The claim that a principle known as Irreducible Complexity (IC) is empirically discoverable is investigated successively from the perspective of engineering, then molecular biology and finally theology, with the aim of evaluating the utility of IC for an interdisciplinary dialogue between all three. In the process, IC is subjected to the principle objections presented against it in the literature, leading to the conclusion that IC is sufficiently resistant to scientific criticism to be accepted as a true property of certain living systems. The ubiquity of machine descriptors in the professional literature of molecular biology is scrutinised in the context of the role of metaphor in science, as well as in the context of entailment models. A Biblical Theological approach to the Bible is harnessed to establish a framework for estimating the extent to which the story of Christ warrants expectation of first order design formalisms in nature, and whether that story within itself provides any homomorphic exemplification of IC. Additionally, key theological criticisms of IC are evaluated as well as criticisms of the Neo Darwinian revisioning of the Biblical account. The overall conclusion is that a true interdisciplinary dialogue where IC is the nexus holds theoretical as well as experimental promise. / Thesis (M.A. (Dogmatics))--North-West University, Potchefstroom Campus, 2008.

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Spatial graphs with 4–valent rigid vertices and two single valent endpoints, called assembly graphs, model DNA recombination processes that appear in certain species of ciliates. Recombined genes are modeled by certain types of paths in an assembly graph that make a ”oper pendicular ” turn at each 4–valent vertex of the graph called polygonal paths. The assembly number of an assembly graph is the minimum number of polygonal paths that visit each vertex exactly once. In particular, an assembly graph is called realizable if the graph has a Hamiltonian polygonal path. An assembly graph ɣ^ obtained from a given assembly graph γ by substituting every edge of γ by a loop is called a loop-saturated graph. We show that a loop- saturated graph ɣ^ has an assembly number a unit larger than the size of ɣ. For a positive integer n, the minimum realization number for n is defined by Rmin(n) = min{|ɣ| : An(ɣ) = n}, where |γ| is the number of 4-valent vertices in γ. A graph γ that gives the minimum for Rmin(n) is called a realization of assembly number n. We denote by Rmin(n) the set of realization graphs for n. We prove that loop-saturated graphs with assembly number nachieve the upper bound of Rmin(n). If a simple assembly graph γ has no loops then γ is not in Rmin(n). With the introduction of left –additive, right–additive and middle additive operations, we study the properties of assembly graphs when composing increases their assembly number. We also introduce the notion of height sequence, a non-increasing sequence of positive integers, that counts the number of 4-valent vertices which the polygonal paths contain. We show properties of a height sequence for loop–saturated graphs. Assembly graphs are represented by double-occurrence words called assembly words. An assembly word is strongly-irreducible if it does not contain a proper subword that is also a double-occurrence word. We prove that, for every positive integer n there is a strongly-irreducible assembly graph with assembly number n, and if a simple assembly graph is strongly-irreducible, then γ ̸∈ Rmin(n).

The claim that a principle known as Irreducible Complexity (IC) is empirically discoverable is investigated successively from the perspective of engineering, then molecular biology and finally theology, with the aim of evaluating the utility of IC for an interdisciplinary dialogue between all three. In the process, IC is subjected to the principle objections presented against it in the literature, leading to the conclusion that IC is sufficiently resistant to scientific criticism to be accepted as a true property of certain living systems. The ubiquity of machine descriptors in the professional literature of molecular biology is scrutinised in the context of the role of metaphor in science, as well as in the context of entailment models. A Biblical Theological approach to the Bible is harnessed to establish a framework for estimating the extent to which the story of Christ warrants expectation of first order design formalisms in nature, and whether that story within itself provides any homomorphic exemplification of IC. Additionally, key theological criticisms of IC are evaluated as well as criticisms of the Neo Darwinian revisioning of the Biblical account. The overall conclusion is that a true interdisciplinary dialogue where IC is the nexus holds theoretical as well as experimental promise. / Thesis (M.A. (Dogmatics))--North-West University, Potchefstroom Campus, 2008.

