It is essential to secure the implementation of cryptosystems in embedded devices agains side-channel attacks. Namely, in order to resist differential (DPA) attacks, randomization techniques should be employed to decorrelate the data processed by the device from secret key parts resulting in the value of this data. Among the countermeasures that appeared in the literature were those that resulted in a random representation of the key known as the binary signed digit representation (BSD). We have discovered some interesting properties related to the number of possible BSD representations for an integer and we have proposed a different randomization algorithm. We have also carried our study to the $\tau$-adic representation of integers which is employed in elliptic curve cryptosystems (ECCs) using Koblitz curves. We have then dealt with another randomization countermeasure which is based on randomly splitting the key. We have investigated the secure employment of this countermeasure in the context of ECCs.

The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the resolution limitations of an imaging device in use and/or by the destructive influence of measurement noise. Specifically, when the noise obeys a Poisson probability law, standard approaches to the problem of image reconstruction are based on using fixed-point algorithms which follow the methodology proposed by Richardson and Lucy in the beginning of the 1970s. The practice of using such methods, however, shows that their convergence properties tend to deteriorate at relatively high noise levels (which typically takes place in so-called low-count settings). This work introduces a novel method for de-noising and/or de-blurring of digital images that have been corrupted by Poisson noise. The proposed method is derived using the framework of MAP estimation, under the assumption that the image of interest can be sparsely represented in the domain of a properly designed linear transform. Consequently, a shrinkage-based iterative procedure is proposed, which guarantees the maximization of an associated maximum-a-posteriori criterion. It is shown in a series of both computer-simulated and real-life experiments that the proposed method outperforms a number of existing alternatives in terms of stability, precision, and computational efficiency.

Youth is a contested term which has been described as difficult to define and ‘pin down analytically’ (De Boek and Honwana 2005:3). In much youth development related issues, youth is categorised as a person between the ages of 15-24, which is defining a person only in terms of one’s chronological age. Age is a good indicator of where in life a person is, I used thus a wider range to include also older youth. Youth are often viewed in relation to other social categories as adults or children, and notions of youth are often as becomings, dependent, powerless, rebellious, risky (behaviour) and irresponsible, a focus merely on ‘negative’ aspects of youthhood, are these notions really describing the general youth? This study explores given youth identities in terms of behavioural patterns of being ‘in place’ and/or ‘out of place’. Identities are in this thesis approached as socially constructed, and people can hold multiple identities. This thesis therefore presents different identity narratives of Jamaican Youth ‘faces’. I used qualitative research methodology to collect and analyse the empirical data generated during fieldwork in Jamaica, Port Antonio in the period of February to beginning of May 2009. Methods such as informal conversations, observations, key informant interviews and photography is the main sources of the collected data, but also secondary data has been used in the analysis to grasp the surrounding realities. The youth participants of this study, 37, are persons who define themselves as youth and are viewed as youth by the Jamaica society based on their activities and behaviour, and are not dependent of their age, gender, class or occupation. In addition twelve (12) adults have contributed to the outsider’s views. The analytical concept of place is used to examine youth’s different behavioural patterns, based on socially accepted activities which are preformed in socially constructed youth places. The social meanings that identity performance have for the sense of being ‘in place’ and belonging to a place are explored to examine how this affects their identity building processes within a specific place. Also outside processes as national youth policy making, media representations and statements from ‘locals’, are evaluated as contributing to the present perceived Jamaican youth identities. I found multiple constructed ‘faces’of Jamaican youth; ‘the naughty’, ‘the nice’, the sexy’, ‘the wise’ and ‘the runner’ , are presented. These identities are fluid and transferable between different places in society and in time. The participants in this study each hold several of these ‘faces’, but often one which are more prominent in relation to the place one uses at that time. The located youth places; the youth centre place, the marina place and the dancehall place, are sites where the identity building processes takes form and social identities are constructed in relations to the socially acceptable conventions in the places in which youth occupy. These social conventions and identities may be negotiated, modified, reconstructed, challenged, contested or resisted in the ‘never-ending’ identity and place production processes. Identity, which is a complex term, holds several of attributes within categories as gender, race, age ect., but none of these attributes exist alone, and place as a contributor to the identity building processes is in this thesis seen as significant in the dynamic relation to all the attributes a person holds, which are preformed at different scales in society, both to be ‘in place’ and/or ‘out of place’. The youth ‘faces’ in Jamaica are also related and part of the national identity, they should therefore be accepted rather than rejected as ‘unwanted behaviour’, since a person rarely just hold one identity.

