This thesis seeks provide an original contribution by extending rational choice theory into a general theory of law which has not been done before. I term this theoretical framework rational constraint to distinguish it from other rational choice and contractarian theories. This is predicated on the increasing heterogeneity of contemporary populations and the claim that moral claims cannot resolve conflicts because they are not truth-apt (as I argue in chapter 1). I seek to extend rational choice theory by further developing the tradition of social contract theory as it applies to law in the contractarian tradition of Thomas Hobbes and David Gauthier. This can roughly be termed the contractarian version of social contract theory (in the introduction I distinguish this tradition from the other social contract tradition of contractualism). This tradition takes rationality to be a practical method for determining action based upon self-interest – this assumes that agents are not concerned about the wellbeing of others. Even so a broad range of restrictions are possible – this thesis seeks to take Gauthier’s theory (as the most contemporary and developed contractarian theory) further by providing a system that takes account of higher-order constraints as well. This approach is not concerned with the application of different competing sets of moral claims – rather the application of self-interested rationality to law is the focus and the original contribution of this thesis. Ultimately, I seek to provide a method for designing legal rules that can minimise conflict and cost in a heterogeneous population. The subject that I apply this framework to is reproduction which is non-economic in nature thus extending rational choice beyond it normal economic haunts. Moreover it is an area of law that concerns a part of life subject to a great deal of moral controversy thus demonstrating the superiority of the extended rational choice framework over moral systems in designing laws.

Constraint programming (CP) is a technology in which a combinatorial problem is modelled as a conjunction of constraints on variables ranging over given initial domains, and optionally an objective function on the variables. Such a model is given to a general-purpose solver performing systematic search to find constraint-satisfying domain values for the variables, giving an optimal value to the objective function. A constraint predicate (also known as a global constraint) does two things: from the modelling perspective, it allows a modeller to express a commonly occurring combinatorial substructure, for example that a set of variables must take distinct values; from the solving perspective, it comes with a propagation algorithm, called a propagator, which removes some but not necessarily all impossible values from the current domains of its variables when invoked during search. Although modern CP solvers have many constraint predicates, often a predicate one would like to use is not available. In the past, the choices were either to reformulate the model or to write one's own propagator. In this dissertation, we contribute to the automatic design of propagators for new predicates. Integer time series are often subject to constraints on the aggregation of the features of all maximal occurrences of some pattern. For example, the minimum width of the peaks may be constrained. Automata allow many constraint predicates for variable sequences, and in particular many time-series predicates, to be described in a high-level way. Our first contribution is an algorithm for generating an automaton-based predicate description from a pattern, a feature, and an aggregator. It has previously been shown how to decompose an automaton-described constraint on a variable sequence into a conjunction of constraints whose predicates have existing propagators. This conjunction provides the propagation, but it is unknown how to propagate it efficiently. Our second contribution is a tool for deriving, in an off-line process, implied constraints for automaton-induced constraint decompositions to improve propagation. Further, when a constraint predicate functionally determines a result variable that is unchanged under reversal of a variable sequence, we provide as our third contribution an algorithm for deriving an implied constraint between the result variables for a variable sequence, a prefix thereof, and the corresponding suffix.

The classic minimum induced drag spanload is not necessarily the best choice for an aircraft. For a single aircraft configuration, variations from the elliptic, minimum drag optimum load distribution can produce wing weight savings that result in airplane performance benefits. For a group of aircraft flying in formation, non-elliptic lift distributions can give high induced drag reductions both for the formation and for each airplane. For single aircraft, a discrete vortex method which performs the calculations in the Trefftz plane has been used to calculate optimum spanloads for non-coplanar multi-surface configurations. The method includes constraints for lift coefficient, pitching moment coefficient and wing root bending moment. This wing structural constraint has been introduced such that wing geometry is not changed but the modified load distributions can be related to wing weight. Changes in wing induced drag and weight were converted to aircraft total gross weight and fuel weight benefits, so that optimum spanloads that give maximum take-off gross weight reductions can be found. Results show that a reduction in root bending moment from a lift distribution that gives minimum induced drag leads to more triangular spanloads, where the loads are shifted towards the root, reducing wing weight and increasing induced drag. A slight reduction in root bending moment is always beneficial, since the initial increase in induced drag is very small compared to the wing weight decrease. Total weight benefits were studied for a Boeing 777-200IGW type configuration, obtaining take-off gross weight improvements of about 1% for maximum range missions. When performing economical, reduced-range missions, improvements can almost double. A long range, more aerodynamically driven aircraft like the Boeing 777-200IGW will experience lower benefits as a result of increasing drag. Short to medium range aircraft will profit the most from more triangular lift distributions. Formation flight configurations can also result in large induced drag reductions for load distributions that deviate from the elliptical one. Optimum spanloads for a group of aircraft flying in an arrow formation were studied using the same discrete vortex method, now under constraints in lift, pitching moment and rolling moment coefficients. It has been shown that large general improvements in induced drag can be obtained when the spanwise and vertical distances between aircraft are small. In certain cases, using our potential flow vortex model, this results in negative (thrust) induced drag on some airplanes in the configuration. The optimum load distributions necessary to achieve these benefits may, however, correspond to a geometry that will produce impractical lift distributions if the aircraft are flying alone. Optimum separation among airplanes in this type of formation is determined by such diverse factors as the ability to generate the required optimum load distributions or the need for collision avoidance. / Master of Science

<p> Transverse vibrations of a beam with one end fixed and the other supported on nonlinear spring have been studied. Theoretical analysis has been carried out for two different cases of springs, viz.; cubic nonlinear and bilinear types. </p> <p> Theoretical results for bilinear case have been compared with those obtained experimentally. The effect of end mass has also been considered in theoretical analysis. </p> / Thesis / Master of Engineering (MEngr)

