cours desquelles les algorithmes donnent de bonnes solutions, i.e. la plupart des contraintes en probabilité sont satisfaites, et nous ne pouvons pas réduire le personnel dans une période donnée sont introduire de violation de contraintes. Un avantage de ces algorithmes, par rapport à d’autres méthodes, est la facilité d’implémentation.

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L’apprentissage supervisé de réseaux hiérarchiques à grande échelle connaît présentement un succès fulgurant. Malgré cette effervescence, l’apprentissage non-supervisé représente toujours, selon plusieurs chercheurs, un élément clé de l’Intelligence Artificielle, où les agents doivent apprendre à partir d’un nombre potentiellement limité de données. Cette thèse s’inscrit dans cette pensée et aborde divers sujets de recherche liés au problème d’estimation de densité par l’entremise des machines de Boltzmann (BM), modèles graphiques probabilistes au coeur de l’apprentissage profond. Nos contributions touchent les domaines de l’échantillonnage, l’estimation de fonctions de partition, l’optimisation ainsi que l’apprentissage de représentations invariantes. Cette thèse débute par l’exposition d’un nouvel algorithme d'échantillonnage adaptatif, qui ajuste (de fa ̧con automatique) la température des chaînes de Markov sous simulation, afin de maintenir une vitesse de convergence élevée tout au long de l’apprentissage. Lorsqu’utilisé dans le contexte de l’apprentissage par maximum de vraisemblance stochastique (SML), notre algorithme engendre une robustesse accrue face à la sélection du taux d’apprentissage, ainsi qu’une meilleure vitesse de convergence. Nos résultats sont présent ́es dans le domaine des BMs, mais la méthode est générale et applicable à l’apprentissage de tout modèle probabiliste exploitant l’échantillonnage par chaînes de Markov. Tandis que le gradient du maximum de vraisemblance peut-être approximé par échantillonnage, l’évaluation de la log-vraisemblance nécessite un estimé de la fonction de partition. Contrairement aux approches traditionnelles qui considèrent un modèle donné comme une boîte noire, nous proposons plutôt d’exploiter la dynamique de l’apprentissage en estimant les changements successifs de log-partition encourus à chaque mise à jour des paramètres. Le problème d’estimation est reformulé comme un problème d’inférence similaire au filtre de Kalman, mais sur un graphe bi-dimensionnel, où les dimensions correspondent aux axes du temps et au paramètre de température. Sur le thème de l’optimisation, nous présentons également un algorithme permettant d’appliquer, de manière efficace, le gradient naturel à des machines de Boltzmann comportant des milliers d’unités. Jusqu’à présent, son adoption était limitée par son haut coût computationel ainsi que sa demande en mémoire. Notre algorithme, Metric-Free Natural Gradient (MFNG), permet d’éviter le calcul explicite de la matrice d’information de Fisher (et son inverse) en exploitant un solveur linéaire combiné à un produit matrice-vecteur efficace. L’algorithme est prometteur: en terme du nombre d’évaluations de fonctions, MFNG converge plus rapidement que SML. Son implémentation demeure malheureusement inefficace en temps de calcul. Ces travaux explorent également les mécanismes sous-jacents à l’apprentissage de représentations invariantes. À cette fin, nous utilisons la famille de machines de Boltzmann restreintes “spike & slab” (ssRBM), que nous modifions afin de pouvoir modéliser des distributions binaires et parcimonieuses. Les variables latentes binaires de la ssRBM peuvent être rendues invariantes à un sous-espace vectoriel, en associant à chacune d’elles, un vecteur de variables latentes continues (dénommées “slabs”). Ceci se traduit par une invariance accrue au niveau de la représentation et un meilleur taux de classification lorsque peu de données étiquetées sont disponibles. Nous terminons cette thèse sur un sujet ambitieux: l’apprentissage de représentations pouvant séparer les facteurs de variations présents dans le signal d’entrée. Nous proposons une solution à base de ssRBM bilinéaire (avec deux groupes de facteurs latents) et formulons le problème comme l’un de “pooling” dans des sous-espaces vectoriels complémentaires.

