On the problems of object restoration and image extrapolation in optics

In this paper we consider the problems of object restoration and image extrapolation, according to the regularization theory of improperly posed problems. In order to take into account the stochastic nature of the noise and to introduce the main concepts of information theory, great attention is devoted to the probabilistic methods of regularization. The kind of the restored continuity is investigated in detail; in particular we prove that, while the image extrapolation presents a Hölder type stability, the object restoration has only a logarithmic continuity. © 1979 American Institute of Physics.

Macroturbulent and rotational broadening in the spectra of B-type supergiants.

The absorption-line spectra of early B-type supergiants show significant broadening that implies that an additional broadening mechanism (characterized here as `macroturbulence') is present in addition to rotational broadening. Using high-resolution spectra with signal-to-noise ratios of typically 500, we have attempted to quantify the relative contributions of rotation and macroturbulence, but even with data of this quality significant problems were encountered. However, for all our targets, a model where macroturbulence dominates and rotation is negligible is acceptable; the reverse scenario leads to poor agreement between theory and observation. Additionally, there is marginal evidence for the degree of broadening increasing with line strength, possibly a result of the stronger lines being formed higher in the atmosphere. Acceptable values of the projected rotational velocity are normally less than or equal to 50 km s-1, which may also be a typical upper limit for the rotational velocity. Our best estimates for the projected rotational velocity are typically 10-20 km s-1 and hence compatible with this limit. These values are compared with those predicted by single star evolutionary models, which are initially rapidly rotating. It is concluded that either these models underestimate the rate of rotational breaking or some of the targets may be evolving through a blue loop or are binaries.

Location-routing problems of semi-obnoxious facilities: approaches and decision support

A presente tese resulta de um trabalho de investigação cujo objectivo se centrou no problema de localização-distribuição (PLD) que pretende abordar, de forma integrada, duas actividades logísticas intimamente relacionadas: a localização de equipamentos e a distribuição de produtos. O PLD, nomeadamente a sua modelação matemática, tem sido estudado na literatura, dando origem a diversas aproximações que resultam de diferentes cenários reais. Importa portanto agrupar as diferentes variantes por forma a facilitar e potenciar a sua investigação. Após fazer uma revisão e propor uma taxonomia dos modelos de localização-distribuição, este trabalho foca-se na resolução de alguns modelos considerados como mais representativos. É feita assim a análise de dois dos PLDs mais básicos (os problema capacitados com procura nos nós e nos arcos), sendo apresentadas, para ambos, propostas de resolução. Posteriormente, é abordada a localização-distribuição de serviços semiobnóxios. Este tipo de serviços, ainda que seja necessário e indispensável para o público em geral, dada a sua natureza, exerce um efeito desagradável sobre as comunidades contíguas. Assim, aos critérios tipicamente utilizados na tomada de decisão sobre a localização destes serviços (habitualmente a minimização de custo) é necessário adicionar preocupações que reflectem a manutenção da qualidade de vida das regiões que sofrem o impacto do resultado da referida decisão. A abordagem da localização-distribuição de serviços semiobnóxios requer portanto uma análise multi-objectivo. Esta análise pode ser feita com recurso a dois métodos distintos: não interactivos e interactivos. Ambos são abordados nesta tese, com novas propostas, sendo o método interactivo proposto aplicável a outros problemas de programação inteira mista multi-objectivo. Por último, é desenvolvida uma ferramenta de apoio à decisão para os problemas abordados nesta tese, sendo apresentada a metodologia adoptada e as suas principais funcionalidades. A ferramenta desenvolvida tem grandes preocupações com a interface de utilizador, visto ser direccionada para decisores que tipicamente não têm conhecimentos sobre os modelos matemáticos subjacentes a este tipo de problemas.

Conventional and Reciprocal Approaches to the Forward and Inverse Problems of Electroencephalography

