Generating functions are important tools that are used in many areas of mathematics and especially statistics. Besides analyzing the general structure of sequences and their asymptotic behavior / these functions, which can be roughly thought as the transformation of sequences into functions, are also used effciently to solve combinatorial problems. In this thesis, the effects of the transformations of generating functions on their corresponding sequences and the effects of the change in sequences on the generating functions are examined. With these knowledge, the generating functions for the resulting sequence of some combinatorial problems such as number of partitions, number of involutions, Fibonacci numbers and Catalan numbers are found. Moreover, some mathematical identities are proved by using generating functions. The sequences are the bases of especially symmetric key cryptosystems in cryptography. It is seen that by using generating functions, linear complexities and periods of sequences generated by constant coeffcient linear homogeneous recursions, which are used in linear feedback shift register (LFSR) based stream ciphers, can be calculated. Hence studying generating functions leads to have a better understanding in them. Therefore, besides combinatorial problems, such recursions are also examined and the results are used to observe the linear complexity and the period of LFSR&rsquo / s combined in different ways to generate &ldquo / better&rdquo / system of stream cipher.

The representation of field elements has a great impact on the performance of the finite field arithmetic. In this thesis, we give modified version of redundant representation which works for any finite fields of arbitrary characteristics to design arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values. We then propose new representations as an alternative way to represent finite fields of characteristic two by using Charlier and Hermite polynomials. We show that multiplication in these representations can be achieved with subquadratic space complexity. Charlier and Hermite representations enable us to find binomial, trinomial or quadranomial irreducible polynomials which allows us faster modular reduction over binary fields when there is no desirable such low weight irreducible polynomial in other representations. These representations are very interesting for the NIST and SEC recommended binary fields GF(2^{283}) and GF(2^{571}) since there is no optimal normal basis (ONB) for the corresponding extensions. It is also shown that in some cases the proposed representations have better space complexity even if there exists an ONB for the corresponding extension.

Business process models are used within a range of organizational initiatives, where every stakeholder has a unique perspective on a process and demands the respective model. As a consequence, multiple process models capturing the very same business process coexist. Keeping such models in sync is a challenge within an ever changing business environment: once a process is changed, all its models have to be updated. Due to a large number of models and their complex relations, model maintenance becomes error-prone and expensive. Against this background, business process model abstraction emerged as an operation reducing the number of stored process models and facilitating model management. Business process model abstraction is an operation preserving essential process properties and leaving out insignificant details in order to retain information relevant for a particular purpose. Process model abstraction has been addressed by several researchers. The focus of their studies has been on particular use cases and model transformations supporting these use cases. This thesis systematically approaches the problem of business process model abstraction shaping the outcome into a framework. We investigate the current industry demand in abstraction summarizing it in a catalog of business process model abstraction use cases. The thesis focuses on one prominent use case where the user demands a model with coarse-grained activities and overall process ordering constraints. We develop model transformations that support this use case starting with the transformations based on process model structure analysis. Further, abstraction methods considering the semantics of process model elements are investigated. First, we suggest how semantically related activities can be discovered in process models-a barely researched challenge. The thesis validates the designed abstraction methods against sets of industrial process models and discusses the method implementation aspects. Second, we develop a novel model transformation, which combined with the related activity discovery allows flexible non-hierarchical abstraction. In this way this thesis advocates novel model transformations that facilitate business process model management and provides the foundations for innovative tool support. / Geschäftsprozessmodelle werden in einer Fülle organisatorischer Initiativen eingesetzt, wobei verschiedene Stakeholder individuelle Ansprüche an die Sicht auf den jeweiligen Prozess haben. Dies führt dazu, dass zu einem Geschäftsprozess eine Vielzahl unterschiedlicher Modelle existiert. In einer sich ständig verändernden Geschäftsumgebung ist es daher schwierig, diese Vielzahl von Modellen konsistent zu halten: Ändert sich sich ein Prozess, müssen alle Modelle, die ihn beschreiben, aktualisiert werden. Aufgrund der schieren Menge an Prozessmodellen und ihrer komplexen Beziehungen zueinander, erhöhen sich Aufwand und Kosten zur Pflege aller Modelle enorm. Vor diesem Hintergrund ermöglicht die Abstraktion von Geschäftsprozessmodellen, die Menge der Modelle zu reduzieren und damit ihre Verwaltung zu vereinfachen. Abstraktion von Geschäftsprozessmodellen bezeichnet eine Transformation eines Prozessmodells, so dass es für einen bestimmten Zweck besonders geeignet ist. Bei der Abstraktion von Geschäftsprozessen bleiben essentielle Eigenschaften eines Modells erhalten, während irrelevante Eigenschaften verworfen werden. Mehrere Studien stellen Prozessmodellabstraktion in den Fokus und konzentrieren sich auf konkrete Anwendungsfälle, für die sie geeignete Transformationen entwickelt haben. Diese Dissertation untersucht das Problem der Prozessmodellabstraktion und systematisiert die Lösung in einem Framework. Aktuelle Anforderungen der Industrie an die Abstraktion von Prozessmodellen wurden recherchiert und in einem Katalog von Anwendungsfällen zusammengefasst, von denen ein besonderer für die weiteren Untersuchungen ausgewählt wurde. In diesem Fall erwartet der Nutzer ein Modell niedrigeren Detailgrades, in welchem die Kontrollflussbeziehungen des Ursprungsmodells erhalten bleiben. Beginnend bei Modelltransformationen, die auf der Analyse der Prozessmodellstruktur aufbauen, entwickeln wir neuartige Abstraktionsoperationen zur Unterstützung dieses Anwendungsfalles. Darüber hinaus untersuchen wir Abstraktionsmethoden, welche die Semantik von Prozessmodellelementen berücksichtigen. Zum einen zeigen wir, wie Aktivitäten ermittelt werden können, die miteinander in semantischer Beziehung stehen - ein Problem, das bisher nur unzureichend betrachtet wurde. Die vorgeschlagenen Methoden werden mithilfe industrieller Prozessmodellsammlungen validiert und deren Umsetzung diskutiert. Zum anderen schlagen wir eine innovative Modelltransformation zur nicht-hierarchischen Abstraktion von Prozessmodellen vor. Dieser liegt die Ermittlung in Beziehung stehender Aktivitäten zugrunde. Demzufolge präsentiert diese Arbeit eine originäre Methode zur Prozessmodellabstraktion, die die Verwaltung von Geschäftsprozessmodellen vereinfacht und den Grundstein für innovative Softwarewerkzeuge legt.

