This research is designed to develop and investigate newly defined problems: the Maximum Convex Sum (MCS), and its generalisation, the K-Maximum Convex Sum (K-MCS), in a two-dimensional (2D) array based on dynamic programming. The study centres on the concept of finding the most useful informative array portion as defined by different parameters involved in data, which is generically expressed in this thesis as the Maximum Sum Problem (MSP). This concept originates in the Maximum Sub-Array (MSA) problem, which relies on rectangular regions to find the informative array portion. From the above it follows that MSA and MCS belong to MSP. This research takes a new stand in using an alternative shape in the MSP context, which is the convex shape. Since 1977, there has been substantial research in the development of the Maximum Sub-Array (MSA) problem to find informative sub-array portions, running in the best possible time complexity. Conventionally the research norm has been to use the rectangular shape in the MSA framework without any investigation into an alternative shape for the MSP. Theoretically there are shapes that can improve the MSP outcome and their utility in applications; research has rarely discussed this. To advocate the use of a different shape in the MSP context requires rigorous investigation and also the creation of a platform to launch a new exploratory research area. This can then be developed further by considering the implications and practicality of the new approach. This thesis strives to open up a new research frontier based on using the convex shape in the MSP context. This research defines the new MCS problem in 2D; develops and evaluates algorithms that serve the MCS problem running in the best possible time complexity; incorporates techniques to advance the MCS algorithms; generalises the MCS problem to cover the K-Disjoint Maximum Convex Sums (K-DMCS) problem and the K-Overlapping Maximum Convex Sums (K-OMCS) problem; and eventually implements the MCS algorithmic framework using real data in an ecology application. Thus, this thesis provides a theoretical and practical framework that scientifically contributes to addressing some of the research gaps in the MSP and the new research path: the MCS problem. The MCS and K-MCS algorithmic models depart from using the rectangular shape as in MSA, and retain a time complexity that is within the best known time complexities of the MSA algorithms. Future in-depth studies on the Maximum Convex Sum (MCS) problem can advance the algorithms developed in this thesis and their time complexity.

This thesis explores several of the major results in list-coloring in an expository fashion. As a specialization of list coloring, the sum list chromatic number is explored in detail. Ultimately, the thesis is designed to motivate the discussion of coloring problems and, hopefully, interest the reader in the branch of coloring problems in graph theory.

Adhesion, heterogeneous catalysis, electrochemistry, and many other important processes and properties are driven by interactions at surfaces and interfaces. Vibrational sum frequency generation spectroscopy (VSFG) is an increasingly popular analytical technique because it can provide information about the nature and physical orientation of functional groups at these surfaces and interfaces. Analysis of VSFG data can be complicated by the presence of SFG signal that is not associated with a resonant vibration. This nonresonant sum frequency generation (NR-SFG) signal can interfere with the resonant signal and influence the detected spectrum. Methods have been developed to remove NR-SFG signal; however, these methods tend to be complicated and expensive. In fact many SFG practitioners do not have the ability to remove NR-SFG signal components, and systems designed to remove NR-SFG signal contributions may not be able to do so for some materials. We have worked to help develop a better understanding of NR-SFG. As part of this work, a better understanding of the temporal and phase behavior of NR-SFG signal has been developed, based on the behavior of NR-SFG signal from Si(111) wafers. This work calls into question some assumptions underlying nonresonant suppression methods based on time-domain detection. A new method for nondestructively testing (NDT) materials has been developed that uses nonresonant second harmonic generation, the degenerate form of SFG. This new NDT technology has the potential to detect several forms of material damage, such as aluminum sensitization, and plastic deformation of materials, which are largely invisible to current NDT technologies. Methods for extracting functional group orientation from VSFG data that contains NR-SFG contributions are also demonstrated and used to investigate how the surface of high density polyethylene changes in response to mechanical deformation. This work shows that the inability to remove NR-SFG contributions from VSFG spectra does not mean that these instruments cannot be used to make important discoveries. It simply means that NR-SFG contributions must be properly understood and accounted for during experimental design, and kept in mind during the analysis of VSFG spectra.

