Béla Bartók's Piano Sonata Sz.80 is known for its integration of modernist language with traditional elements. However, due to Bartók's radical style of writing, it remains challenging to precisely define the piece's motives, voice-leading, and structure, even though pianists who perform it may intuitively comprehend them. Therefore, this study aims to elucidate the Piano Sonata's motivic and tonal structure, genesis and development. First, this study demonstrates Bartók's use of linear motives and progressions to elucidate the Piano Sonata's large-scale structure and demonstrate its internal coherence. Second, by comparing the published score with the facsimile of the Budapest Manuscript, it is possible to shed light on the significance of the changes that Bartók made, facilitating a better understanding of his intentions. Lastly, this study suggests interpretive decisions based on the analysis and manuscripts, thus providing performers with a more thorough understanding of the piece.

Thesis advisor: Henry Braun / The State NAEP program only reports the mean achievement estimate of a subgroup within a given state if it samples at least 62 students who identify with the subgroup. Since some subgroups of students constitute small proportions of certain states’ general student populations, these low-incidence groups of students are seldom sufficiently sampled to meet this rule-of-62 requirement. As a result, education researchers and policymakers are frequently left without a full understanding of how states are supporting the learning and achievement of different subgroups of students.Using grade 8 mathematics results in 2015, this dissertation addresses the problem by comparing the performance of three different techniques in predicting mean subgroup achievement on NAEP. The methodology involves simulating scenarios in which subgroup samples greater or equal to 62 are treated as not available for calculating mean achievement estimates. These techniques comprise an adaptation of Multivariate Imputation by Chained Equations (MICE), a common form of Small Area Estimation known as the Fay-Herriot model (FH), and a Cross-Survey analysis approach that emphasizes flexibility in model specification, referred to as Flexible Cross-Survey Analysis (FLEX CS) in this study. Data used for the prediction study include public-use state-level estimates of mean subgroup achievement on NAEP, restricted-use student-level achievement data on NAEP, public-use state-level administrative data from Education Week, the Common Core of Data, the U.S. Census Bureau, and public-use district-level achievement data in NAEP-referenced units from the Stanford Education Data Archive. To evaluate the accuracy of the techniques, a weighted measure of Mean Absolute Error and a coverage indicator quantify differences between predicted and target values. To evaluate whether a technique could be recommended for use in practice, accuracy measures for each technique are compared to benchmark values established as markers of successful prediction based on results from a simulation analysis with example NAEP data. Results indicate that both the FH and FLEX CS techniques may be suitable for use in practice and that the FH technique is particularly appealing. However, before definitive recommendations are made, the analyses from this dissertation should be conducted employing math achievement data from other years, as well as data from NAEP Reading. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

Several modifications have been suggested to extend binary classifiers to multiclass classification, for instance the One Against All technique, the One Against One technique, or Directed Acyclic Graphs. A recent approach for multiclass classification is the pairwise classification, which relies on two input examples instead of one and predicts whether the two input examples belong to the same class or to different classes. A Support Vector Machine (SVM), which is able to handle pairwise classification tasks, is called pairwise SVM. A common pairwise classification task is face recognition. In this area, a set of images is given for training and another set of images is given for testing. Often, one is interested in the interclass setting. The latter means that any person which is represented by an image in the training set is not represented by any image in the test set. From the mentioned multiclass classification techniques only the pairwise classification