Witten index of supersymmetric chiral theories

The Witten index can be defined in many supersymmetric theories by formulating them in the space-time R×S3. If the index is nonzero for any value of the radius of S3, it can be shown that the theory does not break supersymmetry in Minkowski space. This approach rules out supersymmetry breaking in a large class of models, chiral and otherwise. The index arguments are consistent with previous instanton calculations which indicate supersymmetry breaking in certain theories.

Approximation of Internal Refractive Index Variation Improves Image Guided Diffuse Optical Tomography of Breast

Effective usage of image guidance by incorporating the refractive index (RI) variation in computational modeling of light propagation in tissue is investigated to assess its impact on optical-property estimation. With the aid of realistic patient breast three-dimensional models, the variation in RI for different regions of tissue under investigation is shown to influence the estimation of optical properties in image-guided diffuse optical tomography (IG-DOT) using numerical simulations. It is also shown that by assuming identical RI for all regions of tissue would lead to erroneous estimation of optical properties. The a priori knowledge of the RI for the segmented regions of tissue in IG-DOT, which is difficult to obtain for the in vivo cases, leads to more accurate estimates of optical properties. Even inclusion of approximated RI values, obtained from the literature, for the regions of tissue resulted in better estimates of optical properties, with values comparable to that of having the correct knowledge of RI for different regions of tissue.

Substance misuse problems during pregnancy with special emphasis on buprenorphine

Maternal drug abuse during pregnancy endangers the future health and wellbeing of the infant and growing child. On the other hand, via maternal abstinence, these problems would never occur; so the problems would be totally preventable. Buprenorphine is widely used in opioid maintenance treatment as a substitute medication. In Finland, during 2000 s buprenorphine misuse has steadily increased. In 2009 almost one third of clientele of substance treatment units were in treatment because of buprenorphine dependence. At Helsinki Women s Clinic the first child with prenatal buprenorphine exposure was born in 2001. During 1992-2001 in the three capital area maternity hospitals (Women s clinic, Maternity hospital, Jorvi hospital) 524 women were followed at special antenatal clinics due to substance abuse problems. Three control women were drawn from birth register to each case woman and matched for parity and same place and date of the index birth. According to register data mortality rate was 38-fold higher among cases than controls within 6-15 years after index birth. Especially, the risk for violent or accidental death was increased. The women with substance misuse problems had also elevated risk for viral hepatitis and psychiatric morbidity. They were more often reimbursed for psychopharmaceuticals. Disability pensions and rehabilitation allowances were more often granted to cases than controls. In total 626 children were born from these pregnancies. According to register data 38% of these children were placed in out-of-home care as part of child protection services by the age of two years, and half of them by the age of 12 years, the median follow-up time was 5.8 years. The risk for out-of-home care was associated with factors identifiable during the pre- and perinatal period. In 2002-2005 67 pregnant women with buprenorphine dependence were followed up at the Helsinki University Hospital, Department of Obstetrics and Gynecology. Their pregnancies were uneventful. The prematurity rate was similar and there were no more major anomalies compared to the national statistics. The neonates were lighter compared to the national statistics. They were also born in good condition, with no perinatal hypoxia as defined by standard clinical parameters or certain biochemical markers in the cord blood: erythropoietin, S100 and cardiac troponin-t. Almost 80% of newborns developed neonatal abstinence syndrome (NAS) and two third of them needed morphine medication for it. Maternal smoking over ten cigarettes per day aggravated and benzodiazepine use attenuated NAS. An infant s highest urinary norbuprenorphine concentration during their first 3 days of life correlated with the duration of morphine treatment. The average length of infant s hospital stay was 25 days.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Poststroke survival and ischemic stroke recurrence : the cerebral small-vessel disease perspective

The aim of the present study was to investigate the influence of different manifestations of cerebral SVD on poststroke survival and ischemic stroke recurrence in long-term follow-up. The core imaging features of small-vessel disease (SVD) are confluent and extensive white matter changes (WMC) and lacunar infarcts. These are associated with minor motor deficits but a major negative influence on cognition, mood, and functioning in daily life, resulting from small-vessel lesions in the fronto-subcortical brain network. These sub-studies were conducted as part of the Helsinki Stroke Aging Memory (SAM) study. The SAM cohort consisted of 486 consecutive patients aged 55 to 85 years who were admitted to Helsinki University Central Hospital with acute ischemic stroke. The study included comprehensive clinical, neuropsychological, psychiatric and radiological assessment three months poststroke. The patients were followed up up for 12 years using extensive national registers. The effect of different manifestations of cerebral SVD on poststroke survival and stroke recurrence was analyzed controlling for factors such as age, education, and cardiovascular risk factors. Poststroke dementia and cognitive impairment relate to poor long-term survival. In particular, deficits in executive functions as well as visuospatial and constructional abilities predict poor outcome. The predictive value of cognitive deficits is further underlined by the finding that depression-executive dysfunction syndrome (DES), but not depression in itself, is associated with poor poststroke survival. Delirium is not independently associated with increased risk for long-term poststroke mortality, although it is associated with poststroke dementia. Furthermore, acute index stroke attributable to SVD is associated with poorer long-term survival and a higher risk for cardiac death than other stroke subtypes. Severe WMC, a surrogate of SVD, is independently related to an increased risk of stroke recurrence at five years. In summary, cognitive poststroke outcomes reflecting changes in the executive network brain, and the presence of cerebral SVD are important determinants of poststroke mortality and ischemic stroke recurrence, regardless of whether SVD is the cause of the index stroke or a condition concurrent to some other etiology.

