This thesis studies two topics in sequence analysis. In the first part, we investigate the large deviations of the shape of the random RSK Young diagrams, associated with a random word of size n whose letters are independently drawn from an alphabet of size m=m(n). When the letters are drawn uniformly and when both n and m converge together to infinity, m not growing too fast with respect to n, the large deviations of the shape of the Young diagrams are shown to be the same as that of the spectrum of the traceless GUE. Since the length of the top row of the Young diagrams is the length of the longest (weakly) increasing subsequence of the random word, the corresponding large deviations follow. When the letters are drawn with non-uniform probability, a control of both highest probabilities will ensure that the length of the top row of the diagrams satisfies a large deviation principle. In either case, both speeds and rate functions are identified. To complete our study, non-asymptotic concentration bounds for the length of the top row of the diagrams, are obtained for both models. In the second part, we investigate the order of the r-th, 1<= r < +∞, central moment of the length of the longest common subsequence of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, the r-th central moment is shown to be of order n^{r/2}. In particular, when r=2, we get the order of the variance of the longest common subsequence.

Researchers in software engineering proposed design method for distributed applications to construct a set of communicating system components from a global behavior. The joint behaviors of these components must precisely satisfy the specified global behavior. The next concern is to transform the constructed models of these components into executable business processes by ensuring the exchange of asynchronous messages among the generated business processes. The introduction of Service-Oriented Architecture (SOA) has helped to achieve this goal. SOA provides high flexibility in composing loosely-integrated services that can be used among business domains to carry out business transactions; this composition is known as service orchestration. Moreover, SOA supports Model Driven Architecture (MDA) such that services modeled as UML Activity Diagrams (AD) can be transformed into a set of Business Execution Language (BPEL) processes. Many researchers discussed the transformation of UML AD and the Business Process Modeling Notation (BPMN) into BPEL. However, they did not discuss the practical limitations that some of these transformations impose. This thesis addresses the imitations of the transformation from UML AD to BPEL processes using the IBM Rational Software Architect (RSA). We showed here that the tool is unable to create the correct BPEL artifacts from UML AD components in certain cases, for instance when the behavior includes the alternative for receiving single or concurrent messages, a weak loop, or certain choice activities. Furthermore, we provided novel solutions to the transformations in these cases in order to facilitate the transformation from UML AD to BPEL.

Researchers in software engineering proposed design method for distributed applications to construct a set of communicating system components from a global behavior. The joint behaviors of these components must precisely satisfy the specified global behavior. The next concern is to transform the constructed models of these components into executable business processes by ensuring the exchange of asynchronous messages among the generated business processes. The introduction of Service-Oriented Architecture (SOA) has helped to achieve this goal. SOA provides high flexibility in composing loosely-integrated services that can be used among business domains to carry out business transactions; this composition is known as service orchestration. Moreover, SOA supports Model Driven Architecture (MDA) such that services modeled as UML Activity Diagrams (AD) can be transformed into a set of Business Execution Language (BPEL) processes. Many researchers discussed the transformation of UML AD and the Business Process Modeling Notation (BPMN) into BPEL. However, they did not discuss the practical limitations that some of these transformations impose. This thesis addresses the imitations of the transformation from UML AD to BPEL processes using the IBM Rational Software Architect (RSA). We showed here that the tool is unable to create the correct BPEL artifacts from UML AD components in certain cases, for instance when the behavior includes the alternative for receiving single or concurrent messages, a weak loop, or certain choice activities. Furthermore, we provided novel solutions to the transformations in these cases in order to facilitate the transformation from UML AD to BPEL.

A previous study on students approach to problems of Set Theory in Iran brought me somehypotheses. These encouraged me to test the hypotheses in this supplementary study. Mypurpose of this study was to consider some students' cognitive difficulties in Set Theory. Iinvestigated students’ conceptual understanding of two major concepts of Set Theory – theconcepts of inclusion and belonging. I also studied the ways students use Venn diagram tofigure out problems in Set Theory. I wanted to examine how students figure out the differentmeanings of words in the natural and formal language. To do so, I analyzed six experiments. Icompared three experiments with the experiments of my previous study in Iran. My researchquestions suggested using a qualitative research method. My theoretical framework built aroundtheories of semiotic activities, which were used in the analysis.The results indicated that students can make unfortunate use of Euler–Venn diagrams. A set ofsets was a difficult concept for students. Some words in natural language, even the word "set" inboth natural and formal language, caused confusion for students when introduced in Settheoretic contexts. Students failed sometimes to distinguish between sets and elements. Theexperiments showed that students’ cultural context had affect on students' cognition regardingmathematical objects.