technique provides meaningful results in the interclass setting. For a pairwise classifier the order of the two examples should not influence the classification result. A common approach to enforce this symmetry is the use of selected kernels. Relations between such kernels and certain projections are provided. It is shown, that those projections can lead to an information loss. For pairwise SVMs another approach for enforcing symmetry is the symmetrization of the training sets. In other words, if the pair (a,b) of examples is a training pair then (b,a) is a training pair, too. It is proven that both approaches do lead to the same decision function for selected parameters. Empirical tests show that the approach using selected kernels is three to four times faster. For a good interclass generalization of pairwise SVMs training sets with several million training pairs are needed. A technique is presented which further speeds up the training time of pairwise SVMs by a factor of up to 130 and thus enables the learning of training sets with several million pairs. Another element affecting time is the need to select several parameters. Even with the applied speed up techniques a grid search over the set of parameters would be very expensive. Therefore, a model selection technique is introduced that is much less computationally expensive. In machine learning, the training set and the test set are created by using some data generating process. Several pairwise data generating processes are derived from a given non pairwise data generating process. Advantages and disadvantages of the different pairwise data generating processes are evaluated. Pairwise Bayes' Classifiers are introduced and their properties are discussed. It is shown that pairwise Bayes' Classifiers for interclass generalization tasks can differ from pairwise Bayes' Classifiers for interexample generalization tasks. In face recognition the interexample task implies that each person which is represented by an image in the test set is also represented by at least one image in the training set. Moreover, the set of images of the training set and the set of images of the test set are disjoint. Pairwise SVMs are applied to four synthetic and to two real world datasets. One of the real world datasets is the Labeled Faces in the Wild (LFW) database while the other one is provided by Cognitec Systems GmbH. Empirical evidence for the presented model selection heuristic, the discussion about the loss of information and the provided speed up techniques is given by the synthetic databases and it is shown that classifiers of pairwise SVMs lead to a similar quality as pairwise Bayes' classifiers. Additionally, a pairwise classifier is identified for the LFW database which leads to an average equal error rate (EER) of 0.0947 with a standard error of the mean (SEM) of 0.0057. This result is better than the result of the current state of the art classifier, namely the combined probabilistic linear discriminant analysis classifier, which leads to an average EER of 0.0993 and a SEM of 0.0051. / Es gibt verschiedene Ansätze, um binäre Klassifikatoren zur Mehrklassenklassifikation zu nutzen, zum Beispiel die One Against All Technik, die One Against One Technik oder Directed Acyclic Graphs. Paarweise Klassifikation ist ein neuerer Ansatz zur Mehrklassenklassifikation. Dieser Ansatz basiert auf der Verwendung von zwei Input Examples anstelle von einem und bestimmt, ob diese beiden Examples zur gleichen Klasse oder zu unterschiedlichen Klassen gehören. Eine Support Vector Machine (SVM), die für paarweise Klassifikationsaufgaben genutzt wird, heißt paarweise SVM. Beispielsweise werden Probleme der Gesichtserkennung als paarweise Klassifikationsaufgabe gestellt. Dazu nutzt man eine Menge von Bildern zum Training und ein andere Menge von Bildern zum Testen. Häufig ist man dabei an der Interclass Generalization interessiert. Das bedeutet, dass jede Person, die auf wenigstens einem Bild der Trainingsmenge dargestellt ist, auf keinem Bild der Testmenge vorkommt. Von allen erwähnten Mehrklassenklassifikationstechniken liefert nur die paarweise Klassifikationstechnik sinnvolle Ergebnisse für die Interclass Generalization. Die Entscheidung eines paarweisen Klassifikators sollte nicht von der Reihenfolge der zwei Input Examples abhängen. Diese Symmetrie wird häufig durch die Verwendung spezieller Kerne gesichert. Es werden Beziehungen zwischen solchen Kernen und bestimmten