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With the advances in VLSI and System-On-Chip (SOC) technologies, the complexity of hardware systems has increased manifold. The increasing complexity poses serious challenges to the digital hardware design. Functional verification has become one of the most expensive and time-consuming components of the current product development cycle. Today, design verification alone often surpasses 70% of the total development cost and the situation has been projected to continue to worsen. The two most widely used formal methods for design verification are Equivalence Checking and Model Checking. During the design phase, hardware goes through several stages of optimizations for area, speed, power, etc. Determining the functional correctness of the design after each optimization step by means of exhaustive simulation can be prohibitively expensive. An alternative to prove functional correctness of the optimized design is to determine the design's functional equivalence with respect to some golden model which is known to be functionally correct. Efficient techniques to perform this process is known as Equivalence Checking. Equivalence Checking requires that the implementation circuit should be functionally equivalent to the specification circuit. Complexities in Equivalence Checking can be exponential to the circuit size in the worst case. Since Equivalence Checking of sequential circuits still remains a challenging problem, in this thesis, we first address this problem using efficient learning techniques. In contrast to the traditional learning methods, our method employs a mining algorithm to discover global constraints among several nodes efficiently in a sequential circuit. In a Boolean satisfiability (SAT) based framework for the bounded sequential equivalence checking, by taking advantage of the repeated search space, our mining algorithm is only performed on a small window size of unrolled circuit, and the mined relations could be reused subsequently. These powerful relations, when added as new constraint clauses to the original formula, help to significantly increase the deductive power for the SAT engine, thereby pruning a larger portion of the search space. Likewise, the memory required and time taken to solve these problems are alleviated. We also propose a pseudo-functional test generation method based on effective functional constraints extraction. We use mining techniques to extract a set of multi-node functional constraints which consists of illegal states and internal signal correlation. Then the functional constraints are imposed to a ATPG tool to generate pseudo functional delay tests. / Master of Science

Constraint satisfaction is a very well studied and fundamental artificial intelligence technique. Various forms of knowledge can be represented with constraints, and reasoning techniques from disparate fields can be encapsulated within constraint reasoning algorithms. However, problems involving uncertainty, or which have an adversarial nature (for example, games), are difficult to express and solve in the classical constraint satisfaction problem. This thesis is concerned with an extension to the classical problem: the Quantified Constraint Satisfaction Problem (QCSP). QCSP has recently attracted interest. In QCSP, quantifiers are allowed, facilitating the expression of uncertainty. I examine whether QCSP is a useful formalism. This divides into two questions: whether QCSP can be solved efficiently; and whether realistic problems can be represented in QCSP. In attempting to answer these questions, the main contributions of this thesis are the following: - the definition of two new notions of consistency; - four new constraint propagation algorithms (with eight variants in total), along with empirical evaluations; - two novel schemes to implement the pure value rule, which is able to simplify QCSP instances; - a new optimization algorithm for QCSP; - the integration of these algorithms and techniques into a solver named Queso; - and the modelling of the Connect 4 game, and of faulty job shop scheduling, in QCSP. These are set in context by a thorough review of the QCSP literature.

Efficiently allocating the scarce and expensive radio resources is a key challenge for advanced radio communication systems. To this end, cognitive radio (CR) has emerged as a promising solution which can offer considerable improvements in spectrum utilization. Furthermore, cooperative communication is a concept proposed to obtain spatial diversity gains through relays without requiring multiple antennas. To benefit from both CR and cooperative communications, a combination of CR networks (CRNs) with cooperative relaying referred to as cognitive cooperative relay networks (CCRNs) has recently been proposed. CCRNs can better utilize the radio spectrum by allowing the secondary users (SUs) to opportunistically access spectrum, share spectrum with primary users (PUs), and provide performance gains offered by cooperative relaying. In this thesis, a performance analysis of underlay CRNs and CCRNs in different fading channels is provided based on analytical expressions, numerical results, and simulations. To allocate power in the CCRNs, power allocation policies are proposed which consider the peak transmit power limit of the SUs and the outage probability constraint of the primary network. Thus, the impact of multiuser diversity, peak transmit power, fading parameters, and modulation schemes on the performance of the CRNs and CCRNs can be analyzed. The thesis is divided into an introduction and five research parts based on peer-reviewed conference papers and journal articles. The introduction provides fundamental background on spectrum sharing systems, fading channels, and performance metrics. In the first part, a basic underlay CRN is analyzed where the outage probability and the ergodic capacity of the network over general fading channels is derived. In the second part, the outage probability and the ergodic capacity of an underlay CRN are assessed capturing the effect of multiuser diversity on the network subject to Nakagami-m fading. Considering the presence of a PU transmitter (PU-Tx), a power allocation policy is derived and utilized for CRN performance analysis under Rayleigh fading. In the third part, the impact of multiple PU-Txs and multiple PU receivers (PU-Rxs) on the outage probability of an underlay CCRN is studied. The outage constraint at the PU-Rx and the peak transmit power constraint of the SUs are taken into account to derive the power allocation policies for the SUs. In the fourth part, analytical expressions for the outage probability and symbol error probability for CCRNs are derived where signal combining schemes at the SU receiver (SU-Rx) are compared. Finally, the fifth part applies a sleep/wake-up strategy and the min(N; T) policy to an underlay CRN. The SUs of the network operate as wireless sensor nodes under Nakagami-m fading. A power consumption function of the CRN is derived. Further, the impact of M/G/1 queue and fading channel parameters on the power consumption is assessed.