No description available.

No description available.

The sum-product network (SPN) is a recently-proposed generative, probabilistic model that is guaranteed to compute any joint or any marginal probability in time linear in the size of the model. An SPN is represented as a directed, acyclic graph (DAG) of sum and product nodes, with univariate probability distributions at the leaves. It is important to learn the structure of this DAG since the set of distributions representable by an SPN is constrained by it. We present the first batch structure learning algorithm for SPNs and show its advantage over learning the parameters of an SPN with fixed architecture. We propose a search algorithm for learning the structure of an SPN and show that its ability to learn a DAG-structured SPN makes it better for some tasks than algorithms that only learn tree-structured SPNs. We adapt the structure search algorithm to learn the structure of an SPN in the online setting and show that two other methods for online SPN structure learning are slower or learn models with lower likelihood. We also propose to combine SPNs with an autoencoder to model image data; this application of SPN structure learning shows that both models benefit from being combined.We are also the first to propose a distinction between nonmonotone and monotone SPNs, or SPNs with negative edge-weights and those without, respectively. We prove several important properties of nonmonotone SPNs, propose algorithms for learning a special class of nonmonotone SPN called the twin SPNs, and show that allowing negative edge-weights can help twin SPNs model some distributions more compactly than monotone SPNs.

Ce travail de thèse a pour objectif d’examiner les conséquences du contexte scolaire actuel, marqué par la meilleure réussite scolaire des filles par rapport aux garçons (e.g., OECD, 2015 ; Voyer & Voyer, 2014), sur la perception que les élèves ont de l’école et des relations de genre dans le contexte scolaire. Notre hypothèse de départ est que la supériorité académique des filles qui caractérise actuellement le paysage scolaire pourrait amener les garçons à adopter une vision zéro-sum des relations de genre à l’école. Autrement dit, les garçons seraient susceptibles de penser que la réussite scolaire des filles se fait à leurs dépens. Nous postulons également que cette vision compétitive de l’école et des relations filles-garçons pourrait avoir des conséquences délétères sur la réussite scolaire des garçons, suggérant ainsi un mécanisme de maintien des inégalités de réussite scolaire en faveur des filles. L’étude princeps n°0 met en évidence, en accord avec notre hypothèse, que les collégiens (mais pas les collégiennes) adhèrent plus fortement aux croyances zéro-sum dans un contexte menaçant de réussite scolaire des filles par rapport à un contexte de réussite des garçons ou à une condition de contrôle. Il apparaît cependant qu’au lycée le contexte a un impact uniquement sur les croyances zéro-sum des filles (étude 1) alors qu’à l’université il influence les croyances des filles et des garçons (étude 2). La littérature sur la perspective zéro-sum montrant que le contexte a généralement un impact sur les groupes de haut statut uniquement (e.g., Wilkins, Wellman, Babbitt, Toosi & Schad, 2015), nous explorons ensuite l’hypothèse selon laquelle cette évolution de l’effet du contexte en fonction du niveau d’études des participant.e.s pourrait être liée à une évolution du statut académique perçu des filles et des garçons au cours du cursus scolaire. Les études 3 et 4 ont été conduites afin d’évaluer la perception que les élèves ont du statut académique des filles et des garçons à différents niveaux du cursus scolaire. Les résultats de ces deux études montrent que les filles sont globalement perçues comme ayant un statut académique supérieur à celui des garçons, bien qu’elles soient ensuite considérées comme ayant un statut professionnel inférieur aux hommes. La perception d’une supériorité académique des filles est plus marquée au lycée qu’au collège ou à l’université. Nous avons ensuite testé directement le rôle modérateur du statut académique dans l’effet du contexte sur les croyances zéro-sum et la performance des élèves. En manipulant le statut académique de l’endogroupe, l’étude 5 met en évidence que les individus de haut statut ont de moins bonnes performances dans un contexte de réussite de l’exogroupe par rapport