Projektionen hergeleitet. Zudem wird gezeigt, dass diese Projektionen zu einem Informationsverlust führen können. Für paarweise SVMs ist die Symmetrisierung der Trainingsmengen ein weiter Ansatz zur Sicherung der Symmetrie. Das bedeutet, wenn das Paar (a,b) von Input Examples zur Trainingsmenge gehört, dann muss das Paar (b,a) ebenfalls zur Trainingsmenge gehören. Es wird bewiesen, dass für bestimmte Parameter beide Ansätze zur gleichen Entscheidungsfunktion führen. Empirische Messungen zeigen, dass der Ansatz mittels spezieller Kerne drei bis viermal schneller ist. Um eine gute Interclass Generalization zu erreichen, werden bei paarweisen SVMs Trainingsmengen mit mehreren Millionen Paaren benötigt. Es wird eine Technik eingeführt, die die Trainingszeit von paarweisen SVMs um bis zum 130-fachen beschleunigt und es somit ermöglicht, Trainingsmengen mit mehreren Millionen Paaren zu verwenden. Auch die Auswahl guter Parameter für paarweise SVMs ist im Allgemeinen sehr zeitaufwendig. Selbst mit den beschriebenen Beschleunigungen ist eine Gittersuche in der Menge der Parameter sehr teuer. Daher wird eine Model Selection Technik eingeführt, die deutlich geringeren Aufwand erfordert. Im maschinellen Lernen werden die Trainingsmenge und die Testmenge von einem Datengenerierungsprozess erzeugt. Ausgehend von einem nicht paarweisen Datengenerierungsprozess werden unterschiedliche paarweise Datengenerierungsprozesse abgeleitet und ihre Vor- und Nachteile bewertet. Es werden paarweise Bayes-Klassifikatoren eingeführt und ihre Eigenschaften diskutiert. Es wird gezeigt, dass sich diese Bayes-Klassifikatoren für Interclass Generalization Aufgaben und für Interexample Generalization Aufgaben im Allgemeinen unterscheiden. Bei der Gesichtserkennung bedeutet die Interexample Generalization, dass jede Person, die auf einem Bild der Testmenge dargestellt ist, auch auf mindestens einem Bild der Trainingsmenge vorkommt. Außerdem ist der Durchschnitt der Menge der Bilder der Trainingsmenge mit der Menge der Bilder der Testmenge leer. Paarweise SVMs werden an vier synthetischen und an zwei Real World Datenbanken getestet. Eine der verwendeten Real World Datenbanken ist die Labeled Faces in the Wild (LFW) Datenbank. Die andere wurde von Cognitec Systems GmbH bereitgestellt. Die Annahmen der Model Selection Technik, die Diskussion über den Informationsverlust, sowie die präsentierten Beschleunigungstechniken werden durch empirische Messungen mit den synthetischen Datenbanken belegt. Zudem wird mittels dieser Datenbanken gezeigt, dass Klassifikatoren von paarweisen SVMs zu ähnlich guten Ergebnissen wie paarweise Bayes-Klassifikatoren führen. Für die LFW Datenbank wird ein paarweiser Klassifikator bestimmt, der zu einer durchschnittlichen Equal Error Rate (EER) von 0.0947 und einem Standard Error of The Mean (SEM) von 0.0057 führt. Dieses Ergebnis ist besser als das des aktuellen State of the Art Klassifikators, dem Combined Probabilistic Linear Discriminant Analysis Klassifikator. Dieser führt zu einer durchschnittlichen EER von 0.0993 und einem SEM von 0.0051.

Traditional tests for large-scale assessment of mathematics learning have been criticized for several reasons, such as their mismatch between the vision of mathematical competence and the content covered by the test, and their failure to provide relevant information for guiding further learning and instruction. To achieve that large-scale assessments can function as tools for monitoring and improving learning and teaching, one has to move away from the rationale, the constraints, and the practices of traditional tests. As an illustration this paper presents an alternative approach to largescale assessment of elementary school mathematics developed in Flanders, Belgium Using models of item response theory, 14 measurement scales were constructed, each representing a cluster of curriculum standards and covering as a whole the mathematics curriculum relating to numbers, measurement and geometry. A representative sample of 5,763 sixth-graders (12-year-olds) belonging to 184 schools participated in the study. Based on expert judgments a cut-off score was set that determines the minimum level that students must achieve on each scale to master the standards. Overall, the more innovative curriculum standards were mastered less well than the more traditional ones. Few gender differences in performance were observed. The advantages of this approach and its further development are discussed.