It is essential to secure the implementation of cryptosystems in embedded devices agains side-channel attacks. Namely, in order to resist differential (DPA) attacks, randomization techniques should be employed to decorrelate the data processed by the device from secret key parts resulting in the value of this data. Among the countermeasures that appeared in the literature were those that resulted in a random representation of the key known as the binary signed digit representation (BSD). We have discovered some interesting properties related to the number of possible BSD representations for an integer and we have proposed a different randomization algorithm. We have also carried our study to the $\tau$-adic representation of integers which is employed in elliptic curve cryptosystems (ECCs) using Koblitz curves. We have then dealt with another randomization countermeasure which is based on randomly splitting the key. We have investigated the secure employment of this countermeasure in the context of ECCs.

The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the resolution limitations of an imaging device in use and/or by the destructive influence of measurement noise. Specifically, when the noise obeys a Poisson probability law, standard approaches to the problem of image reconstruction are based on using fixed-point algorithms which follow the methodology proposed by Richardson and Lucy in the beginning of the 1970s. The practice of using such methods, however, shows that their convergence properties tend to deteriorate at relatively high noise levels (which typically takes place in so-called low-count settings). This work introduces a novel method for de-noising and/or de-blurring of digital images that have been corrupted by Poisson noise. The proposed method is derived using the framework of MAP estimation, under the assumption that the image of interest can be sparsely represented in the domain of a properly designed linear transform. Consequently, a shrinkage-based iterative procedure is proposed, which guarantees the maximization of an associated maximum-a-posteriori criterion. It is shown in a series of both computer-simulated and real-life experiments that the proposed method outperforms a number of existing alternatives in terms of stability, precision, and computational efficiency.

This thesis comprises of two separate game theoretic models that fall under the general umbrella of network formation games. The first is a coalitional model of interaction in social networks that is based on the idea of social distance, in which players seek interactions with similar others. Our model captures some of the phenomena observed on such networks, such as homophily driven interactions and the formation of small worlds for groups of players. Using social distance games, we analyze the interactions between players on the network, study the properties of efficient and stable networks, relate them to the underlying graphical structure of the game, and give an approximation algorithm for finding optimal social welfare. We then show that efficient networks are not necessarily stable, and stable networks do not necessarily maximise welfare. We use the stability gap to investigate the welfare of stable coalition structures, and propose two new solution concepts with improved welfare guarantees. The second model is a compact formulation of matchings with externalities. Our formulation achieves tractability of the representation at the expense of full expressivity. We formulate a template of solution concept that applies to games where externalities are involved, and instantiate it in the context of optimistic, neutral, and pessimistic reasoning. Then we investigate the complexity of the representation in the context of many-to-many and one-to-one matchings, and provide both computational hardness results and polynomial time algorithms where applicable.

A narrative qualitative research approach was used to understand the role that spiritual journeys had on the lives of emerging adults. Participants were four emerging adults (2 female, 2 male) ranging in age from 20 to 29 years. All participants were of middle class social economic status and lived in a mid-size Canadian prairie city. Three of the participants were Caucasian and the fourth was of Spanish-Caucasian ancestry. Semi-structured interviews provided the opportunity for the participants to share their stories regarding the role that their spiritual journey played in their life. Data were analyzed for themes within and across the participants stories. A visual representation of their collective journeys was created along with four-part poetic representations of each participants individual story. The stories that the participants shared revealed that emerging adults spiritual journeys were cyclical in that the journeys began with feelings of discontent, which led them to seek spiritual resources and experiences to address the unhappiness in their lives. In acquiring new knowledge, the participants were faced with different theories, ideas and experiences that brought forth additional questions. These new areas of thought led these individuals to search for further answers and meaning, bring forth new questions, new meaning, and in turn, the process became a cycle. The cycle that began with their initial discontent continued because of a desire for further knowledge.<p> Findings are discussed in terms of the current literature on spirituality in emerging adulthood and spirituality in relation to meaning making; implications are discussed for counselors, educators, and researchers and recommendations are made for future research.

