<p>New emission legislations introduced in the European Union and the U.S. have made truck manufacturers face stricter requirements for low emissions and on-board diagnostic systems. The on-board diagnostic system typically consists of several tests that are run when the truck is driving. One way to construct such tests is to use so called consistency relations. A consistency relation is a relation with known variables that in the fault free case always holds. Calculation of a consistency relation typically involves eliminating unknown variables from a set of equations.</p><p>To eliminate variables from a differential polynomial system, methods from differential algebra can be used. In this thesis, the purely algebraic Gröbner basis algorithm and the differential Rosenfeld-Gröbner algorithm implemented in the Maple package Diffalg have been compared and evaluated. The conclusion drawn is that there are no significant differences between the methods. However, since using Gröbner basis requires differentiations to be made in advance, the recommendation is to use the Rosenfeld-Gröbner algorithm.</p><p>Further, attempts to calculate consistency relations using the Rosenfeld-Gröbner algorithm have been made to a real application, a model of a Scania diesel engine. These attempts did not yield any successful results. It was only possible to calculate one consistency relation. This can be explained by the high complexity of the model.</p>

<p>Denna uppsats syftar till att öka förståelsen för hur ämneslärare uppfattar och använder sig av begreppet forskningsanknytning. Undersökningen har gjorts utifrån en fallstudie där fem ämneslärare i svenska har intervjuats genom semistrukturerade intervjuer. Resultatet visar att de intervjuade lärarna har uppfattat forskningsanknytning dels via kursinnehåll, dels som ett arbetssätt, och att de främst har upplevt forskningsanknytningen som punktvisa nedslag vid vissa kursavsnitt, framförallt vid uppsatsskrivande. Lärarna använder sig av forskningsanknytning i sin lärarverksamhet genom val av metoder och material, och genom att tillämpa delar av forskningsprocessen när de planerar och genomför undervisning. Studien visar också att de intervjuade lärarna förefaller dels kunna mer om, dels använda sig av forskningsanknytning i större utsträckning än vad de själva ger uttryck för.</p>

In this thesis we consider four topics all related to using problem reformulations in order to solve integer programs, i.e. optimization problems in which the decision variables must be integer. We first consider the polyhedral approach. We start by addressing the question of lifting valid inequalities, i.e. finding a valid inequality for a set Y from the knowledge of a valid inequality for a lower-dimensional restriction X of Y. We simplify and clarify the presentation of the procedure. This allows us to derive conditions under which the computation of the lifting is tractable. The second topic is the study of valid inequalities for the single node flow set. The single node flow set is the problem obtained by considering one node of a fixed charge network flow problem. We derive valid inequalities for this set and various generalizations. Our approach is a systematic procedure using only basic tools of integer programming: fixing and complementing variables, mixed-integer rounding and lifting. The method allows us to explain and generate a large range of inequalities describing the convex hull of such sets. The last two topics are based on non-standard approaches for integer programming. We first show how the group relaxation approach can be used to provide reformulations for the integral basis method. This is based on a study of extended formulations for the group problem. We present four extended formulations and show that the projections of three of these formulations provide the convex hull of the original group problem. Initial computational tests of the approach are also reported. Finally we consider a problem that is difficult for the standard branch-and-bound approach even for small instances. A reformulation based on lattice basis reduction is known to be more effective. However the step to compute the reduced basis is O(n^4) and becomes a bottleneck for small to medium instances. By using the structure of the problem, we show that we can decompose the problem and obtain the basis by taking the kronecker product of two smaller bases easier to compute. Furthermore, if the two small bases are reduced, the kronecker product is also reduced up to a reordering of the vectors. Computational results show the gain from such an approach.

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations -- Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -- relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -- methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage -- in which, given a new parameter value, we calculate the output of interest and associated error bound -- depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. / Singapore-MIT Alliance (SMA)

We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models, Breiman's hinge functions and some forms of Projection Pursuit Regression. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we also show a relation between activation functions of the Gaussian and sigmoidal type.

Denna uppsats syftar till att öka förståelsen för hur ämneslärare uppfattar och använder sig av begreppet forskningsanknytning. Undersökningen har gjorts utifrån en fallstudie där fem ämneslärare i svenska har intervjuats genom semistrukturerade intervjuer. Resultatet visar att de intervjuade lärarna har uppfattat forskningsanknytning dels via kursinnehåll, dels som ett arbetssätt, och att de främst har upplevt forskningsanknytningen som punktvisa nedslag vid vissa kursavsnitt, framförallt vid uppsatsskrivande. Lärarna använder sig av forskningsanknytning i sin lärarverksamhet genom val av metoder och material, och genom att tillämpa delar av forskningsprocessen när de planerar och genomför undervisning. Studien visar också att de intervjuade lärarna förefaller dels kunna mer om, dels använda sig av forskningsanknytning i större utsträckning än vad de själva ger uttryck för.