In this dissertation, we present several main research thrusts involving thermodynamic stabilization via energy dissipating hybrid controllers and nonlinear control of network systems. Specifically, a novel class of fixed-order, energy-based hybrid controllers is presented as a means for achieving enhanced energy dissipation in Euler-Lagrange, lossless, and dissipative dynamical systems. These dynamic controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switching. In addition, we construct hybrid dynamic controllers that guarantee that the closed-loop system is consistent with basic thermodynamic principles. In particular, the existence of an entropy function for the closed-loop system is established that satisfies a hybrid Clausius-type inequality. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and the framework is applied to aerospace system models. The overall framework demonstrates that energy-based hybrid resetting controllers provide an extremely efficient mechanism for dissipating energy in nonlinear dynamical systems. Next, we present finite-time coordination controllers for multiagent network systems. Recent technological advances in communications and computation have spurred a broad interest in autonomous, adaptable vehicle formations. Distributed decision-making for coordination of networks of dynamic agents addresses a broad area of applications including cooperative control of unmanned air vehicles, microsatellite clusters, mobile robotics, and congestion control in communication networks. In this part of the dissertation we focus on finite-time consensus protocols for networks of dynamic agents with undirected information flow. The proposed controller architectures are predicated on the recently developed notion of system thermodynamics resulting in thermodynamically consistent continuous controller architectures involving the exchange of information between agents that guarantee that the closed-loop dynamical network is consistent with basic thermodynamic principles.

The multi-net Global Routing Problem (GRP) in VLSI physical design is a problem of routing a set of nets subject to limited resources and delay constraints. Various state-of-the-art routers are available but their main focus is to optimize the wire length and minimize the over ow. However optimizing wire length do not necessarily meet timing constraints at the sink nodes. Also, in modern nano-meter scale VLSI process the consideration of process variations is a necessity for ensuring reasonable yield at the fab. In this work, we try to nd a fundamental strategy to address the timing-driven Steiner tree construction (i.e., the routing) problem subject to congestion constraints and process variation. For congestion mitigation, a gradient based concurrent approach (over all nets) of Erzin et. al., rather than the traditional (sequential) rip-and-reroute is adopted in or- der to propagate the timing/delay-driven property of the Steiner tree candidates. The existing sequential rip-up and reroute methods meet the over ow constraint locally but cannot propagate the timing constraint which is non-local in nature. We build on this approach to accommodate the variation-aware statistical delay/timing requirements. To further reduce the congestion, the cost function of the tree generation method is updated by adding history based congestion penalty to the base cost (delay). Iterative use of the timing-driven Steiner tree construction method and history based tree construction procedure generate a diverse pool of candidate Steiner trees for each net. The gradient algorithm picks one tree for each net from the pool of trees such that congestion is e ciently controlled. As the technology scales down, process variation makes process dependent param- eters like resistance, capacitance etc non-deterministic. As a result, Statistical Static Timing Analysis or SSTA has replaced the traditional static timing in nano-meter scale VLSI processes. However, this poses a challenge regarding the max/min-plus algebra of Dijkstra like approximation algorithm that builds the Steiner trees. A new approach based on distance between distributions for nding maximum/minimum at the nodes is presented in this thesis. Under this metric, the approximation algorithm for variation aware timing driven congestion constrained routing is shown to be provably tight and one order of magnitude faster than existing approaches (which are not tight) such as the MVERT. The results (mean value) of our variation aware router are quite close to the mean of the several thousand Monte Carlo simulations of the deterministic router, i.e the results converge in mean. Therefore, instead of running so many deterministic Monte Carlo simulations, we can generate an average design with a probability distribution reasonably close to that of the actual behaviour of the design by running the proposed statistical router only once and at a small fraction of the computational e ort involved in physical design in the nano regime VLSI. The above approximation algorithm is extended to local routing, especially non- Manhattan lambda routing which is increasingly being allowed by the recent VLSI tech- nology nodes. Here also, we can meet delay driven constraints better and keep related wire lengths reasonable.