High-precision diode-laser-based temperature measurement for air refractive index compensation

We present a laser-based system to measure the refractive index of air over a long path length. In optical distance measurements it is essential to know the refractive index of air with high accuracy. Commonly, the refractive index of air is calculated from the properties of the ambient air using either Ciddor or Edlén equations, where the dominant uncertainty component is in most cases the air temperature. The method developed in this work utilises direct absorption spectroscopy of oxygen to measure the average temperature of air and of water vapor to measure relative humidity. The method allows measurement of temperature and humidity over the same beam path as in optical distance measurement, providing spatially well matching data. Indoor and outdoor measurements demonstrate the effectiveness of the method. In particular, we demonstrate an effective compensation of the refractive index of air in an interferometric length measurement at a time-variant and spatially non-homogenous temperature over a long time period. Further, we were able to demonstrate 7 mK RMS noise over a 67 m path length using 120 s sample time. To our knowledge, this is the best temperature precision reported for a spectroscopic temperature measurement.

Lypsylehmän energiataseen mallintaminen tuotoskauden alkuvaiheessa

Energiataseen mallinnus on osa KarjaKompassi-hankkeeseen liittyvää kehitystyötä. Tutkielman tavoitteena oli kehittää lypsylehmän energiatasetta etukäteen ennustavia ja tuotoskauden aikana saatavia tietoja hyödyntäviä matemaattisia malleja. Selittävinä muuttujina olivat dieetti-, rehu-, maitotuotos-, koelypsy-, elopaino- ja kuntoluokkatiedot. Tutkimuksen aineisto kerättiin 12 Suomessa tehdyistä 8 – 28 laktaatioviikon pituisesta ruokintakokeesta, jotka alkoivat heti poikimisen jälkeen. Mukana olleista 344 lypsylehmästä yksi neljäsosa oli friisiläis- ja loput ayshire-rotuisia. Vanhempien lehmien päätiedosto sisälsi 2647 havaintoa (koe * lehmä * laktaatioviikko) ja ensikoiden 1070. Aineisto käsiteltiin SAS-ohjelmiston Mixed-proseduuria käyttäen ja poikkeavat havainnot poistettiin Tukeyn menetelmällä. Korrelaatioanalyysillä tarkasteltiin energiataseen ja selittävien muuttujien välisiä yhteyksiä. Energiatase mallinnettiin regressioanalyysillä. Laktaatiopäivän vaikutusta energiataseeseen selitettiin viiden eri funktion avulla. Satunnaisena tekijänä mallissa oli lehmä kokeen sisällä. Mallin sopivuutta aineistoon tarkasteltiin jäännösvirheen, selitysasteen ja Bayesin informaatiokriteerin avulla. Parhaat mallit testattiin riippumattomassa aineistossa. Laktaatiopäivän vaikutusta energiataseeseen selitti hyvin Ali-Schaefferin funktio, jota käytettiin perusmallina. Kaikissa energiatasemalleissa vaihtelu kasvoi laktaatioviikosta 12. alkaen, kun havaintojen määrä väheni ja energiatase muuttui positiiviseksi. Ennen poikimista käytettävissä olevista muuttujista dieetin väkirehuosuus ja väkirehun syönti-indeksi paransivat selitysastetta ja pienensivät jäännösvirhettä. Ruokinnan onnistumista voidaan seurata maitotuotoksen, maidon rasvapitoisuuden ja rasva-valkuaissuhteen tai EKM:n sisältävillä malleilla. EKM:n vakiointi pienensi mallin jäännösvirhettä. Elopaino ja kuntoluokka olivat heikkoja selittäjiä. Malleja voidaan hyödyntää karjatason ruokinnan suunnittelussa ja seurannassa, mutta yksittäisen lehmän energiataseen ennustamiseen ne eivät sovellu.

A reexamination of the permeability index of clays

The permeability index Ck, similar to the compression index, is the slope of the void ratio – coefficient of permeability relationship. Literature shows that, in general, for sensitive clays it can be related to initial void ratio by Ck = 0.5e0. The possibility of obtaining such a relationship for Cochin marine clays in terms of liquid limit void ratio is indicated in this paper. Analysis of permeability behaviour of Cochin marine clays and the test results available in published literature using generalized state parameter approach show that, in principle, these forms of equations for the permeability index are tenable, even though they were obtained based on experimental observation alone.

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

Tropical Clays .1. Index Properties And Microstructural Aspects

Soils showing changes in plasticity characteristics upon driving form an important group in tropical soils. These changes are attributed to the grouping of particles into aggregates either due to mineralogy or presence of cementing agents and/or pore fluid characteristics. These changes are found to be permanent. In this paper, the effect of these changes leading to changes in index properties is discussed. The coefficient of permeability has been found to be comparable at liquid limit water content for different soils of varying liquid limit values. Permeability is an indirect reflection of microstructure and indicates the flow rate, which depends upon pore geometry. Other mechanical properties like compressibility and shear strength also depend upon pore geometry. These microstructural aspects of liquid limit as a reference state for the analysis of engineering behavior of tropical soils are examined in detail.