Minimal state-space realizations of 2D convolutional codes

In this thesis we consider two-dimensional (2D) convolutional codes. As happens in the one-dimensional (1D) case one of the major issues is obtaining minimal state-space realizations for these codes. It turns out that the problem of minimal realization of codes is not equivalent to the minimal realization of encoders. This is due to the fact that the same code may admit different encoders with different McMillan degrees. Here we focus on the study of minimality of the realizations of 2D convolutional codes by means of separable Roesser models. Such models can be regarded as a series connection between two 1D systems. As a first step we provide an algorithm to obtain a minimal realization of a 1D convolutional code starting from a minimal realization of an encoder of the code. Then, we restrict our study to two particular classes of 2D convolutional codes. The first class to be considered is the one of codes which admit encoders of type n 1. For these codes, minimal encoders (i.e., encoders for which a minimal realization is also minimal as a code realization) are characterized enabling the construction of minimal code realizations starting from such encoders. The second class of codes to be considered is the one constituted by what we have called composition codes. For a subclass of these codes, we propose a method to obtain minimal realizations by means of separable Roesser models.

WHICH TOPOLOGIES HAVE IMMEDIATE PREDECESSORS IN THE POSET OF HAUSDORFF TOPOLOGIES?

We study which topology have an immediate predecessor in the poset of Sigma(2) of Hausdorff topologies on set X. We show that certain classes of H-closed topologies, do have predecessors. and we give examples of second countable H-closed topologies which are not upper Sigma(2.)

Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

Regular homomorphisms of minimal sets

The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter I. Given a flow on a compact Hausdorff space, the action extends naturally to the space of closed subsets, taken with the Hausdorff topology. These hyperspaces are discussed and used to give a new characterization of almost periodic homomorphisms. Regular minimal sets may be described as minimal subsets of enveloping semigroups. Regular homomorphisms are defined in Chapter II by extending this notion to homomorphisms with minimal range. Several characterizations are obtained. In Chapter III, some additional results on homomorphisms are obtained by relativizing enveloping semigroup notions. In Veech's paper on point distal flows, hyperspaces are used to associate an almost one-to-one homomorphism with a given homomorphism of metric minimal sets. In Chapter IV, a non-metric generalization of this construction is studied in detail using the new notion of a highly proximal homomorphism. An abstract characterization is obtained, involving only the abstract properties of homomorphisms. A strengthened version of the Veech Structure Theorem for point distal flows is proved. In Chapter V, the work in the earlier chapters is applied to the study of homomorphisms for which the almost periodic elements of the associated hyperspace are all finite. In the metric case, this is equivalent to having at least one fiber finite. Strong results are obtained by first assuming regularity, and then assuming that the relative proximal relation is closed as well.

ON NONSYMMETRIC THEOREMS FOR (H, G)-COINCIDENCES

Let X be a compact Hausdorff space, phi: X -> S(n) a continuous map into the n-sphere S(n) that induces a nonzero homomorphism phi*: H(n)(S(n); Z(p)) -> H(n)(X; Z(p)), Y a k-dimensional CW-complex and f: X -> a continuous map. Let G a finite group which acts freely on S`. Suppose that H subset of G is a normal cyclic subgroup of a prime order. In this paper, we define and we estimate the cohomological dimension of the set A(phi)(f, H, G) of (H, G)-coincidence points of f relative to phi.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Delayed gadolinium-enhanced magnetic resonance imaging of cartilage (dGEMRIC), after slipped capital femoral epiphysis

OBJECTIVE: The aim of this study was to assess the glycosaminoglycan (GAG) content in hip joint cartilage in mature hips with a history of slipped capital femoral epiphysis (SCFE) using delayed gadolinium-enhanced MRI of cartilage (dGEMRIC). METHODS: 28 young-adult subjects (32 hips) with a mean age of 23.8+/-4.0 years (range: 18.1-30.5 years) who were treated for mild or moderate SCFE in adolescence were included into the study. Hip function and clinical symptoms were evaluated with the Harris hip score (HHS) system at the time of MRI. Plain radiographic evaluation included Tonnis grading, measurement of the minimal joint space width (JSW) and alpha-angle measurement. The alpha-angle values were used to classify three sub-groups: group 1=subjects with normal femoral head-neck offset (alpha-angle <50 degrees ), group 2=subjects with mild offset decrease (alpha-angle 50 degrees -60 degrees ), and group 3=subjects with severe offset decrease (alpha-angle >60 degrees ). RESULTS: There was statistically significant difference noted for the T1(Gd) values, lateral and central, between group 1 and group 3 (p-values=0.038 and 0.041). The T1(Gd) values measured within the lateral portion were slightly lower compared with the T1(Gd) values measured within the central portion that was at a statistically significance level (p-value <0.001). HHS, Tonnis grades and JSW revealed no statistically significant difference. CONCLUSION: By using dGEMRIC in the mid-term follow-up of SCFE we were able to reveal degenerative changes even in the absence of joint space narrowing that seem to be related to the degree of offset pathology. The dGEMRIC technique may be a potential diagnostic modality in the follow-up evaluation of SCFE.

Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Study of flow behaviour in a three-product cyclone using computational fluid dynamics

Simplicity in design and minimal floor space requirements render the hydrocyclone the preferred classifier in mineral processing plants. Empirical models have been developed for design and process optimisation but due to the complexity of the flow behaviour in the hydrocyclone these do not provide information on the internal separation mechanisms. To study the interaction of design variables, the flow behaviour needs to be considered, especially when modelling the new three-product cyclone. Computational fluid dynamics (CFD) was used to model the three-product cyclone, in particular the influence of the dual vortex finder arrangement on flow behaviour. From experimental work performed on the UG2 platinum ore, significant differences in the classification performance of the three-product cyclone were noticed with variations in the inner vortex finder length. Because of this simulations were performed for a range of inner vortex finder lengths. Simulations were also conducted on a conventional hydrocyclone of the same size to enable a direct comparison of the flow behaviour between the two cyclone designs. Significantly, high velocities were observed for the three-product cyclone with an inner vortex finder extended deep into the conical section of the cyclone. CFD studies revealed that in the three-product cyclone, a cylindrical shaped air-core is observed similar to conventional hydrocyclones. A constant diameter air-core was observed throughout the inner vortex finder length, while no air-core was present in the annulus. (c) 2006 Elsevier Ltd. All rights reserved.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Compressão fractal de imagens

Neste trabalho será apresentado um método recente de compressão de imagens baseado na teoria dos Sistemas de Funções Iteradas (SFI), designado por Compressão Fractal. Descrever-se-á um modelo contínuo para a compressão fractal sobre o espaço métrico completo Lp, onde será definido um operador de transformação fractal contractivo associado a um SFI local com aplicações. Antes disso, será introduzida a teoria dos SFIs no espaço de Hausdorff ou espaço fractal, a teoria dos SFIs Locais - uma generalização dos SFIs - e dos SFIs no espaço Lp. Fornecida a fundamentação teórica para o método será apresentado detalhadamente o algoritmo de compressão fractal. Serão também descritas algumas estratégias de particionamento necessárias para encontrar o SFI com aplicações, assim como, algumas estratégias para tentar colmatar o maior entrave da compressão fractal: a complexidade de codificação. Esta dissertação assumirá essencialmente um carácter mais teórico e descritivo do método de compressão fractal, e de algumas técnicas, já implementadas, para melhorar a sua eficácia.