Single-Walled Carbon Nanotube (SWCNT) based Very Large Scale Integrated circuit (VLSI) interconnect is one of the emerging technologies, and has the potential to overcome the thermal issues persisting even with the advanced copper based interconnect. This is because of it’s promising electrical and thermal transport properties. It can be stated that thermal energy transport in SWCNTs is highly anisotropic due to the quasi one dimensionality, and like in other allotropes of carbon, phonons are the dominant energy carriers of heat conduction. In case of conventional interconnect materials, copper and aluminium, although their thermal conductivity varies over orders of magnitude at temperatures below100 K, near room temperature and above they have almost constant value. On the other hand, the reported experimental studies on suspended metallic SWCNTs illustrate a wide variation of the longitudinal lattice thermal conductivity (κl) with respect to the temperature(T)and the tube length(L)at low, room and high temperatures. Physics based analytical formulation of κl of metallic SWCNT as a function of L and T is essential to efficiently quantify this emerging technology’s impact on the rising thermal management issues of Integrated Circuits. In this work, a physics based diameter independent analytical model for κl of metallic SWCNT is addressed as a function of Lover a wide range of T. Heat conduction in metallic SWCNTs is governed by three resistive phonon scattering processes; second order three phonon Umklapp scattering, mass difference scattering and boundary scattering. For this study, all the above processes are considered, and the effective mode dependent relaxation time is determined by the Matthiessen’s rule. Phonon Boltzmann transport equation under the single mode relaxation time approximation is employed to derive the non-equilibrium distribution function. The heat flux as a function of temperature gradient is obtained from this non-equilibrium distribution function. Based on the Fourier’s definition of thermal conductivity, κl of metallic SWCNT is formulated and the Debye approximations are used to arrive at analytical model. The model developed is validated against both the low and high temperature experimental investigations. At low temperatures, thermal resistance of metallic SWCNT is due to phonon-boundary scattering process, while at high temperatures it is governed by three phonon Umklapp scattering process. It is understood that apart from form factor due to mass difference scattering, boundary scattering also plays the key role in determining the peak value. At room temperature, κl of metallic SWCNT is found to be an order of magnitude higher than that of most of metals. The reason can be attributed to the fact that both sound velocity and Debye temperature which have direct effect on the phonon transport in a solid, are reasonably higher in SWCNTs. Though Umk lapp processes reduce the κl steeper than 1/T beyond room-temperature, it’s magnitude is round1000 W/m/K upto 800 K for various tube lengths, which confirms that this novel material is indeed an efficient conductor of heat also, at room-temperature and above.

Several modifications have been suggested to extend binary classifiers to multiclass classification, for instance the One Against All technique, the One Against One technique, or Directed Acyclic Graphs. A recent approach for multiclass classification is the pairwise classification, which relies on two input examples instead of one and predicts whether the two input examples belong to the same class or to different classes. A Support Vector Machine (SVM), which is able to handle pairwise classification tasks, is called pairwise SVM. A common pairwise classification task is face recognition. In this area, a set of images is given for training and another set of images is given for testing. Often, one is interested in the interclass setting. The latter means that any person which is represented by an image in the training set is not represented by any image in the test set. From the mentioned multiclass classification techniques only the pairwise classification technique provides meaningful results in the interclass setting. For a pairwise classifier the order of the two examples should not influence the classification result. A common approach to enforce this symmetry is the use of selected