The outsourcing of the business logistics activities have became a trend. The goals of my research want to understand that: (1) The outsourcing extent of the logistics activities. (2) The logistics outsourcing considered factors. (3) How the firm size affect the (1) and (2). (4) How the logistics network complexity affect the (1) and (2). The research¡¯s samples are the PC and peripheral equipment companies in Taiwan. The capital, the revenue, and the number of the employee measure the size of a firm. The logistics network complexity is measured by the number of the customers, the number of the suppliers, the number of the countries that customers in, and the number of the countries that the suppliers in. The result shows that the companies think the cost saving factors is most important when they decide to outsource the activity. The great extent of the traffic transportation, salvage and scrap disposal and return goods handling are outsourced. The companies whose sizes are small put great emphasis on the ¡°logistics information systems¡± factors. The big companies have a tendency to outsource the physical moved activities like traffic transportation, salvage and scrap disposal. The small companies are apt to outsource the process handling activities. In the logistics network complexity, the suppliers make greater difference in the outsourcing logistics activities than the customers. The numbers of the countries affect the logistics outsourcing considered factors.

According to the theory of NPcompleteness, many problems that have important realworld applications are NPhard. This excludes the possibility of solving them in polynomial time unless P=NP. A number of approaches have been proposed in dealing with NPhard problems, among them are approximation algorithms and parameterized algorithms. The study of approximation algorithms tries to find good enough solutions instead of optimal solutions in polynomial time, while parameterized algorithms try to give exact solutions when a natural parameter is small. In this thesis, we study the structural properties of parameterized computation and approximation algorithms for NP optimization problems. In particular, we investigate the relationship between parameterized complexity and polynomialtime approximation scheme (PTAS) for NP optimization problems. We give nice characterizations for two important subclasses in PTAS: Fully Polynomial Time Approximation Scheme (FPTAS) and Effcient Polynomial Time Approximation Scheme (EPTAS), using the theory of parameterized complexity. Our characterization of the class FPTAS has its advantages over the former characterizations, and our characterization of EPTAS is the first systematic investigation of this new but important approximation class. We develop new techniques to derive strong computational lower bounds for certain parameterized problems based on the theory of parameterized complexity. For example, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the clique problem could not be solved in time O(f (k)no(k)) for any function f . This lower bound matches the upper bound of the trivial algorithm that simply enumerates and checks all subsets of k vertices in the given graph of n vertices. We then extend our techniques to derive computational lower bounds for PTAS and EPTAS algorithms of NP optimization problems. We prove that certain NP optimization problems with known PTAS algorithms have no PTAS algorithms of running time O(f (1/Epsilon)no(1/Epsilon)) for any function f . Therefore, for these NP optimization problems, although theoretically they can be approximated in polynomial time to an arbitrarily small error bound Epsilon, they have no practically effective approximation algorithms for small error bound Epsilon. To our knowledge, this is the first time such lower bound results have been derived for PTAS algorithms. This seems to open a new direction for the study of computational lower bounds on the approximability of NP optimization problems.

