The first part is a study of an ecological model with one herbivore and $N$ plants. The system has a new type of functional response due to the speculation that the plants compete with each other and have different levels of toxin which inhibit the herbivore's ability to eat up to a certain amount. We first derive the model mathematically and then investigate, both analytically and numerically, the possible dynamics for this model, including the bifurcation and chaos. We also discuss the conditions under which all the species can coexist. The second part is a study in the normal form theory. In particular, we study the relations between the normal forms and the first integrals in analytic vector fields. We are able to generalize one of Poincare's classical results on the nonexistence of first integrals in an autonomous system. Then in the space of 2n-dimensional analytic autonomous systems with exactly n resonances and n functionally independent first integrals, we obtain some results related to the convergence and generic divergence of the normalizations. Lastly we give a new proof of the necessary and sufficient conditions for a planar Hamiltonian system to have an isochronous center.

An NNF circuit is a directed acyclic graph (DAG), where each leaf is labelled with either true/false or a literal, and each inner node represents either a conjunction (∧) or a disjunction (∨). A decomposable NNF (DNNF) is an NNF satisfying the decomposabi- lity property for each conjunction node. The C-BDMC language generalizes the DNNF language. In a C-BDMC, the leaves can contain CNF formulae from a given base class C. In this paper, we focus only on renamable Horn formulae. We experimentally compare the sizes of d-BDMC and d-DNNF representations. We describe a new compilation langu- age, called cara DNNF (c-DNNF), that generalizes the DNNF language. A c-DNNF circuit can be considered as a compressed representation of a DNNF circuit. We present a new experimental knowledge compiler, called CaraCompiler, for converting a CNF formula into a d-BDMC or a (c)d-DNNF circuit. CaraCompiler is based on the state-of-the-art compiler D4. Also, we mention some extensions for the compiler D4, such as caching hypergraph cuts that can reduce the compilation times. 1

ITC/USA 2008 Conference Proceedings / The Forty-Fourth Annual International Telemetering Conference and Technical Exhibition / October 27-30, 2008 / Town and Country Resort & Convention Center, San Diego, California / In a multi-user cognitive radio network, there arises a need for coordination among the network users for efficient utilization of the available electromagnetic spectrum. While adaptive modulation alone helps cognitive radios actively determine the channel quality metric for the next transmission, Game theory combined with an adaptive modulation system helps them achieve mutual coordination among channel users and avoids any possible confusion about transmitting/receiving through a channel in the future. This paper highlights how the concepts of game theory and adaptive modulation can be incorporated in a cognitive radio framework to achieve better communication for telemetry applications.

År 1970 introducerades normalisering med syfte att organisera data i relationsdatabaser för att undvika redundant data och reducera risker för anomalier. Idag finns indikationer på att en mer nyanserad bild av normalisering behövs då dagens databaser ställs inför nya utmaningar och krav. Det här arbetet utförs i form av en fallstudie där en analys av tre databaser inom olika verksamheter genomförs. Med utgångspunkt i normalformerna genomförs en explorativ analys för att identifiera vilka aspekter som påverkar normalisering i industrin. Slutsatsen av arbetet är att det är svårt för en oberoende part till databasen att avgöra och tolka normalformernas uppfyllnad. Faktorer som påverkar normalisering av databaser är: utvecklarens intuition, användarens påverkan av datakvalitet samt den tekniska skuld som quickfixes orsakar. / Normalization was first introduced in 1970 with the purpose to organize data within relational databases in a way to avoid data redundancy and reduce the number of anomalies. As databases are facing new challenges and requirements, indications have been identified which points to a need for a more detailed view of normalization. This work is the outcome of a case study where three databases are analyzed. With the normal forms as starting point, an explorative analysis is made with the goal to identify different aspects that affects the way normalization is conducted within the industry. The conclusion is that it is difficult for an outsider to the database to interpret and determine whether the normal forms are fulfilled or not. Aspects affecting normalization are: the developer's intuition, users' impact on data quality and the technical debt that quickfixes creates.