kernels. Relations between such kernels and certain projections are provided. It is shown, that those projections can lead to an information loss. For pairwise SVMs another approach for enforcing symmetry is the symmetrization of the training sets. In other words, if the pair (a,b) of examples is a training pair then (b,a) is a training pair, too. It is proven that both approaches do lead to the same decision function for selected parameters. Empirical tests show that the approach using selected kernels is three to four times faster. For a good interclass generalization of pairwise SVMs training sets with several million training pairs are needed. A technique is presented which further speeds up the training time of pairwise SVMs by a factor of up to 130 and thus enables the learning of training sets with several million pairs. Another element affecting time is the need to select several parameters. Even with the applied speed up techniques a grid search over the set of parameters would be very expensive. Therefore, a model selection technique is introduced that is much less computationally expensive. In machine learning, the training set and the test set are created by using some data generating process. Several pairwise data generating processes are derived from a given non pairwise data generating process. Advantages and disadvantages of the different pairwise data generating processes are evaluated. Pairwise Bayes' Classifiers are introduced and their properties are discussed. It is shown that pairwise Bayes' Classifiers for interclass generalization tasks can differ from pairwise Bayes' Classifiers for interexample generalization tasks. In face recognition the interexample task implies that each person which is represented by an image in the test set is also represented by at least one image in the training set. Moreover, the set of images of the training set and the set of images of the test set are disjoint. Pairwise SVMs are applied to four synthetic and to two real world datasets. One of the real world datasets is the Labeled Faces in the Wild (LFW) database while the other one is provided by Cognitec Systems GmbH. Empirical evidence for the presented model selection heuristic, the discussion about the loss of information and the provided speed up techniques is given by the synthetic databases and it is shown that classifiers of pairwise SVMs lead to a similar quality as pairwise Bayes' classifiers. Additionally, a pairwise classifier is identified for the LFW database which leads to an average equal error rate (EER) of 0.0947 with a standard error of the mean (SEM) of 0.0057. This result is better than the result of the current state of the art classifier, namely the combined probabilistic linear discriminant analysis classifier, which leads to an average EER of 0.0993 and a SEM of 0.0051. / Es gibt verschiedene Ansätze, um binäre Klassifikatoren zur Mehrklassenklassifikation zu nutzen, zum Beispiel die One Against All Technik, die One Against One Technik oder Directed Acyclic Graphs. Paarweise Klassifikation ist ein neuerer Ansatz zur Mehrklassenklassifikation. Dieser Ansatz basiert auf der Verwendung von zwei Input Examples anstelle von einem und bestimmt, ob diese beiden Examples zur gleichen Klasse oder zu unterschiedlichen Klassen gehören. Eine Support Vector Machine (SVM), die für paarweise Klassifikationsaufgaben genutzt wird, heißt paarweise SVM. Beispielsweise werden Probleme der Gesichtserkennung als paarweise Klassifikationsaufgabe gestellt. Dazu nutzt man eine Menge von Bildern zum Training und ein andere Menge von Bildern zum Testen. Häufig ist man dabei an der Interclass Generalization interessiert. Das bedeutet, dass jede Person, die auf wenigstens einem Bild der Trainingsmenge dargestellt ist, auf keinem Bild der Testmenge vorkommt. Von allen erwähnten Mehrklassenklassifikationstechniken liefert nur die paarweise Klassifikationstechnik sinnvolle Ergebnisse für die Interclass Generalization. Die Entscheidung eines paarweisen Klassifikators sollte nicht von der Reihenfolge der zwei Input Examples abhängen. Diese Symmetrie wird häufig durch die Verwendung spezieller Kerne gesichert. Es werden Beziehungen zwischen solchen Kernen und bestimmten Projektionen hergeleitet. Zudem wird gezeigt, dass diese Projektionen zu einem Informationsverlust führen können. Für paarweise SVMs ist die Symmetrisierung