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.

On-Line Analytical Processing of Inventory Turnover

Operatiivisen tiedon tuottaminen loppukäyttäjille analyyttistä tarkastelua silmällä pitäen aiheuttaa ongelmia useille yrityksille. Diplomityö pyrkii ratkaisemaan ko. ongelman Teleste Oyj:ssä. Työ on jaettu kolmeen pääkappaleeseen. Kappale 2 selkiyttää On-Line Analytical Processing (OLAP)- käsitteen. Kappale 3 esittelee muutamia OLAP-tuotteiden valmistajia ja heidän arkkitehtuurejaan sekä tyypillisten sovellusalueiden lisäksi huomioon otettavia asioita OLAP käyttöönoton yhteydessä. Kappale 4, tuo esille varsinaisen ratkaisun. Teknisellä arkkitehtuurilla on merkittävä asema ratkaisun rakenteen kannalta. Tässä on sovellettu Microsoft:n tietovarasto kehysrakennetta. Kappaleen 4 edetessä, tapahtumakäsittelytieto muutetaan informaatioksi ja edelleen loppukäyttäjien tiedoksi. Loppukäyttäjät varustetaan tehokkaalla ja tosiaikaisella analysointityökalulla moniulotteisessa ympäristössä. Vaikka kiertonopeus otetaan työssä sovellusesimerkiksi, työ ei pyri löytämään optimaalista tasoa Telesten varastoille. Siitä huolimatta eräitä parannusehdotuksia mainitaan.

Langevin equations with multiplicative noise: Application to domain growth

Langevin Equations of Ginzburg-Landau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hiliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.

Absoluuttisten solmukoordinaattien menetelmä kuorimaisten kappaleiden mallinnuksessa

Työn tavoitteena oli kehittää nopeasti konvergoiva kuorielementti epälineaarisesti joustavien kappaleiden analysointiin. Kuorielementti perustuu absoluuttisten solmukoordinaattien menetelmään ja se hyödyntää kaarevuuden kuvausta elastisten voimien määrityksessä. Kehitettyä elementtiä verrattiin kontinuumimekaniikalla kehitettyyn kuorielementtiin ja kaupallisen elementtimenetelmän kuorielementtiin. Yksinkertaisimman kuormitustapauksen tuloksia verrattiin teknisen taivutusteorian mukaiseen analyyttiseen ratkaisuun. Staattisten testien tulokset tässä työssä kehitetyllä kuorielementillä vastasivat hyvin kaupallisella elementtimenetelmällä saatuja tuloksia. Deformaatioiden ollessa geometrisesti lineaarisella alueella, kehitetyllä kuorielementillä saadut tulokset vastasivat paremmin sekä analyyttistä ratkaisua että kaupallisella elementtimenetelmällä saatuja tuloksia kuin aiemman kontinuumimekaniikkaan perustuvan kuorielementin tulokset. Kehitetyn kuorielementin ongelmana verrattuna kontinuumimekaniikkaan perustuvaan elementtiin on monimutkaisempi kinematiikan kuvaus. Tästä on seurauksena laskenta-ajan huomattava kasvaminen. Jatkossa kannattaisi keskittyä numeeristen ratkaisumenetelmien kehittämiseen.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission. II. Reactive collisions

The classical theory of collision induced emission (CIE) from pairs of dissimilar rare gas atoms was developed in Paper I [D. Reguera and G. Birnbaum, J. Chem. Phys. 125, 184304 (2006)] from a knowledge of the straight line collision trajectory and the assumption that the magnitude of the dipole could be represented by an exponential function of the inter-nuclear distance. This theory is extended here to deal with other functional forms of the induced dipole as revealed by ab initio calculations. Accurate analytical expression for the CIE can be obtained by least square fitting of the ab initio values of the dipole as a function of inter-atomic separation using a sum of exponentials and then proceeding as in Paper I. However, we also show how the multi-exponential fit can be replaced by a simpler fit using only two analytic functions. Our analysis is applied to the polar molecules HF and HBr. Unlike the rare gas atoms considered previously, these atomic pairs form stable bound diatomic molecules. We show that, interestingly, the spectra of these reactive molecules are characterized by the presence of multiple peaks. We also discuss the CIE arising from half collisions in excited electronic states, which in principle could be probed in photo-dissociation experiments.

Energetics and mechanics of walking in patients with chronic low back pain and healthy matched controls.