à des contextes scolaires moins menaçants. Enfin, les résultats des études 6a et 6b montrent qu’alors que les collégien.ne.s (étude 6b) comme les lycéen.ne.s (étude 6a) attribuent un statut académique supérieur aux filles, la réaction des élèves face à la réussite de l’exogroupe varie selon leur âge. / The aim of the present research program is to examine the consequences of the current academic context, in which girls generally outperform boys (e.g., OECD, 2015; Voyer & Voyer, 2014), on students’ perception of school and gender relations in the academic context. Our main hypothesis is that girls’ academic superiority, which currently characterize the school context, could lead boys to endorse a zero-sum perspective of gender relations at school. In other words, boys are likely to think that girls’ academic achievement is made at their expense. We also hypothesize that this competitive approach of school and gender relations could have negative consequences on boys’ academic achievement, which could contribute to maintain gender inequalities in academic achievement favoring girls. The princeps study n°0 shows that, consistent with our hypothesis, middle-school boys (but not girls) are more likely to endorse gender zero-sum beliefs in a threatening context emphasizing girls’ academic achievement than in a less threatening context highlighting boys’ achievement or in a control condition. However, results of the two following studies reveal that school context only affects high-school girls’ beliefs (study 1) but influences both male and female students beliefs in university (study 2). As the literature on zero-sum perspective shows that the context generally has an impact on high-status group members only (e.g., Wilkins, Wellman, Babbitt, Toosi & Schad, 2015), we then explore the hypothesis that the evolution of the effect of school context depending of students’ school level might be related to an evolution of boys’ and girls’ perceived academic status. We conduct studies 3 and 4 in order to investigate students’ perception of the academic status of boys and girls at different school levels. The results show that overall girls are perceived to have a higher academic status than boys, even though that are then considered to have a lower professional status than men. The perception of girls’ academic superiority seems to be more important in high school compared to middle school or university. In the next chapter, we directly test if the academic status could moderate the impact of context on students’ endorsement of zero-sum beliefs and their performance. Manipulating the ingroup’s academic status, the results of study 5 show that high-status students underperform in a context emphasizing the outgroup’s success compared to less threatening contexts. Finally, studies 6a and 6b revealed that, even if middle-school (study 6b) and high-school students (study 6a) both attribute a higher academic status to girls, students’ reaction to outgroup’s success depend on their age. To conclude, this research work highlights the consequences girls’ academic superiority can have on how students perceive gender relations in the academic context, even though it does not seem to question the gender system in place in the society.

In a stopping rule problem, a real-time player decides to stop or continue at stage n based on the observations up to that stage, but in a k-step look-ahead stopping rule problem, we suppose the player knows k steps ahead. The aim of this Ph.D. dissertation is to study this type of prophet problems for simple random walk, determine the optimal stopping rule and calculate the expected return for them. The optimal one-step look-ahead stopping rule for a finite simple random walk is determined in this work. We also study two infinite horizon stopping rule problems, sum with negative drift problems and discounted sum problems. The optimal one, two and three-step look-ahead stopping rules are introduced for the sum with negative drift problem for simple random walk. We also compare the maximum expected returns and calculate the upper bound for the advantage of the prophet over the decision maker. The last chapter of this dissertation concentrates on the discounted sum problem for simple random walk. Optimal one-step look-ahead stopping rule is defined and lastly we compare the optimal expected return for one-step look-ahead prophet with a real-time decision maker.

