Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Colligation and Cross Moment-Based Approaches for Independent Component Analysis

Diplomityössä on käsitelty uudenlaisia menetelmiä riippumattomien komponenttien analyysiin(ICA): Menetelmät perustuvat colligaatioon ja cross-momenttiin. Colligaatio menetelmä perustuu painojen colligaatioon. Menetelmässä on käytetty kahden tyyppisiä todennäköisyysjakaumia yhden sijasta joka perustuu yleiseen itsenäisyyden kriteeriin. Työssä on käytetty colligaatio lähestymistapaa kahdella asymptoottisella esityksellä. Gram-Charlie ja Edgeworth laajennuksia käytetty arvioimaan todennäköisyyksiä näissä menetelmissä. Työssä on myös käytetty cross-momentti menetelmää joka perustuu neljännen asteen cross-momenttiin. Menetelmä on hyvin samankaltainen FastICA algoritmin kanssa. Molempia menetelmiä on tarkasteltu lineaarisella kahden itsenäisen muuttajan sekoituksella. Lähtö signaalit ja sekoitetut matriisit ovattuntemattomia signaali lähteiden määrää lukuunottamatta. Työssä on vertailtu colligaatio menetelmään ja sen modifikaatioita FastICA:an ja JADE:en. Työssä on myös tehty vertailu analyysi suorituskyvyn ja keskusprosessori ajan suhteen cross-momenttiin perustuvien menetelmien, FastICA:n ja JADE:n useiden sekoitettujen parien kanssa.

Moment's notice

Soitinnus: big band.

The multicultural moment : the history of the idea and politics of multiculturalism in Sweden in comparative, transnational and biographical context, 1964–1975

The emergence of the idea of multiculturalism in Swedish public discourse and social science in the latter half of the 1960s and introduction of official multiculturalism in 1975 constituted a major intellectual and political shift in the post-war history of Sweden. The ambition of the 1975 immigrant and minority policy to enable the preservation of ethno-cultural minorities and to create a positive attitude towards the new multicultural society among the majority population was also incorporated into Swedish cultural, educational and media policies. The rejection of assimilationism and the new commitment to ethno-cultural diversity, the multicultural moment, has earned Sweden a place on the list of the early adopters of official multiculturalism, together with Canada and Australia. This compilation thesis examines the origins and early post-war history of the idea of multiculturalism as well as the interplay between idea and politics in the shift from a public ideal of homogeneity to an ideal of multiculturalism in Sweden. It does so from a range of conceptual, comparative, transnational, and biographical perspectives. The thesis consists of an introduction (Part I) and four previously published studies (Part II). The primary research result of the thesis concerns the agency involved in the break-through and formal establishment of the idea of multiculturalism in Sweden. Actors such as ethnic activists, experts and officials were instrumental in the introduction and establishment of multiculturalism in Sweden, as they also had been in Canada and in Australia. These actors have, however, not previously been recognized and analysed as significant idea-makers and political agents in the case of Sweden. The intertwined connections between activists, social scientists, linguists, and officials facilitated the transfer of the idea of multiculturalism from a publically contested idea to public policy via the way of The Swedish Trade Union Confederation, academia and the Royal Commission of Immigration. The thesis furthermore shows that the political success of the idea of multiculturalism, such as it was within the limits of the universalist social democratic welfare state, was dependent on whom the claims-makers were, the status and positions they held, and the way the idea of multiculturalism was conceptualised and used. It was also dependent on the migratory context of labour immigration in the 1960s and 1970s and on whose behalf the advocates of multiculturalism made their claims. The majority of the labour immigrants were Finnish citizens from the former eastern half of the kingdom of Sweden who were net contributors to the Swedish welfare state. This facilitated the recognition of their ethno-cultural difference, and, following the logic of universalism, the ethno-cultural difference of other minority groups in Sweden. The historical significance of the multicultural moment is still evident in the contemporary immigration and integration policies of Sweden. The affirmation of diversity continues to set Sweden apart from the rest of Europe, now more so than in the 1970s, even though the migratory context has changed radically in the last 40 years.