PURPOSE: Walking in patients with chronic low back pain (cLBP) is characterized by motor control adaptations as a protective strategy against further injury or pain. The purpose of this study was to compare the preferred walking speed, the biomechanical and the energetic parameters of walking at different speeds between patients with cLBP and healthy men individually matched for age, body mass and height. METHODS: Energy cost of walking was assessed with a breath-by-breath gas analyser; mechanical and spatiotemporal parameters of walking were computed using two inertial sensors equipped with a triaxial accelerometer and gyroscope and compared in 13 men with cLBP and 13 control men (CTR) during treadmill walking at standard (0.83, 1.11, 1.38, 1.67 m s(-1)) and preferred (PWS) speeds. Low back pain intensity (visual analogue scale, cLBP only) and perceived exertion (Borg scale) were assessed at each walking speed. RESULTS: PWS was slower in cLBP [1.17 (SD = 0.13) m s(-1)] than in CTR group [1.33 (SD = 0.11) m s(-1); P = 0.002]. No significant difference was observed between groups in mechanical work (P ≥ 0.44), spatiotemporal parameters (P ≥ 0.16) and energy cost of walking (P ≥ 0.36). At the end of the treadmill protocol, perceived exertion was significantly higher in cLBP [11.7 (SD = 2.4)] than in CTR group [9.9 (SD = 1.1); P = 0.01]. Pain intensity did not significantly increase over time (P = 0.21). CONCLUSIONS: These results do not support the hypothesis of a less efficient walking pattern in patients with cLBP and imply that high walking speeds are well tolerated by patients with moderately disabling cLBP.

Standardisation of elemental analytical techniques applied to provenance studies of archaeological ceramics: an inter laboratory calibration study

Chemical analysis is a well-established procedure for the provenancing of archaeological ceramics. Various analytical techniques are routinely used and large amounts of data have been accumulated so far in data banks. However, in order to exchange results obtained by different laboratories, the respective analytical procedures need to be tested in terms of their inter-comparability. In this study, the schemes of analysis used in four laboratories that are involved in archaeological pottery studies on a routine basis were compared. The techniques investigated were neutron activation analysis (NAA), X-ray fluorescence analysis (XRF), inductively coupled plasma optical emission spectrometry (ICP-OES) and inductively coupled plasma mass spectrometry (ICP-MS). For this comparison series of measurements on different geological standard reference materials (SRM) were carried out and the results were statistically evaluated. An attempt was also made towards the establishment of calibration factors between pairs of analytical setups in order to smooth the systematic differences among the results.

Analytical Strategies for Doping Control Purposes: Needs, Challenges, and Perspectives.

The fight against doping in sports has been governed since 1999 by the World Anti-Doping Agency (WADA), an independent institution behind the implementation of the World Anti-Doping Code (Code). The intent of the Code is to protect clean athletes through the harmonization of anti-doping programs at the international level with special attention to detection, deterrence and prevention of doping.1 A new version of the Code came into force on January 1st 2015, introducing, among other improvements, longer periods of sanctioning for athletes (up to four years) and measures to strengthen the role of anti-doping investigations and intelligence. To ensure optimal harmonization, five International Standards covering different technical aspects of the Code are also currently in force: the List of Prohibited Substances and Methods (List), Testing and Investigations, Laboratories, Therapeutic Use Exemptions (TUE) and Protection of Privacy and Personal Information. Adherence to these standards is mandatory for all anti-doping stakeholders to be compliant with the Code. Among these documents, the eighth version of International Standard for Laboratories (ISL), which also came into effect on January 1st 2015, includes regulations for WADA and ISO/IEC 17025 accreditations and their application for urine and blood sample analysis by anti-doping laboratories.2 Specific requirements are also described in several Technical Documents or Guidelines in which various topics are highlighted such as the identification criteria for gas chromatography (GC) and liquid chromatography (LC) coupled to mass spectrometry (MS) techniques (IDCR), measurements and reporting of endogenous androgenic anabolic agents (EAAS) and analytical requirements for the Athlete Biological Passport (ABP).

New insight in the relationship between regional patterns of knee cartilage thickness, osteoarthritis disease severity, and gait mechanics.

To test if the relationship between knee kinetics during walking and regional patterns of cartilage thickness is influenced by disease severity we tested the following hypotheses in a cross-sectional study of medial compartment osteoarthritis (OA) subjects: (1) the peak knee flexion (KFM) and adduction moments (KAM) during walking are associated with regional cartilage thickness and medial-to-lateral cartilage thickness ratios, and (2) the associations between knee moments and cartilage thickness data are dependent on disease severity. Seventy individuals with medial compartment knee OA were studied. Gait analysis was used to determine the knee moments and cartilage thickness was measured from magnetic resonance imaging. Multiple linear regression analyses tested for associations between cartilage thickness and knee kinetics. Medial cartilage thickness and medial-to-lateral cartilage thickness ratios were lower in subjects with greater KAM for specific regions of the femoral condyle and tibial plateau with no associations for KFM in patients of all disease severities. When separated by severity, the association between KAM and cartilage thickness was found only in patients with more severe OA, and KFM was significantly associated with cartilage thickness only for the less severe OA subjects for specific tibial plateau regions. The results support the idea that the KAM is larger in patients with more severe disease and the KFM has greater influence early in the disease process, which may lessen as pain increases with disease severity. Each component influences different regions of cartilage. Thus the relative contributions of both KAM and KFM should be considered when evaluating gait mechanics and the influence of any intervention for knee OA.