Le problème inverse en électroencéphalographie (EEG) est la localisation de sources de courant dans le cerveau utilisant les potentiels de surface sur le cuir chevelu générés par ces sources. Une solution inverse implique typiquement de multiples calculs de potentiels de surface sur le cuir chevelu, soit le problème direct en EEG. Pour résoudre le problème direct, des modèles sont requis à la fois pour la configuration de source sous-jacente, soit le modèle de source, et pour les tissues environnants, soit le modèle de la tête. Cette thèse traite deux approches bien distinctes pour la résolution du problème direct et inverse en EEG en utilisant la méthode des éléments de frontières (BEM): l’approche conventionnelle et l’approche réciproque. L’approche conventionnelle pour le problème direct comporte le calcul des potentiels de surface en partant de sources de courant dipolaires. D’un autre côté, l’approche réciproque détermine d’abord le champ électrique aux sites des sources dipolaires quand les électrodes de surfaces sont utilisées pour injecter et retirer un courant unitaire. Le produit scalaire de ce champ électrique avec les sources dipolaires donne ensuite les potentiels de surface. L’approche réciproque promet un nombre d’avantages par rapport à l’approche conventionnelle dont la possibilité d’augmenter la précision des potentiels de surface et de réduire les exigences informatiques pour les solutions inverses. Dans cette thèse, les équations BEM pour les approches conventionnelle et réciproque sont développées en utilisant une formulation courante, la méthode des résidus pondérés. La réalisation numérique des deux approches pour le problème direct est décrite pour un seul modèle de source dipolaire. Un modèle de tête de trois sphères concentriques pour lequel des solutions analytiques sont disponibles est utilisé. Les potentiels de surfaces sont calculés aux centroïdes ou aux sommets des éléments de discrétisation BEM utilisés. La performance des approches conventionnelle et réciproque pour le problème direct est évaluée pour des dipôles radiaux et tangentiels d’excentricité variable et deux valeurs très différentes pour la conductivité du crâne. On détermine ensuite si les avantages potentiels de l’approche réciproquesuggérés par les simulations du problème direct peuvent êtres exploités pour donner des solutions inverses plus précises. Des solutions inverses à un seul dipôle sont obtenues en utilisant la minimisation par méthode du simplexe pour à la fois l’approche conventionnelle et réciproque, chacun avec des versions aux centroïdes et aux sommets. Encore une fois, les simulations numériques sont effectuées sur un modèle à trois sphères concentriques pour des dipôles radiaux et tangentiels d’excentricité variable. La précision des solutions inverses des deux approches est comparée pour les deux conductivités différentes du crâne, et leurs sensibilités relatives aux erreurs de conductivité du crâne et au bruit sont évaluées. Tandis que l’approche conventionnelle aux sommets donne les solutions directes les plus précises pour une conductivité du crâne supposément plus réaliste, les deux approches, conventionnelle et réciproque, produisent de grandes erreurs dans les potentiels du cuir chevelu pour des dipôles très excentriques. Les approches réciproques produisent le moins de variations en précision des solutions directes pour différentes valeurs de conductivité du crâne. En termes de solutions inverses pour un seul dipôle, les approches conventionnelle et réciproque sont de précision semblable. Les erreurs de localisation sont petites, même pour des dipôles très excentriques qui produisent des grandes erreurs dans les potentiels du cuir chevelu, à cause de la nature non linéaire des solutions inverses pour un dipôle. Les deux approches se sont démontrées également robustes aux erreurs de conductivité du crâne quand du bruit est présent. Finalement, un modèle plus réaliste de la tête est obtenu en utilisant des images par resonace magnétique (IRM) à partir desquelles les surfaces du cuir chevelu, du crâne et du cerveau/liquide céphalorachidien (LCR) sont extraites. Les deux approches sont validées sur ce type de modèle en utilisant des véritables potentiels évoqués somatosensoriels enregistrés à la suite de stimulation du nerf médian chez des sujets sains. La précision des solutions inverses pour les approches conventionnelle et réciproque et leurs variantes, en les comparant à des sites anatomiques connus sur IRM, est encore une fois évaluée pour les deux conductivités différentes du crâne. Leurs avantages et inconvénients incluant leurs exigences informatiques sont également évalués. Encore une fois, les approches conventionnelle et réciproque produisent des petites erreurs de position dipolaire. En effet, les erreurs de position pour des solutions inverses à un seul dipôle sont robustes de manière inhérente au manque de précision dans les solutions directes, mais dépendent de l’activité superposée d’autres sources neurales. Contrairement aux attentes, les approches réciproques n’améliorent pas la précision des positions dipolaires comparativement aux approches conventionnelles. Cependant, des exigences informatiques réduites en temps et en espace sont les avantages principaux des approches réciproques. Ce type de localisation est potentiellement utile dans la planification d’interventions neurochirurgicales, par exemple, chez des patients souffrant d’épilepsie focale réfractaire qui ont souvent déjà fait un EEG et IRM.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

The effect of nonlinearity on the variational assimilation of satellite observations using a simple column model