The claim that a principle known as Irreducible Complexity (IC) is empirically discoverable is investigated successively from the perspective of engineering, then molecular biology and finally theology, with the aim of evaluating the utility of IC for an interdisciplinary dialogue between all three. In the process, IC is subjected to the principle objections presented against it in the literature, leading to the conclusion that IC is sufficiently resistant to scientific criticism to be accepted as a true property of certain living systems. The ubiquity of machine descriptors in the professional literature of molecular biology is scrutinised in the context of the role of metaphor in science, as well as in the context of entailment models. A Biblical Theological approach to the Bible is harnessed to establish a framework for estimating the extent to which the story of Christ warrants expectation of first order design formalisms in nature, and whether that story within itself provides any homomorphic exemplification of IC. Additionally, key theological criticisms of IC are evaluated as well as criticisms of the Neo Darwinian revisioning of the Biblical account. The overall conclusion is that a true interdisciplinary dialogue where IC is the nexus holds theoretical as well as experimental promise. / Thesis (M.A. (Dogmatics))--North-West University, Potchefstroom Campus, 2008.

We prove that a torus transverse to an Axiom A vector field that does not exhibit sinks, sources or null homotopic periodic orbits on a closed irreducible 3-manifold is incompressible. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Provaremos que um toro transversal a um campo de vetores Axioma A que não exibe poço, fonte e órbita periódica homotópica a um ponto sobre uma variedade tridimensional, fechada, irredutível é incompressível.

O objetivo deste trabalho é estudar a estrutura dos módulos sobre uma álgebra trivial de dimensão dois na variedade M das álgebras comutativas de potências associativas. Em particular classificamos os módulos irredutíveis. Estes resultados nos permitem compreender melhor a estrutura das nilálgebras comutativas de dimensão finita e nilíndice 4. Finalmente classificamos, sob isomorfismos, as nilálgebras comutativas de potências associativas de dimensão n e nilíndice n. / The aim of this work is to study the structure of the modules over a trivial algebra of dimension two in the variety M of commutative and power-associative algebras. In particular we classify the irreducible modules. These results enables us to understand better the structure of finite-dimensional power-associative nilalgebras of nilindex 4. Finally, we classify, up to isomorphism, commutative power associative nilalgebras of nilindex n and dimension n.

The Rijndael cryptosystem uses a particular polynomial to create its constants. All calculations within the encryption and decryption layers are based on this polynomial. This arouse the curiosity to see what happens if the polynomial is substituted by other polynomials. This paper’s main area of study is to investigate the consequences of using different polynomials to construct the Rijndael cryptosystem. To do so, as a phase of this study, a Mathematica package has been created to ease the investigations. As the second phase, using the aforementioned package, some kind of diffusion analysis has been done on the newly constructed Rijndael-like cryptosystems. The fundamental challenge was to figure out the reason of having the particular polynomial chosen. By the end of the experiment, we concluded that choosing other polynomials with the same characteristics as an ingredient of the Rijndael algorithm, does not have any perceptible effects on the diffusion level.

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Logic-based Benders decomposition (LBBD) is a strategy for solving discrete optimisation problems. In LBBD, the optimisation problem is divided into a master problem and a subproblem and each part is solved separately. LBBD methods that combine mixed-integer programming and constraint programming have been successfully applied to solve large-scale scheduling and resource allocation problems. Such combinations typically solve an assignment-type master problem and a scheduling-type subproblem. However, a challenge with LBBD methods that have feasibility subproblems are that they do not provide a feasible solution until an optimal solution is found.  In this thesis, we show that feasible solutions can be obtained by finding and combining feasible parts of an infeasible master problem assignment. We use these insights to develop an acceleration technique for LBBD that solves a series of subproblems, according to algorithms for constructing a maximal feasible subset of constraints (MaFS). Using a multiprocessor scheduling problem as a benchmark, we study the computational impact from using this technique. We evaluate three variants of LBBD schemes. The first uses MaFS, the second uses irreducible subset of constraints (IIS) and the third combines MaFS with IIS. Computational tests were performed on an instance set of multiprocessor scheduling problems. In total, 83 instances were tested, and their number of tasks varied between 2794 and 10,661. The results showed that when applying our acceleration technique in the decomposition scheme, the pessimistic bounds were strong, but the convergence was slow. The decomposition scheme combining our acceleration technique with the acceleration technique using IIS showed potential to accelerate the method.