der Trainingsmengen ein weiter Ansatz zur Sicherung der Symmetrie. Das bedeutet, wenn das Paar (a,b) von Input Examples zur Trainingsmenge gehört, dann muss das Paar (b,a) ebenfalls zur Trainingsmenge gehören. Es wird bewiesen, dass für bestimmte Parameter beide Ansätze zur gleichen Entscheidungsfunktion führen. Empirische Messungen zeigen, dass der Ansatz mittels spezieller Kerne drei bis viermal schneller ist. Um eine gute Interclass Generalization zu erreichen, werden bei paarweisen SVMs Trainingsmengen mit mehreren Millionen Paaren benötigt. Es wird eine Technik eingeführt, die die Trainingszeit von paarweisen SVMs um bis zum 130-fachen beschleunigt und es somit ermöglicht, Trainingsmengen mit mehreren Millionen Paaren zu verwenden. Auch die Auswahl guter Parameter für paarweise SVMs ist im Allgemeinen sehr zeitaufwendig. Selbst mit den beschriebenen Beschleunigungen ist eine Gittersuche in der Menge der Parameter sehr teuer. Daher wird eine Model Selection Technik eingeführt, die deutlich geringeren Aufwand erfordert. Im maschinellen Lernen werden die Trainingsmenge und die Testmenge von einem Datengenerierungsprozess erzeugt. Ausgehend von einem nicht paarweisen Datengenerierungsprozess werden unterschiedliche paarweise Datengenerierungsprozesse abgeleitet und ihre Vor- und Nachteile bewertet. Es werden paarweise Bayes-Klassifikatoren eingeführt und ihre Eigenschaften diskutiert. Es wird gezeigt, dass sich diese Bayes-Klassifikatoren für Interclass Generalization Aufgaben und für Interexample Generalization Aufgaben im Allgemeinen unterscheiden. Bei der Gesichtserkennung bedeutet die Interexample Generalization, dass jede Person, die auf einem Bild der Testmenge dargestellt ist, auch auf mindestens einem Bild der Trainingsmenge vorkommt. Außerdem ist der Durchschnitt der Menge der Bilder der Trainingsmenge mit der Menge der Bilder der Testmenge leer. Paarweise SVMs werden an vier synthetischen und an zwei Real World Datenbanken getestet. Eine der verwendeten Real World Datenbanken ist die Labeled Faces in the Wild (LFW) Datenbank. Die andere wurde von Cognitec Systems GmbH bereitgestellt. Die Annahmen der Model Selection Technik, die Diskussion über den Informationsverlust, sowie die präsentierten Beschleunigungstechniken werden durch empirische Messungen mit den synthetischen Datenbanken belegt. Zudem wird mittels dieser Datenbanken gezeigt, dass Klassifikatoren von paarweisen SVMs zu ähnlich guten Ergebnissen wie paarweise Bayes-Klassifikatoren führen. Für die LFW Datenbank wird ein paarweiser Klassifikator bestimmt, der zu einer durchschnittlichen Equal Error Rate (EER) von 0.0947 und einem Standard Error of The Mean (SEM) von 0.0057 führt. Dieses Ergebnis ist besser als das des aktuellen State of the Art Klassifikators, dem Combined Probabilistic Linear Discriminant Analysis Klassifikator. Dieser führt zu einer durchschnittlichen EER von 0.0993 und einem SEM von 0.0051.

Traditional tests for large-scale assessment of mathematics learning have been criticized for several reasons, such as their mismatch between the vision of mathematical competence and the content covered by the test, and their failure to provide relevant information for guiding further learning and instruction. To achieve that large-scale assessments can function as tools for monitoring and improving learning and teaching, one has to move away from the rationale, the constraints, and the practices of traditional tests. As an illustration this paper presents an alternative approach to largescale assessment of elementary school mathematics developed in Flanders, Belgium Using models of item response theory, 14 measurement scales were constructed, each representing a cluster of curriculum standards and covering as a whole the mathematics curriculum relating to numbers, measurement and geometry. A representative sample of 5,763 sixth-graders (12-year-olds) belonging to 184 schools participated in the study. Based on expert judgments a cut-off score was set that determines the minimum level that students must achieve on each scale to master the standards. Overall, the more innovative curriculum standards were mastered less well than the more traditional ones. Few gender differences in performance were observed. The advantages of this approach and its further development are discussed.

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