On the optimal usage of labelled examples in semi-supervised multi-class classification problems

In recent years, the performance of semi-supervised learning has been theoretically investigated. However, most of this theoretical development has focussed on binary classification problems. In this paper, we take it a step further by extending the work of Castelli and Cover [1] [2] to the multi-class paradigm. Particularly, we consider the key problem in semi-supervised learning of classifying an unseen instance x into one of K different classes, using a training dataset sampled from a mixture density distribution and composed of l labelled records and u unlabelled examples. Even under the assumption of identifiability of the mixture and having infinite unlabelled examples, labelled records are needed to determine the K decision regions. Therefore, in this paper, we first investigate the minimum number of labelled examples needed to accomplish that task. Then, we propose an optimal multi-class learning algorithm which is a generalisation of the optimal procedure proposed in the literature for binary problems. Finally, we make use of this generalisation to study the probability of error when the binary class constraint is relaxed.

Matrices whose hermitian part is positive definite

We are concerned with the class ∏_n of nxn complex matrices A for which the Hermitian part H(A) = A+A*/2 is positive definite.

Various connections are established with other classes such as the stable, D-stable and dominant diagonal matrices. For instance it is proved that if there exist positive diagonal matrices D, E such that DAE is either row dominant or column dominant and has positive diagonal entries, then there is a positive diagonal F such that FA ϵ ∏_n.

Powers are investigated and it is found that the only matrices A for which A^m ϵ ∏_n for all integers m are the Hermitian elements of ∏_n. Products and sums are considered and criteria are developed for AB to be in ∏_n.

Since ∏_n n is closed under inversion, relations between H(A)^-1 and H(A^-1) are studied and a dichotomy observed between the real and complex cases. In the real case more can be said and the initial result is that for A ϵ ∏_n, the difference H(adjA) - adjH(A) ≥ 0 always and is ˃ 0 if and only if S(A) = A-A*/2 has more than one pair of conjugate non-zero characteristic roots. This is refined to characterize real c for which cH(A^-1) - H(A)^-1 is positive definite.

The cramped (characteristic roots on an arc of less than 180°) unitary matrices are linked to ∏_n and characterized in several ways via products of the form A ^-1A*.

Classical inequalities for Hermitian positive definite matrices are studied in ∏_n and for Hadamard's inequality two types of generalizations are given. In the first a large subclass of ∏_n in which the precise statement of Hadamardis inequality holds is isolated while in another large subclass its reverse is shown to hold. In the second Hadamard's inequality is weakened in such a way that it holds throughout ∏_n. Both approaches contain the original Hadamard inequality as a special case.

Esporte contemporâneo: um novo templo do capital monopolista

Esta pesquisa teve por objetivo abrir uma discussão sobre o papel do esporte contemporâneo junto ao processo de alienação humana em tempos de domínio do capitalismo monopolista e do fortalecimento da ideologia dominante. Para tal, no primeiro capítulo, analisou-se as principais transformações vividas historicamente pelo capitalismo com a intenção de identificar o impacto do capitalismo monopolista sobre o novo ordenamento da humanidade. No segundo capítulo, demonstrou-se como o esporte contemporâneo constituiu-se como uma instituição burguesa, socialmente determinada e integrada ao conjunto de normas, ideias e estratégias inerentes ao modo de produção capitalista, participando do processo de mascaramento da questão social. Destaca-se neste capítulo o uso de fontes documentais que demonstraram como o esporte contemporâneo tem ocupado lugar estratégico tanto junto à produção da ideologia dominante, quanto junto ao controle da queda da taxa de lucro. Identificou-se que sob tais condições o esporte contemporâneo compõe os processos compensatórios frente à queda tendencial da taxa de lucro e, ao mesmo tempo, integra-se ao processo de alienação humana, tendo por maior expressão a sua materialização sob a forma dos megaeventos esportivos. Neste ponto, a pesquisa concentra-se na análise dos megaeventos esportivos no Brasil e na criação das políticas do esporte, desde o primeiro governo Lula da Silva até os dias atuais. Identificou-se que os projetos de desenvolvimento do esporte no país, no período em tela, têm participado do processo de gerenciamento da crise do capital e do refluxo das lutas dos trabalhadores. O último capítulo abordou as particularidades que envolvem a ideologia pós-moderna, tendo por objetivo identificar as relações desta com fenômeno esportivo. Constatou-se que, em tempos de domínio do capitalismo monopolista e de suas políticas neoliberais, as contradições que aguçam o processo de alienação sob o qual encontra-se a classe trabalhadora de todo o mundo, coloca a humanidade em um novo patamar de alienação, ainda mais brutal e desumanizador. Nesta conjuntura, o esporte contemporâneo destaca-se por ser funcional tanto ao mercado globalizado, quanto ao projeto imperialista, impondo-se como instrumento da contenção de conflitos em nome da tolerância e da paz no mundo. A presente pesquisa pôde concluir que as condições impostas pela fase monopolista do capitalismo ocultam a natureza dialética do esporte transforma-o num instrumento eficiente ao projeto dominante de incremento da alienação humana. O esporte, sob a forma assumida na contemporaneidade, não contribui para o avanço da consciência da classe trabalhadora, pois vem colaborando para adiamento do projeto de emancipação da humanidade. Projeto este que só será produzido pela organização consciente da classe trabalhadora em busca da superação do modo de produção capitalista.