Evaluation of steroidomics by liquid chromatography hyphenated to mass spectrometry as a powerful analytical strategy for measuring human steroid perturbations.

This review presents the evolution of steroid analytical techniques, including gas chromatography coupled to mass spectrometry (GC-MS), immunoassay (IA) and targeted liquid chromatography coupled to mass spectrometry (LC-MS), and it evaluates the potential of extended steroid profiles by a metabolomics-based approach, namely steroidomics. Steroids regulate essential biological functions including growth and reproduction, and perturbations of the steroid homeostasis can generate serious physiological issues; therefore, specific and sensitive methods have been developed to measure steroid concentrations. GC-MS measuring several steroids simultaneously was considered the first historical standard method for analysis. Steroids were then quantified by immunoassay, allowing a higher throughput; however, major drawbacks included the measurement of a single compound instead of a panel and cross-reactivity reactions. Targeted LC-MS methods with selected reaction monitoring (SRM) were then introduced for quantifying a small steroid subset without the problems of cross-reactivity. The next step was the integration of metabolomic approaches in the context of steroid analyses. As metabolomics tends to identify and quantify all the metabolites (i.e., the metabolome) in a specific system, appropriate strategies were proposed for discovering new biomarkers. Steroidomics, defined as the untargeted analysis of the steroid content in a sample, was implemented in several fields, including doping analysis, clinical studies, in vivo or in vitro toxicology assays, and more. This review discusses the current analytical methods for assessing steroid changes and compares them to steroidomics. Steroids, their pathways, their implications in diseases and the biological matrices in which they are analysed will first be described. Then, the different analytical strategies will be presented with a focus on their ability to obtain relevant information on the steroid pattern. The future technical requirements for improving steroid analysis will also be presented.

Titaanisen valkaisutornin korjaussuunnitelma

Tämän työn tarkoituksena on poistaa toistuvasti esiintyneet vauriot titaanisessa valkaisutornissa Kuusankosken paperitehtailla. Vauriot esiintyivät melko pian käyttöönoton jälkeen ja niitä esiintyi toistuvasti jokaisen korjauksen jälkeen. Jatkuvatoimisen prosessin vuoksi käyttökatkokset eivät olleet suotavia. Aikataulu suunnittelulle ja korjaukselle oli erittäin tiukka, jolloin kenttämittauksia ei ollut mahdollista tehdä laskelmien tueksi. Tämän vuoksi tähän työtön parhaiten soveltuvaksi menetelmäksi valittiin FEA. Alkuperäisessä rakenteessa pääsäiliöön oli hitsattu pintatasku, jota käytettiin välisäiliönä varastoimaan suuri määrä vaarallista nestettä. Tämä aiheutti valkaisutornin vaipalle murtumia ja vuotoja sekä suuronnettomuuden riskin koko valkaisutornille. Kuormitustietojen puutteesta johtuen kuormitukset mallinnettiin virtuaalisesti FE-menetelmällä ja analyyttisin keinoin. Kuormitusten suuruudet arvioitiin konservatiivisesti. Tämän työn tärkein oivallus oli määritellä uudelleen pintataskun toiminto siten, että sitä ei enää käytetty nesteen välivarastona, vaan ohjaimena nesteelle. Tämä innovatiivinen ongelmankorjauskonsepti on havaittu onnistuneeksi, koska vaurioita ei ole enää esiintynyt viimeisimmän korjauksen jälkeen.

Comparison of Four Sections for Analyzing Running Mechanics Alterations During Repeated Treadmill Sprints.

We compared different approaches to analyze running mechanics alterations during repeated treadmill sprints. Thirteen active male athletes performed five 5-second sprints with 25 seconds of recovery on an instrumented treadmill. This approach allowed continuous measurement of running kinetics/kinematics and calculation of vertical and leg stiffness variables that were subsequently averaged over 3 distinct sections of the 5-second sprint (steps 2-5, 7-10, and 12-15) and for all steps (steps 2-15). Independently from the analyzed section, propulsive power and step frequency decreased with fatigue, while contact time and step length increased (P < .05). Except for step frequency, all mechanical variables varied (P < .05) across sprint sections. The only parameters that highly depend on running velocity (propulsive power and vertical stiffness) showed a significant interaction (P < .05) between the analyzed sections, with smaller magnitude of fatigue-induced change observed for steps 2-5. Considering all steps or only a few steps during early, middle, or late phases of 5-second sprints provides similar mechanical outcomes during repeated treadmill sprinting, although acceleration induces noticeable differences between the sections studied. Furthermore, quantifying mechanical alterations from the early acceleration phase may not be readily detectable, and is not recommended.