In this thesis we study algorithms for computing normal forms for matrices of Ore polynomials while controlling coefficient growth. By formulating row reduction as a linear algebra problem, we obtain a fraction-free algorithm for row reduction for matrices of Ore polynomials. The algorithm allows us to compute the rank and a basis of the left nullspace of the input matrix. When the input is restricted to matrices of shift polynomials and ordinary polynomials, we obtain fraction-free algorithms for computing row-reduced forms and weak Popov forms. These algorithms can be used to compute a greatest common right divisor and a least common left multiple of such matrices. Our fraction-free row reduction algorithm can be viewed as a generalization of subresultant algorithms. The linear algebra formulation allows us to obtain bounds on the size of the intermediate results and to analyze the complexity of our algorithms. We then make use of the fraction-free algorithm as a basis to formulate modular algorithms for computing a row-reduced form, a weak Popov form, and the Popov form of a polynomial matrix. By examining the linear algebra formulation, we develop criteria for detecting unlucky homomorphisms and determining the number of homomorphic images required.

In this thesis we study algorithms for computing normal forms for matrices of Ore polynomials while controlling coefficient growth. By formulating row reduction as a linear algebra problem, we obtain a fraction-free algorithm for row reduction for matrices of Ore polynomials. The algorithm allows us to compute the rank and a basis of the left nullspace of the input matrix. When the input is restricted to matrices of shift polynomials and ordinary polynomials, we obtain fraction-free algorithms for computing row-reduced forms and weak Popov forms. These algorithms can be used to compute a greatest common right divisor and a least common left multiple of such matrices. Our fraction-free row reduction algorithm can be viewed as a generalization of subresultant algorithms. The linear algebra formulation allows us to obtain bounds on the size of the intermediate results and to analyze the complexity of our algorithms. We then make use of the fraction-free algorithm as a basis to formulate modular algorithms for computing a row-reduced form, a weak Popov form, and the Popov form of a polynomial matrix. By examining the linear algebra formulation, we develop criteria for detecting unlucky homomorphisms and determining the number of homomorphic images required.

We study maximum entropy correlated equilibria in (multi-player)games and provide two gradient-based algorithms that are guaranteedto converge to such equilibria. Although we do not provideconvergence rates for these algorithms, they do have strong connectionsto other algorithms (such as iterative scaling) which are effectiveheuristics for tasks such as statistical estimation.

Since its introduction in 1999, bounded model checking (BMC) has quickly become a serious and indispensable tool for the formal verification of hardware designs and, more recently, software. By leveraging propositional satisfiability (SAT) solvers, BMC overcomes some of the shortcomings of more conventional model checking methods. In model checking we automatically verify whether a state transition system (STS) describing a design has some property, commonly expressed in linear temporal logic (LTL). BMC is the restriction to only checking the looping and non-looping runs of the system that have bounded descriptions. The conventional BMC approach is to translate the STS runs and LTL formulae into propositional logic and then conjunctive normal form (CNF). This CNF expression is then checked by a SAT solver. In this thesis we study the effect on the performance of BMC of changing the translation to propositional logic. One novelty is to use a normal form for LTL which originates in resolution theorem provers. We introduce the normal form conversion early on in the encoding process and examine the simplifications that it brings to the generation of propositional logic. We further enhance the encoding by specialising the normal form to take advantage of the types of runs peculiar to BMC. We also improve the conversion from propositional logic to CNF. We investigate the behaviour of the new encodings by a series of detailed experimental comparisons using both hand-crafted and industrial benchmarks from a variety of sources. These reveal that the new normal form based encodings can reduce the solving time by a half in most cases, and up to an order of magnitude in some cases, the size of the improvement corresponding to the complexity of the LTL expression. We also compare our method to the popular automata-based methods for model checking and BMC.

When we interpret the input vector of a Boolean function as a binary number, we define interval Boolean function fn [a,b] so that fn [a,b](x) = 1 if and only if a ≤ x ≤ b. Disjunctive normal form is a common way of representing Boolean functions. Minimization of DNF representation of an interval Boolean function can be per- formed in linear time. The natural generalization to k-interval functions seems to be significantly harder to tackle. In this thesis, we discuss the difficulties with finding an optimal solution and introduce a 2k-approximation algorithm.

Sejam X um espaço topológico não necessariamente compacto e T:X->X uma aplicação contínua. Se f:X->R é contínua, daremos condições sobre f que garantam a existência de medidas maximizantes caracterizadas em termos de seu suporte. / Let X be a topological space not necessarily compact, and T:X->X a continuous map. If f:X->R is a continuous function, we seek conditions on f in order to guarantee existence of maximizing measures that are characterized in terms of its support.