Skolans uppdrag är att säkerhetsställa att alla elever har samma möjligheter att tillgodogöra sig kunskap och därmed utvecklas. Alla elever lär sig på olika vis och har också behov av att visa sina kunskaper på olika sätt. Ur ett specialpedagogiskt perspektiv blir vår roll som speciallärare att arbeta för en tillgänglig lärmiljö, där vi också ser till att elever som är i särskilda utbildningsbehov i matematik får rätt förutsättningar att visa sina kunskaper. För att kunna genomföra ovanstående behövs kunskap om bedömningsformer utifrån ett elevperspektiv. Syftet med studien är därför att bidra med kunskap om elevers uppfattningar av skriftliga summativa bedömningssituationer, i synnerhet elever i särskilda utbildningsbehov i matematik, SUM, och hur bedömningssituationen påverkar deras möjligheter att visa sina kunskaper. Utifrån studiens syfte och frågeställningar genomfördes ett antal kvalitativa djupintervjuer som analyserades med hjälp av fenomenografin. Studiens empiri visar att elever generellt uppfattar summativa bedömningssituationer som stressande. Den visar också att vissa elever uppfattar att de får möjlighet att visa vad de kan. Elever i SUM däremot uppfattar situationen starkare, där stressen tar sig i uttryck i en negativ påverkan av arbetsminnet samt ger fysiska symptom såsom magont, illamående och huvudvärk. Slutsatsen som kan dras utifrån empirin är att elever i SUM påverkas i högre grad av summativa bedömningssituationer, vilket i sin tur leder till att de inte får rätt förutsättningar att visa sina kunskaper. Här blir vårt uppdrag som speciallärare att agera kvalificerad samtalspartner och rådgivare för att föra elevernas talan och se till att de får rätt förutsättningar att lyckas i skolan. / The mission of the school system is to ensure equal opportunities for all students to acquire knowledge and thereby develop. All students learn using different strategies and therefore have the need to demonstrate their knowledge in various ways. From a special education perspective, our role as special educators is to work towards an accessible learning environment, where we ensure that students with special educational needs in mathematics are provided with the right conditions to demonstrate their knowledge. To achieve this, knowledge of assessment methods from a student perspective is needed. The purpose of this study is to highlight students' perceptions, especially students with special educational needs in mathematics (SUM), and how summative assessment methods affect their opportunities to demonstrate knowledge. The study can contribute knowledge of opportunities and barriers based on the chosen assessment method. Based on the purpose of the study and the research questions, a number of qualitative in-depth interviews were conducted and analyzed using phenomenography. The study's empirical data shows that students generally perceive summative assessment situations as stressful. It also shows that some students perceive that they have an opportunity to show their knowledge. However, SUM students perceive the situation more deeply, with stress having a negative impact on working memory and causing physical symptoms such as stomachaches, nausea, and headaches. The conclusion drawn from the empirical data is that SUM students are more affected by summative assessment situations, which in turn means that they do not have the right conditions to demonstrate their knowledge. In this context, our role as special educators is to act as qualified conversation partners and advisors to advocate for students and ensure that they have the right conditions to succeed in school.

A Factor Graph (FG -- http://en.wikipedia.org/wiki/Factor_graph) is a structure used to find solutions to problems that can be represented as a Probabilistic Graphical Model (PGM). They consist of interconnected variable nodes and factor nodes, which iteratively compute and pass messages to each other. FGs can be applied to solve decoding of forward error correcting codes, Markov chains and Markov Random Fields, Kalman Filtering, Fourier Transforms, and even some games such as Sudoku. In this paper, a framework is presented for rapid prototyping of hardware implementations of FG-based applications. The FG developer specifies aspects of the application, such as graphical structure, factor computation, and message passing algorithm, and the framework returns a design. A system of Python scripts and Verilog Hardware Description Language templates together are used to generate the HDL source code for the application. The generated designs are vendor/platform agnostic, but currently target the Xilinx Virtex-6-based ML605. The framework has so far been primarily applied to construct Low Density Parity Check (LDPC) decoders. The characteristics of a large basket of generated LDPC decoders, including contemporary 802.11n decoders, have been examined as a verification of the system and as a demonstration of its capabilities. As a further demonstration, the framework has been applied to construct a Sudoku solver. / Master of Science