This dissertation investigated several aspects of middle graders’ mathematical understanding based on representational models. Twenty (11 male, 9 female) sixth grade students were interviewed about their solution strategies and answer justifications when solving difficult mathematics problems. The interview participants represented a stratified demographic sampling of the student body of a culturally diverse middle school in a suburban school district in the southwestern United States. Data from the interviews were analyzed qualitatively. This involved “chunking” cognitive interview transcripts into sections. Major themes were identified and manuscripts were developed around those themes. One theme examined the interviewers’ ethic of care behaviors. Carol Gilligan noted differences in male and female ethic of care behaviors, but it was Nel Noddings who discussed the importance of such behaviors in the educational community. So what impact could the gender of the interviewer have on cognitive interviews? After considering ethic of care behaviors explicated by Hayes, Ryan and Zseller’s (1994) study with middle grades students, the interview transcripts were examined for specific positive and negative ethic of care behaviors. The theme of students’ justifications of mathematical solutions was also selected. The major undertaking involved developing a justification scheme applicable across mathematical strands and grade levels. The justification scheme that emerged was based on the work of Guershon Harel and Larry Sowder. The first-level schemes of Language, Mechanistic, Authoritarian, and Visual were used to classify and define the justifications. Several second-level schemes were also defined. The justification scheme framework was applied to students’ cognitive interview responses on four difficult mathematics problems. The third theme investigated the symbiosis of justification schemes with mathematical representations. This study examined possible links between representational formats and justification scheme categories. The premise of this study was that representations “trigger” students’ choices of justification schemes. Student responses were analyzed as to which aspect of the mathematical representation received the students’ initial attention. The students’ understanding of the representation was pivotal to their solution, as well as the students’ reasoning, or justification, of the answer. Students focused on key aspects of the problem and developed solutions based on that information.

The purpose of this study was to determine eighth grade students&rsquo / skills of translating among different representations / graphic, table, equation, and verbal sentence / of algebraic concepts. Moreover, it was also aimed to investigate if there is any gender difference regarding the translation skills of students translating multiple representations, and their most common errors in making these translations. For data collection, 18 schools were selected randomly from 103 elementary schools in &Ccedil / ankaya district of Ankara. Then all of the eighth grade students in each school were selected as sample. In total 705 eighth grade students were participated in the study. To assess students&rsquo / translation skills &ldquo / Translation among different representations of algebraic concepts test&rdquo / (TADRACT) was developed by researcher. Descriptive statistics were obtained to understand students&rsquo / achievement in translation process. To compare mean scores of female and male students, the statistical analysis of Independent Samples t-test was used. Every question were examined in detail to determine any misconceptions, and most frequent errors students made in translating among different algebraic representations. The results of test indicated that 8th grade students had poor skill in translations of four different representations / verbal statement, equation, table, graphic / in algebraic concepts. There was no significant difference between mean scores of girls and mean scores of boys. The most problematic translations were from other representations / equation, table, graphic / to verbal statement, and translations from other three representations / verbal statement, equation, graphic / to table were the easiest translations.

The main aim of this study was to reveal the prevailing social representations of European Union. In order to fulfill the aim, first a semi-structured interview was conducted to 13 demographically different individuals and the content analysis of the interviews revealed five categories namely, Turkey&rsquo / s membership to EU, Problems of Turkey, Structure of EU, EU as Disadvantageous and EU as Advantageous. Second, in order to examine the media representation of EU, three newspapers representing different political views were qualitatively analyzed and the dimensions of EU as a must, EU as a threat, and EU as difficult were exposed. Finally, according to the thematic units and categories generated from the qualitative analyses / a &ldquo / Social Representations of EU&rdquo / scale was formed and applied to 243 university students. Four sub-scales, namely EU membership is disadvantageous, EU membership is advantageous, religious and cultural threats and EU membership is difficult were extracted from the scale with the reliability coefficients varying from .61 to .88. In order to investigate whether the different factors of social representations of EU are differing on particular dimensions as political view, exposure to media, newspapers read or SES levels, variance analyses were performed. On the other hand, for answering the question of whether the representations of EU could be predicted from life expectations, perceived political agenda or individual dimensions multiple regression analyses were held. Significant differences were found in EU membership is disadvantageous representation in terms of university (Gazi University-METU), gender, and political views of newspapers read. EU membership is advantageous representation differed along the levels of gender and newspapers read. Religious and cultural threats were to be differed along the levels of university, gender, political view, newspapers read and exposure to media. Finally significant differences in EU as difficult representation was found in terms of the ideology of the newspapers read. Feelings toward EU and evaluation of the membership dimensions were found to contribute to the prediction of EU as disadvantageous, EU as advantageous, religious and cultural threats, and EU as difficult representations. Moreover, religious and cultural threats representation is significantly predicted from political view and media exposure.