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Data mining is one of the hottest research areas nowadays as it has got wide variety of applications in common man’s life to make the world a better place to live. It is all about finding interesting hidden patterns in a huge history data base. As an example, from a sales data base, one can find an interesting pattern like “people who buy magazines tend to buy news papers also” using data mining. Now in the sales point of view the advantage is that one can place these things together in the shop to increase sales. In this research work, data mining is effectively applied to a domain called placement chance prediction, since taking wise career decision is so crucial for anybody for sure. In India technical manpower analysis is carried out by an organization named National Technical Manpower Information System (NTMIS), established in 1983-84 by India's Ministry of Education & Culture. The NTMIS comprises of a lead centre in the IAMR, New Delhi, and 21 nodal centres located at different parts of the country. The Kerala State Nodal Centre is located at Cochin University of Science and Technology. In Nodal Centre, they collect placement information by sending postal questionnaire to passed out students on a regular basis. From this raw data available in the nodal centre, a history data base was prepared. Each record in this data base includes entrance rank ranges, reservation, Sector, Sex, and a particular engineering. From each such combination of attributes from the history data base of student records, corresponding placement chances is computed and stored in the history data base. From this data, various popular data mining models are built and tested. These models can be used to predict the most suitable branch for a particular new student with one of the above combination of criteria. Also a detailed performance comparison of the various data mining models is done.This research work proposes to use a combination of data mining models namely a hybrid stacking ensemble for better predictions. A strategy to predict the overall absorption rate for various branches as well as the time it takes for all the students of a particular branch to get placed etc are also proposed. Finally, this research work puts forward a new data mining algorithm namely C 4.5 * stat for numeric data sets which has been proved to have competent accuracy over standard benchmarking data sets called UCI data sets. It also proposes an optimization strategy called parameter tuning to improve the standard C 4.5 algorithm. As a summary this research work passes through all four dimensions for a typical data mining research work, namely application to a domain, development of classifier models, optimization and ensemble methods.

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Post-transcriptional gene silencing by RNA interference is mediated by small interfering RNA called siRNA. This gene silencing mechanism can be exploited therapeutically to a wide variety of disease-associated targets, especially in AIDS, neurodegenerative diseases, cholesterol and cancer on mice with the hope of extending these approaches to treat humans. Over the recent past, a significant amount of work has been undertaken to understand the gene silencing mediated by exogenous siRNA. The design of efficient exogenous siRNA sequences is challenging because of many issues related to siRNA. While designing efficient siRNA, target mRNAs must be selected such that their corresponding siRNAs are likely to be efficient against that target and unlikely to accidentally silence other transcripts due to sequence similarity. So before doing gene silencing by siRNAs, it is essential to analyze their off-target effects in addition to their inhibition efficiency against a particular target. Hence designing exogenous siRNA with good knock-down efficiency and target specificity is an area of concern to be addressed. Some methods have been developed already by considering both inhibition efficiency and off-target possibility of siRNA against agene. Out of these methods, only a few have achieved good inhibition efficiency, specificity and sensitivity. The main focus of this thesis is to develop computational methods to optimize the efficiency of siRNA in terms of “inhibition capacity and off-target possibility” against target mRNAs with improved efficacy, which may be useful in the area of gene silencing and drug design for tumor development. This study aims to investigate the currently available siRNA prediction approaches and to devise a better computational approach to tackle the problem of siRNA efficacy by inhibition capacity and off-target possibility. The strength and limitations of the available approaches are investigated and taken into consideration for making improved solution. Thus the approaches proposed in this study extend some of the good scoring previous state of the art