In Software Product Lines (SPLs), a feature model can be used to represent the similarities and differences within a family of software systems. This allows describing the systems derived from the product line as a unique combination of the features in the model. What makes feature models particularly appealing is the fact that the constraints in the model prevent incompatible features from being part of the same product. Despite the benefits of feature models, constructing and maintaining these models can be a laborious task especially in product lines with a large number of features and constraints. As a result, the study of automated techniques to reason on feature models has become an important research topic in the SPL community in recent years. Two techniques, in particular, have significant appeal for researchers: SAT solvers and Binary Decision Diagrams (BDDs). Each technique has been applied successfully for over four decades now to tackle many practical combinatorial problems in various domains. Currently, several approaches have proposed the compilation of feature models to specific logic representations to enable the use of SAT solvers and BDDs. In this thesis, we argue that several critical issues related to the use of SAT solvers and BDDs have been consistently neglected. For instance, satisfiability is a well-known NP-complete problem which means that, in theory, a SAT solver might be unable to check the satisfiability of a feature model in a feasible amount of time. Similarly, it is widely known that the size of BDDs can become intractable for large models. At the same time, we currently do not know precisely whether these are real issues when feature models, especially large ones, are compiled to SAT and BDD representations. Therefore, in our research we provide a significant step forward in the state-of-the-art by examining deeply many relevant properties of the feature modeling domain and the mechanics of SAT solvers and BDDs and the sensitive issues related to these techniques when applied in that domain. Specifically, we provide more accurate explanations for the space and/or time (in)tractability of these techniques in the feature modeling domain, and enhance the algorithmic performance of these techniques for reasoning on feature models. The contributions of our work include the proposal of novel heuristics to reduce the size of BDDs compiled from feature models, several insights on the construction of efficient domain-specific reasoning algorithms for feature models, and empirical studies to evaluate the efficiency of SAT solvers in handling very large feature models.

In Software Product Lines (SPLs), a feature model can be used to represent the similarities and differences within a family of software systems. This allows describing the systems derived from the product line as a unique combination of the features in the model. What makes feature models particularly appealing is the fact that the constraints in the model prevent incompatible features from being part of the same product. Despite the benefits of feature models, constructing and maintaining these models can be a laborious task especially in product lines with a large number of features and constraints. As a result, the study of automated techniques to reason on feature models has become an important research topic in the SPL community in recent years. Two techniques, in particular, have significant appeal for researchers: SAT solvers and Binary Decision Diagrams (BDDs). Each technique has been applied successfully for over four decades now to tackle many practical combinatorial problems in various domains. Currently, several approaches have proposed the compilation of feature models to specific logic representations to enable the use of SAT solvers and BDDs. In this thesis, we argue that several critical issues related to the use of SAT solvers and BDDs have been consistently neglected. For instance, satisfiability is a well-known NP-complete problem which means that, in theory, a SAT solver might be unable to check the satisfiability of a feature model in a feasible amount of time. Similarly, it is widely known that the size of BDDs can become intractable for large models. At the same time, we currently do not know precisely whether these are real issues when feature models, especially large ones, are compiled to SAT and BDD representations. Therefore, in our research we provide a significant step forward in the state-of-the-art by examining deeply many relevant properties of the feature modeling domain and the mechanics of SAT solvers and BDDs and the sensitive issues related to these techniques when applied in that domain. Specifically, we provide more accurate explanations for the space and/or time (in)tractability of these techniques in the feature modeling domain, and enhance the algorithmic performance of these techniques for reasoning on feature models. The contributions of our work include the proposal of novel heuristics to reduce the size of BDDs compiled from feature models, several insights on the construction of efficient domain-specific reasoning algorithms for feature models, and empirical studies to evaluate the efficiency of SAT solvers in handling very large feature models.

<p>In this thesis we explore and extend the theory of persistent homology, which captures topological features of a function by pairing its critical values. The result is represented by a collection of points in the extended plane called persistence diagram.</p><p>We start with the question of ridding the function of topological noise as suggested by its persistence diagram. We give an algorithm for hierarchically finding such epsilon-simplifications on 2-manifolds as well as answer the question of when it is impossible to simplify a function in higher dimensions.</p><p>We continue by examining time-varying functions. The original algorithm computes the persistence pairing from an ordering of the simplices in a triangulation and takes worst-case time cubic in the number of simplices. We describe how to maintain the pairing in linear time per transposition of consecutive simplices. A side effect of the update algorithm is an elementary proof of the stability of persistence diagrams. We introduce a parametrized family of persistence diagrams called persistence vineyards and illustrate the concept with a vineyard describing a folding of a small peptide. We also base a simple algorithm to compute the rank invariant of a collection of functions on the update procedure.</p><p>Guided by the desire to reconstruct stratified spaces from noisy samples, we use the vineyard of the distance function restricted to a 1-parameter family of neighborhoods of a point to assess the local homology of a sampled stratified space at that point. We prove the correctness of this assessment under the assumption of a sufficiently dense sample. We also give an algorithm that constructs the vineyard and makes the local assessment in time at most cubic in the size of the Delaunay triangulation of the point sample.</p><p>Finally, to refine the measurement of local homology the thesis extends the notion of persistent homology to sequences of kernels, images, and cokernels of maps induced by inclusions in a filtration of pairs of spaces. Specifically, we note that persistence in this context is well defined, we prove that the persistence diagrams are stable, and we explain how to compute them. Additionally, we use image persistence to cope with functions on noisy domains.</p> / Dissertation