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Enhancement of three-photon absorption cross-sections in a novel class of symmetrical charge transfer fluorene-based molecules

The three-photon absorption effect (3PA) of two novel symmetrical charge transfer fluorene-based molecules (abbreviated as BASF and BMOSF) has been determined by using a Q-switched Nd:YAG laser pumped with 38 ps pulses at 1064 nm in DMF. The measured 3PA cross-sections are 84 x 10(-78) and 114 x 10(-78) cm(6) s(2), respectively. The geometries and electronic excitations of these two molecules are systematically studied by PM3 and ZINDO/S methods. The relationships between 3PA cross-sections and intramolecular charge transfer are discussed micromechanically. The experimental and theoretical results have shown that the larger intramolecular charge transfer, which was characterized by the charge density difference between the ground state (SO) and the first excited state (S-I), the greater enhancement of the 3PA cross-sections. (c) 2005 Elsevier B.V. All rights reserved.

Large three-photon absorption cross-section in a novel class of bis-(N-carbazolyl) fluorene derivatives

Two novel symmetrical charge transfer fluorene derivatives (abbreviated as BCZF and BVCZF) with carbazole end-group as the donor moieties have been synthesized. Three-photon absorption cross-sections of these two compounds have been determined by using a Q-switched Nd:YAG laser pumped with 38 ps pulses at 1064 nm in DMF. The measured 3PA cross-sections are 140 x 10(-78) and 400 x 10(-78) cm(6) s(2) for BCZF and BVCZF, respectively. The geometries, electronic structures and electronic spectra of these two compounds are systematically studied by AM1 and ZINDO/S methods. On the basis of correct UV-vis spectra, the influence of different molecular structure on three-photon absorption cross-sections is discussed micromechanically. (C) 2005 Elsevier B.V. All rights reserved.

Advantages and Versatility of Fluorescence-Based Methodology to Characterize the Functionality of LDLR and Class Mutation Assignment

Familial hypercholesterolemia (FH) is a common autosomal codominant disease with a frequency of 1:500 individuals in its heterozygous form. The genetic basis of FH is most commonly mutations within the LDLR gene. Assessing the pathogenicity of LDLR variants is particularly important to give a patient a definitive diagnosis of FH. Current studies of LDLR activity ex vivo are based on the analysis of I-125-labeled lipoproteins (reference method) or fluorescent-labelled LDL. The main purpose of this study was to compare the effectiveness of these two methods to assess LDLR functionality in order to validate a functional assay to analyse LDLR mutations. LDLR activity of different variants has been studied by flow cytometry using FITC-labelled LDL and compared with studies performed previously with I-125-labeled lipoproteins. Flow cytometry results are in full agreement with the data obtained by the I-125 methodology. Additionally confocal microscopy allowed the assignment of different class mutation to the variants assayed. Use of fluorescence yielded similar results than I-125-labeled lipoproteins concerning LDLR activity determination, and also allows class mutation classification. The use of FITC-labelled LDL is easier in handling and disposal, cheaper than radioactivity and can be routinely performed by any group doing LDLR functional validations.

Diasporization and family relations in Nella Larsens Quicksand and Jamaica Kincaids Lucy: the construction of female identity

O principal objetivo desta dissertação é investigar e analisar como os movimentos diaspóricos e as relações familiares exercem influência na construção das identidades das mulheres em Quicksand, de Nella Larsen, e Lucy, de Jamaica Kincaid. As questões a que pretendo responder são: Como as personagens principais, Helga Crane e Lucy, lidam com as diferentes culturas que encontram nas suas trajetórias ? ; Como essas diferentes culturas lidam com essas mesmas personagens?; e Como o encontro entre essas diferentes culturas e as relações familiares são descritos e influenciam na construção da identidade feminina nessas obras?. Minha hipótese é que encontraremos nas obras selecionadas duas jornadas, portadoras tanto de aspectos comuns quanto distintos, que começam com o desejo das personagens principais de escapar da opressão patriarcal. Isto é, Helga Crane e Lucy passam por um período de muitas descobertas sobre elas mesmas e as sociedades com que têm que lidar, o que determina dois produtos diferentes: a construção das identidades híbridas de Lucy, em meio a sua solidão, na obra de Kincaid, e a construção e o sufocamento das identidades de Helga pela religião, o patriarcado e as relações familiares, na obra de Larsen