Structural equation models are systems of simultaneous linear equations that are generalizations of linear regression, and have many applications in the social, behavioural and biological sciences. A serious barrier to applications is that it is easy to specify models for which the parameter vector is not identifiable from the distribution of the observable data, and it is often difficult to tell whether a model is identified or not. In this thesis, we study the most straightforward method to check for identification – solving a system of simultaneous equations. However, the calculations can easily get very complex. Grobner basis is introduced to simplify the process. The main idea of checking identification is to solve a set of finitely many simultaneous equations, called identifying equations, which can be transformed into polynomials. If a unique solution is found, the model is identified. Grobner basis reduces the polynomials into simpler forms making them easier to solve. Also, it allows us to investigate the model-induced constraints on the covariances, even when the model is not identified. With the explicit solution to the identifying equations, including the constraints on the covariances, we can (1) locate points in the parameter space where the model is not identified, (2) find the maximum likelihood estimators, (3) study the effects of mis-specified models, (4) obtain a set of method of moments estimators, and (5) build customized parametric and distribution free tests, including inference for non-identified models.

Elliptic curve cryptosystem is one type of public-key system, and it can guarantee the same security level with Rivest, Shamir and Adleman (RSA) with a smaller key size. Therefore, the key of elliptic curve cryptography (ECC) can be more compact, and it brings many advantages such as circuit area, memory requirement, power consumption, performance and bandwidth. However, compared to private key system, like Advanced Encryption Standard (AES), ECC is still much more complicated and computationally intensive. In some real applications, people usually combine private-key system with public-key system to achieve high performance. The ultimate goal of this research is to architect a high performance ECC processor for high performance applications such as network server and cellular sites.<p> In this thesis, a high performance processor for ECC over Galois field (GF)(2^163) by using polynomial presentation is proposed for high-performance applications. It has three finite field (FF) reduced instruction set computer (RISC) cores and a main controller to achieve instruction-level parallelism (ILP) with pipeline so that the largely parallelized algorithm for elliptic curve point multiplication (PM) can be well suited on this platform. Instructions for combined FF operation are proposed to decrease clock cycles in the instruction set. The interconnection among three FF cores and the main controller is obtained by analyzing the data dependency in the parallelized algorithm. Five-stage pipeline is employed in this architecture. Finally, the u-code executed on these three FF cores is manually optimized to save clock cycles. The proposed design can reach 185 MHz with 20; 807 slices when implemented on Xilinx XC4VLX80 FPGA device and 263 MHz with 217,904 gates when synthesized with TSMC .18um CMOS technology. The implementation of the proposed architecture can complete one ECC PM in 1428 cycles, and is 1.3 times faster than the current fastest implementation over GF(2^163) reported in literature while consumes only 14:6% less area on the same FPGA device.

Structural equation models are systems of simultaneous linear equations that are generalizations of linear regression, and have many applications in the social, behavioural and biological sciences. A serious barrier to applications is that it is easy to specify models for which the parameter vector is not identifiable from the distribution of the observable data, and it is often difficult to tell whether a model is identified or not. In this thesis, we study the most straightforward method to check for identification – solving a system of simultaneous equations. However, the calculations can easily get very complex. Grobner basis is introduced to simplify the process. The main idea of checking identification is to solve a set of finitely many simultaneous equations, called identifying equations, which can be transformed into polynomials. If a unique solution is found, the model is identified. Grobner basis reduces the polynomials into simpler forms making them easier to solve. Also, it allows us to investigate the model-induced constraints on the covariances, even when the model is not identified. With the explicit solution to the identifying equations, including the constraints on the covariances, we can (1) locate points in the parameter space where the model is not identified, (2) find the maximum likelihood estimators, (3) study the effects of mis-specified models, (4) obtain a set of method of moments estimators, and (5) build customized parametric and distribution free tests, including inference for non-identified models.

New emission legislations introduced in the European Union and the U.S. have made truck manufacturers face stricter requirements for low emissions and on-board diagnostic systems. The on-board diagnostic system typically consists of several tests that are run when the truck is driving. One way to construct such tests is to use so called consistency relations. A consistency relation is a relation with known variables that in the fault free case always holds. Calculation of a consistency relation typically involves eliminating unknown variables from a set of equations. To eliminate variables from a differential polynomial system, methods from differential algebra can be used. In this thesis, the purely algebraic Gröbner basis algorithm and the differential Rosenfeld-Gröbner algorithm implemented in the Maple package Diffalg have been compared and evaluated. The conclusion drawn is that there are no significant differences between the methods. However, since using Gröbner basis requires differentiations to be made in advance, the recommendation is to use the Rosenfeld-Gröbner algorithm. Further, attempts to calculate consistency relations using the Rosenfeld-Gröbner algorithm have been made to a real application, a model of a Scania diesel engine. These attempts did not yield any successful results. It was only possible to calculate one consistency relation. This can be explained by the high complexity of the model.