Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

Differential evolution based classification with pool of distances and aggregation operators

The objective of this thesis is to develop and generalize further the differential evolution based data classification method. For many years, evolutionary algorithms have been successfully applied to many classification tasks. Evolution algorithms are population based, stochastic search algorithms that mimic natural selection and genetics. Differential evolution is an evolutionary algorithm that has gained popularity because of its simplicity and good observed performance. In this thesis a differential evolution classifier with pool of distances is proposed, demonstrated and initially evaluated. The differential evolution classifier is a nearest prototype vector based classifier that applies a global optimization algorithm, differential evolution, to determine the optimal values for all free parameters of the classifier model during the training phase of the classifier. The differential evolution classifier applies the individually optimized distance measure for each new data set to be classified is generalized to cover a pool of distances. Instead of optimizing a single distance measure for the given data set, the selection of the optimal distance measure from a predefined pool of alternative measures is attempted systematically and automatically. Furthermore, instead of only selecting the optimal distance measure from a set of alternatives, an attempt is made to optimize the values of the possible control parameters related with the selected distance measure. Specifically, a pool of alternative distance measures is first created and then the differential evolution algorithm is applied to select the optimal distance measure that yields the highest classification accuracy with the current data. After determining the optimal distance measures for the given data set together with their optimal parameters, all determined distance measures are aggregated to form a single total distance measure. The total distance measure is applied to the final classification decisions. The actual classification process is still based on the nearest prototype vector principle; a sample belongs to the class represented by the nearest prototype vector when measured with the optimized total distance measure. During the training process the differential evolution algorithm determines the optimal class vectors, selects optimal distance metrics, and determines the optimal values for the free parameters of each selected distance measure. The results obtained with the above method confirm that the choice of distance measure is one of the most crucial factors for obtaining higher classification accuracy. The results also demonstrate that it is possible to build a classifier that is able to select the optimal distance measure for the given data set automatically and systematically. After finding optimal distance measures together with optimal parameters from the particular distance measure results are then aggregated to form a total distance, which will be used to form the deviation between the class vectors and samples and thus classify the samples. This thesis also discusses two types of aggregation operators, namely, ordered weighted averaging (OWA) based multi-distances and generalized ordered weighted averaging (GOWA). These aggregation operators were applied in this work to the aggregation of the normalized distance values. The results demonstrate that a proper combination of aggregation operator and weight generation scheme play an important role in obtaining good classification accuracy. The main outcomes of the work are the six new generalized versions of previous method called differential evolution classifier. All these DE classifier demonstrated good results in the classification tasks.

A Study of Morphological Operators with Applications

The present work deals with the A study of morphological opertors with applications. Morphology is now a.necessary tool for engineers involved with imaging applications. Morphological operations have been viewed as filters the properties of which have been well studied (Heijmans, 1994). Another well-known class of non-linear filters is the class of rank order filters (Pitas and Venetsanopoulos, 1990). Soft morphological filters are a combination of morphological and weighted rank order filters (Koskinen, et al., 1991, Kuosmanen and Astola, 1995). They have been introduced to improve the behaviour of traditional morphological filters in noisy environments. The idea was to slightly relax the typical morphological definitions in such a way that a degree of robustness is achieved, while most of the desirable properties of typical morphological operations are maintained. Soft morphological filters are less sensitive to additive noise and to small variations in object shape than typical morphological filters. They can remove positive and negative impulse noise, preserving at the same time small details in images. Currently, Mathematical Morphology allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets.Fuzzy sets have proved to be strongly advantageous when representing in accuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods.

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 0operators, , which ensure that, if λ≠0 and λφ=Kkφ has only the trivial solution in X, for all k∈W, then, for 0⩽a⩽b, (λ−K)φ=ψ has exactly one solution φ∈Xa for every k∈W and ψ∈Xa. These conditions ensure further that is bounded uniformly in k∈W, for 0⩽a⩽b. As a particular application we consider the case when the kernel takes the form k(s,t)=κ(s−t)z(t), with , , and κ(s)=O(|s|−b) as |s|→∞, for some b>1. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

On Semi-weakly n-Hyponormal Weighted Shifts

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W (alpha) with alpha (0) = alpha (1) < alpha (2) which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.

Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.

Land use intensification alters ecosystem multifunctionality via loss of biodiversity and changes to functional composition

Global change, especially land-use intensification, affects human well-being by impacting the deliv-ery of multiple ecosystem services (multifunctionality). However, whether biodiversity loss is amajor component of global change effects on multifunctionality in real-world ecosystems, as inexperimental ones, remains unclear. Therefore, we assessed biodiversity, functional compositionand 14 ecosystem services on 150 agricultural grasslands differing in land-use intensity. We alsointroduce five multifunctionality measures in which ecosystem services were weighted according torealistic land-use objectives. We found that indirect land-use effects, i.e. those mediated by biodi-versity loss and by changes to functional composition, were as strong as direct effects on average.Their strength varied with land-use objectives and regional context. Biodiversity loss explainedindirect effects in a region of intermediate productivity and was most damaging when land-useobjectives favoured supporting and cultural services. In contrast, functional composition shifts,towards fast-growing plant species, strongly increased provisioning services in more inherentlyunproductive grasslands.

Molecular dissolved organic matter composition and environmental parameters from a laboratory incubation study

Dissolved organic matter (DOM) in the oceans constitutes a major carbon pool involved in global biogeochemical cycles. More than 96% of the marine DOM resists microbial degradation for thousands of years. The composition of this refractory DOM (RDOM) exhibits a molecular signature which is ubiquitously detected in the deep oceans. Surprisingly efficient microbial transformation of labile into RDOM was shown experimentally, implying that microorganisms produce far more RDOM than needed to sustain the global pool. By assessing the microbial formation and transformation of DOM in unprecedented molecular detail for 3 years, we show that most of the newly formed RDOM is molecularly different from deep sea RDOM. Only <0.4% of the net community production was channeled into RDOM molecularly undistinguishable from deep sea DOM. Our study provides novel experimentally derived molecular evidence and data for global models on the production, turnover and accumulation of marine DOM.

Composition of Fe-Mn nodules and crusts from the Cape Basin

Facies zonation of the Cape basin with respect to Fe-Mn nodules based on data from Cruise 43 of R/V Akademik Kurchatov and published data is presented. Three facies regions are distinguished: the southern end of the Walvis Ridge and seamounts, the continental slope of the Southwest Africa and the deep-water Cape Basin. Iron-manganese nodules in the first of these areas are predominantly sedimentary, those in the second area are diagenetic and those in the third are sedimentary-diagenetic. Chemical characteristics and type of metallogenic specialization for each of the regions are identified.