techniques by incorporating machine learning and statistical approaches and thermodynamic features like whole stacking energy to improve the prediction accuracy, inhibition efficiency, sensitivity and specificity. Here, we propose one Support Vector Machine (SVM) model, and two Artificial Neural Network (ANN) models for siRNA efficiency prediction. In SVM model, the classification property is used to classify whether the siRNA is efficient or inefficient in silencing a target gene. The first ANNmodel, named siRNA Designer, is used for optimizing the inhibition efficiency of siRNA against target genes. The second ANN model, named Optimized siRNA Designer, OpsiD, produces efficient siRNAs with high inhibition efficiency to degrade target genes with improved sensitivity-specificity, and identifies the off-target knockdown possibility of siRNA against non-target genes. The models are trained and tested against a large data set of siRNA sequences. The validations are conducted using Pearson Correlation Coefficient, Mathews Correlation Coefficient, Receiver Operating Characteristic analysis, Accuracy of prediction, Sensitivity and Specificity. It is found that the approach, OpsiD, is capable of predicting the inhibition capacity of siRNA against a target mRNA with improved results over the state of the art techniques. Also we are able to understand the influence of whole stacking energy on efficiency of siRNA. The model is further improved by including the ability to identify the “off-target possibility” of predicted siRNA on non-target genes. Thus the proposed model, OpsiD, can predict optimized siRNA by considering both “inhibition efficiency on target genes and off-target possibility on non-target genes”, with improved inhibition efficiency, specificity and sensitivity. Since we have taken efforts to optimize the siRNA efficacy in terms of “inhibition efficiency and offtarget possibility”, we hope that the risk of “off-target effect” while doing gene silencing in various bioinformatics fields can be overcome to a great extent. These findings may provide new insights into cancer diagnosis, prognosis and therapy by gene silencing. The approach may be found useful for designing exogenous siRNA for therapeutic applications and gene silencing techniques in different areas of bioinformatics.

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Diese Arbeit umfaßt das elektromechanische Design und die Designoptimierung von weit durchstimmbaren optischen multimembranbasierten Bauelementen, mit vertikal orientierten Kavitäten, basierend auf der Finiten Element Methode (FEM). Ein multimembran InP/Luft Fabry-Pérot optischer Filter wird dargestellt und umfassend analysiert. In dieser Arbeit wird ein systematisches strukturelles Designverfahren dargestellt. Genaue analytische elektromechanischer Modelle für die Bauelemente sind abgeleitet worden. Diese können unschätzbare Werkzeuge sein, um am Anfang der Designphase schnell einen klaren Einblick zur Verfügung zu stellen. Mittels des FEM Programms ist der durch die nicht-lineare Verspannung hervorgerufene versteifende Effekt nachgeforscht und sein Effekt auf die Verlängerung der mechanischen Durchstimmungsstrecke der Bauelemente demonstriert worden. Interessant war auch die Beobachtung, dass die normierte Relation zwischen Ablenkung und Spannung ein unveränderliches Profil hat. Die Deformation der Membranflächen der in dieser Arbeit dargestellten Bauelementformen erwies sich als ein unerwünschter, jedoch manchmal unvermeidbarer Effekt. Es zeigt sich aber, dass die Wahl der Größe der strukturellen Dimensionen den Grad der Membrandeformation im Falle der Aktuation beeinflusst. Diese Arbeit stellt ein elektromechanisches in FEMLAB implementierte quasi-3D Modell, das allgemein für die Modellierung dünner Strukturen angewendet werden kann, dar; und zwar indem man diese als 2D-Objekte betrachtet und die dritte Dimension als eine konstante Größe (z.B. die Schichtdicke) oder eine Größe, welche eine mathematische Funktion ist, annimmt. Diese Annahme verringert drastisch die Berechnungszeit sowie den erforderlichen Arbeitsspeicherbedarf. Weiter ist es für die Nachforschung des Effekts der Skalierung der durchstimmbaren Bauelemente verwendet worden. Eine neuartige Skalierungstechnik wurde abgeleitet und verwendet. Die Ergebnisse belegen, dass das daraus resultierende, skalierte Bauelement fast genau die gleiche mechanische Durchstimmung wie das unskalierte zeigt. Die Einbeziehung des Einflusses von axialen Verspannungen und Gradientenverspannungen in die Berechnungen erforderte die Änderung der Standardimplementierung des 3D Mechanikberechnungsmodus, der mit der benutzten FEM Software geliefert wurde. Die Ergebnisse dieser Studie zeigen einen großen Einfluss der Verspannung auf die Durchstimmungseigenschaften der untersuchten Bauelemente. Ferner stimmten die Ergebnisse der theoretischen Modellrechnung mit den experimentellen Resultaten sehr gut überein.