For the thinking of System Dynamics guidance the priority is the understanding and governing the Dynamic Complexity of management strategy in the enterprise operation, how to get over the maze of Dynamic Complexity in the field of strategy management has been becoming the necessary thinking, and also be required as the basic element of enterprise management for all remarkable entrepreneurs. Dynamic Complexity is existing in the nature (Marco Cycling), also embodying in each human being (Micro Cycling), which is changing in every mil-second, interacting and maintaining the cyclic operation in harmonic balance skillfully. As likely, the internal, external environment and conditions of the enterprise operation are also varing, inter-complementing, inter-restricting all the time so as to reciprocally create the constant rule of Causal Feedback. The philosophy concept and method of System Dynamics, System Thinking is completely furnishing a key to release the Dynamic Complexity, so the management strategy can be reviewed, integrated by this marco thinking to the fullness. General reviewing on the operation status of Small-Medium Enterprise (SME) in Taiwan are being become more strictly constricted by the marco economical environment and the owned resource of each self. The sustained years of enterprise operational life and the ratio of survived company numbers of SME are becoming lower-down year by year. Therefore, in the front of management the System Complexity has been more serious now, then how to find out a key to pass thru this maze is the focus of thinking in this thesys researching. By a Questionnaire Investigation in this study the Strategy Themes of SME in Taiwan have been selected by the management of bench-marking enterprises for which they are most concerning about, there-after the Strategy Themes of System Complexity on Strategy Map, Balanced Scorecard are infrastructed. The dynamic inter-relation of Strategy Themes are displayed in the four perspectives of Balanced Scorecard and Strategy Map, there-after the real example of an enterprise is substantially applied to illustrate KPI and target of Balanced Scorecard and the Action Plan in this study. The core of System Complexity for these Strategy Themes are guidied to study by the System Thinking of Causual Diagram, One General Diagram is arised and ten of Causual Diagram are constructed separately from it to present the inter-relative of these Strategy Themes connections, there-after ¡§Positive Loop¡¨ (Reinforcing Loop), Negative Loop (Balancing Loop), Time Delay in each Loop are reviewed and explained the presentation of its inter-relative and followed up the workable leverage solutions as per the experienced reality of business practice. The presentation in each Causual Diagram doesn¡¦t mean to only one implication exclusively, it is giving the management to have the non-linear, marco reviewing more widely on these Strategy Themes and it will be able to find out the solutions and settlement when they are facing or tired-up by the same or similar strategy concerns in the substantial of business operation. This will be the favorable way of the management to find out a key for getting over the maze of System Complexity. Keyword: System Dynamics, System Thinking, Dynamic Complexity, Balanced Scorecard, Strategy Map, Small-Medium Enterprise.

Due to Cable-TV by special permission with high restriction and monopolize that the customers forced to accept without choices. The result of customer satisfaction inquire unable to understand what¡¦s the enterprise real needed and expect of customer. Formerly scholar research of relationship and interaction between customer satisfaction and enterprise by using inquire tools and result for strategy. But, That¡¦s not only one condition to judge the customer satisfaction. Such as channel content, network quality, manner of customer service ¡K etc. The multi condition to judge of customer satisfaction for the enterprise. Because, Every condition has causality of an event or a situation. It¡¦s not easy to explain the complicated with time delay. The system thinking will be solved such as this case In my research. The purpose of research : 1. Using BSC(Balance Score Card) and strategy map for case analysis in my research and find out what¡¦s critical problem in this case. 2. Using SD(System Dynamic) to simulation what is causality between system and customer satisfaction. The simulation result will verify with real system and provide for decision.