Disability is seen as a result of an interaction between a person and that person's contextual factors. Viewing disability in the context of the built environment, a better design of this environment helps to reduce the disability faced by an individual. In spite of significant research in Universal Design (UD), the existing methods provide insufficient guidance for designers: designers demand more specific examples of, and methods for, good universal design. Within the overarching goal of improving universal product design, the specific goal of this research is to determine if the ADA guidelines for architectural design can be adapted to product design. A methodology that foresees the accessibility issues while designing a product would be constructive. The new technique should be built on the pre-existing principles and guidelines. A user activity and product function framework is proposed for this translation using actionfunction diagrams. Specific goals include determining if the function-based approach is able to anticipate a functional change that improves product accessibility. Further, generate user activity and product function association rules that can be applied to the universal design of products. Proposed research activities are to identify thirty existing universal products and compare with its typical version to identify the function that introduces an accessibility feature. Next, categorize the observed changes in a product function systematically and extract trends from accessible architectural systems to generate rules for universal design of consumer products. For validation, the task is to select around fifteen consumer product pairs for validation of the generated rules to determine if the ADA guidelines can be adapted for universal product design using the proposed framework. The results of this research show promise in using the International Classification of Functioning, Disability and Health (ICF) lexicon to model user limitation. The actionfunction diagram provides a structured way to approach a problem in the early stage of design. The rules generated in this research translate to products having similar user-product interface.

In this thesis, we present real Lefschetz fibrations. We first study real Lefschetz fibrations around a real singular fiber. We obtain a classification of real Lefschetz fibrations around a real singular fiber by a study of monodromy properties of real Lefschetz fibrations. Using this classification, we obtain some invariants, called real Lefschetz chains, of real Lefschetz fibrations which admit only real critical values. We show that in case the fiber genus is greater then 1, the real Lefschetz chains are complete invariants of directed real Lefschetz fibrations with only real critical values. If the genus is 1, we obtain complete invariants by decorating real Lefschetz chains. For elliptic Lefschetz fibrations we define a combinatorial object which we call necklace diagrams. Using necklace diagrams we obtain a classification of directed elliptic real Lefschetz fibrations which admit a real section and which have only real critical values. We obtain 25 real Lefschetz fibrations which admit a real section and which have 12 critical values all of which are real. We show that among 25 real Lefschetz fibrations, 8 of them are not algebraic. Moreover, using necklace diagrams we show the existence of real elliptic Lefschetz fibrations which can not be written as the fiber sum of two real elliptic Lefschetz fibrations. We define refined necklace diagrams for real elliptic Lefschetz fibrations without a real section and show that refined necklace diagrams classify real elliptic Lefschetz fibrations which have only real critical values.

Abstract The military is the foundation of a nation¡¦s safety. To ensure the safety, prosperity and a continuous development of a country, the commanding officer of each troop in the armed forces should adopt a kind of leadership which can meet the needs of a country and its people thus fulfilling the mission of defending a country and protecting its people. The writer thoroughly observed and interviewed two commanding officers who were the subjects of this case study. The study is aimed to discuss the leadership behavior of the air-force colonels who are commanding officers. The study discusses the organization structure, the characteristics of missions and the number of people in troops, the difference between the leadership behavior between the commanding officers. The study tries to find a suitable leadership behavior which can be served as a reference for commanding officers in different troops in the future. The study has found the following phenomenon: 1. To lead a huge organization which has many people and facilities and units, the most important job is to know how to control. To lead an organization which has less people and it has a professional unit, the most important job is to plan and to know how to communicate to the subordinates. 2. There are many unnecessary meetings in the troops. The meetings are too long. Only a few items need to be discussed are relevant to the units, so it is a waste of time. 3. Due to different units, some commanding officers have too much work, some have less work. Some can not fully use his talents. Responsibility and power do not match. 4. If the unit has less people and resources, the conflict between subordinates are less. If the leader has better skill of eloquence, he can persuade his subordinates and convince them easily. 5. The leadership behavior at this stage in the military is ¡§people-centered¡¨ which produces good effects in leadership. In summary, the leadership behavior of the commanding officer can directly influence the behavior and attitude of his subordinates. The more the commanding officer cares his subordinates, the better meets the psychological needs of his subordinates. Key Words: Leadership behavior and effectiveness, 4 diagrams of leadership behavior,System and person-oriented, Initiating and consideration structure,Situational factors.