An Architecture Real Options Complexity-Based Valuation Methodology (ARC-VM) is developed for use to aid in the acquisition of military systems-of-systems (SoS). ARC-VM is suitable for acquisition-level decision making, where there is a stated desire for more informed tradeoffs between cost, schedule, and performance during the early phases of design. First, a framework is introduced to measure architecture complexity as it directly relates to military SoS. Development of the framework draws upon a diverse set of disciplines, including Complexity Science, software architecting, measurement theory, and utility theory. Next, a Real Options based valuation strategy is developed using techniques established for financial stock options that have recently been adapted for use in business and engineering decisions. The derived complexity measure provides architects with an objective measure of complexity that focuses on relevant complex system attributes. These attributes are related to the organization and distribution of SoS functionality and the sharing and processing of resources. The use of Real Options provides the necessary conceptual and visual framework to quantifiably and traceably combine measured architecture complexity, time-valued performance levels, as well as programmatic risks and uncertainties. An example suppression of enemy air defenses (SEAD) capability demonstrates the development and utility of the resulting architecture complexity&Real Options based valuation methodology. Different portfolios of candidate system types are used to generate an array of architecture alternatives that are then evaluated using an engagement model. This performance data is combined with both measured architecture complexity and programmatic data to assign an acquisition value to each alternative. This proves useful when selecting alternatives most likely to meet current and future capability needs.

Sebbene le regioni (territori che ospitano comunità integrate di abitanti, attività economiche ed istituzioni) siano diventati attori fondamentali dell'economia internazionale, le scienze economiche non sono ancora in grado di fornire un modello capace di interpretare le dinamiche economiche e fornire supporto alle politiche. Il motivo di questo limite è che gli approcci tradizionali non riescono a modellizare la complessità che caratterizza le economie regionali. Il progetto di ricerca si è dunque posto l'obiettivo di discutere tale complessità e verificare la possibilità di fornire un controfattuale. L'analisi ha tenuto in conto l'eterogeneità degli agenti e l'effetto di shock esogeni. Inoltre si è discusso come, a causa della complessità, i policy-makers siano confrontati alla difficoltà di predisporre politiche capaci di anticipare gli shock endogeni ed esogeni. I risultati teorici sono stati utilizzati, in parte, per analizzare la regione metropolitana di Madrid. In particolare si è analizzata la capacità locale di riprodurre una dinamica di crescita. I risultati indicano che anche regioni che attraversano cicli positivi hanno la necessità di ottimizzare l'utilizzo dei fattori di produzione e specializzare la propria economia in settori sostenuti dalla domanda internazionale. Una eccessiva specializzazione in settori non-tradable può, infatti, mettere in discussione la sostenibilità della crescita. / Regions (territories hosting integrated communities of citizens, firms, and institutions) have become key actors within the International economy, yet conventional economics cannot provide a model to explain local dynamics and to support policy-making. Such limit is due to complexity characterizing regional economies. Therefore, the present research aims at assessing complexity in regions and verifying the possibility of modelling regional economies. to assess regional economies, The research takes into account heterogeneity of agents as well as exogenous shocks. Moreover the research focuses on the effect of complexity on policy-making. Because of complexity, to be effective, regional policy has to take into account local and external shocks. Such theoretical background is partly used to assess the metropolitan region of Madrid. The empirical analysis shows that even a successful region can be challenged by the sustainability of economic growth. To enhance its international competitiveness, the region has to improve the use of local factors of production and to increase its specialization in sectors that are traded on the international market. An excessive specialization in non-tradable goods may, in fact, challenge growth sustainability.

<p>The purpose with this essay is to investigate how Ernest Hemingway uses his style of writing in his short stories “A Clean, Well-Lighted Place” and “Hills Like White Elephants”. The questions at issue are: What is characteristic of Hemingway's style when looking at the use of adjectives and sentence complexity? How is the Iceberg Technique used? What stylistic differences and similarities are there between the stories?</p><p>In my investigation I used a stylistic approach, in which adjectives are counted and sentence length is measured (creating mainly a quantitative analysis). The frequency of adjectives is calculated and compared against the norm in imaginative prose. Sentence length is compared against the norm for modern English. Previous research has provided a foundation for further analysis of the Iceberg Technique.</p><p>The analysis shows that the frequency of adjectives is very low compared with the norm and that many adjectives are used repeatedly. The sentences are very short, not even reaching half the length of the norm presented. Hemingway’s Iceberg Technique shows in the scarce use of dialogue tags and a plot that does not reveal much about the characters or the setting. The real plot is often hidden, leaving it to the reader to interpret and “feel” what the story is really about.</p><p>In conclusion: it may be said that both short stories are told in a minimalistic style, using only what is necessary to tell the story. They have a simple plot and simple characters, just like the Hemingway style we know.</p>