Cloud imagery is not currently used in numerical weather prediction (NWP) to extract the type of dynamical information that experienced forecasters have extracted subjectively for many years. For example, rapidly developing mid-latitude cyclones have characteristic signatures in the cloud imagery that are most fully appreciated from a sequence of images rather than from a single image. The Met Office is currently developing a technique to extract dynamical development information from satellite imagery using their full incremental 4D-Var (four-dimensional variational data assimilation) system. We investigate a simplified form of this technique in a fully nonlinear framework. We convert information on the vertical wind field, w(z), and profiles of temperature, T(z, t), and total water content, qt (z, t), as functions of height, z, and time, t, to a single brightness temperature by defining a 2D (vertical and time) variational assimilation testbed. The profiles of w, T and qt are updated using a simple vertical advection scheme. We define a basic cloud scheme to obtain the fractional cloud amount and, when combined with the temperature field, we convert this information into a brightness temperature, having developed a simple radiative transfer scheme. With the exception of some matrix inversion routines, all our code is developed from scratch. Throughout the development process we test all aspects of our 2D assimilation system, and then run identical twin experiments to try and recover information on the vertical velocity, from a sequence of observations of brightness temperature. This thesis contains a comprehensive description of our nonlinear models and assimilation system, and the first experimental results.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

The dynamics of early-type galaxies as a tool to understand their hot coronae and their IMF

Dynamical models of galaxies are a powerful tool to study and understand several astrophysical problems related to galaxy formation and evolution. This thesis is focussed on a particular type of dynamical models, that are widely used in literature, and are based on the solution of the Jeans equations. By means of a numerical Jeans solver code, developed on purpose and able to build state-of-the-art advanced axisymmetric galaxy models, two of the main currently investigated issues in the field of research of early-type galaxies (ETGs) are addressed. The first topic concerns the hot and X-ray emitting gaseous coronae that surround ETGs. The main goal is to explain why flat and rotating galaxies generally exhibit haloes with lower gas temperatures and luminosities with respect to rounder and velocity dispersion supported systems. The second astrophysical problem addressed concerns instead the stellar initial mass function (IMF) of ETGs. Nowadays, this is a very controversial issue due to a growing number of works on ETGs, based on different and independent techniques, that show evidences of a systematic variation of the IMF normalization as a function of galaxy velocity dispersion or mass. These studies are changing the previous opinion that the IMF of ETGs was the same as that of spiral galaxies, and hence universal throughout the whole large family of galaxies.

Die operative Behandlung der Azetabulum-T-Fraktur über eine chirurgische Hüftluxation oder einen Stoppa-Zugang. [Operative treatment of T-type fractures of the acetabulum via surgical hip dislocation or Stoppa approach]

OBJECTIVE: Anatomic reduction and stable fixation by means of tissue- preserving surgical approaches. INDICATIONS Displaced acetabular fractures. Surgical hip dislocation approach with larger displacement of the posterior column in comparison to the anterior column, transtectal fractures, additional intraarticular fragments, marginal impaction. Stoppa approach with larger displacement of the anterior column in comparison to the posterior column. A combined approach might be necessary with difficult reduction. CONTRAINDICATIONS Fractures > 15 days (then ilioinguinal or extended iliofemoral approaches). Suprapubic catheters and abdominal problems (e.g., previous laparotomy due to visceral injuries) with Stoppa approach (then switch to classic ilioinguinal approach). SURGICAL TECHNIQUE: Surgical hip dislocation: lateral decubitus position. Straight lateral incision centered over the greater trochanter. Entering of the Gibson interval. Digastric trochanteric osteotomy with protection of the medial circumflex femoral artery. Opening of the interval between the piriformis and the gluteus minimus muscle. Z-shaped capsulotomy. Dislocation of the femoral head. Reduction and fixation of the posterior column with plate and screws. Fixation of the anterior column with a lag screw in direction of the superior pubic ramus. Stoppa approach: supine position. Incision according to Pfannenstiel. Longitudinal splitting of the anterior portion of the rectus sheet and the rectus abdominis muscle. Blunt dissection of the space of Retzius. Ligation of the corona mortis, if present. Blunt dissection of the quadrilateral plate and the anterior column. Reduction of the anterior column and fixation with a reconstruction plate. Fixation of the posterior column with lag screws. If necessary, the first window of the ilioinguinal approach can be used for reduction and fixation of the posterior column. POSTOPERATIVE MANAGEMENT: During hospital stay, intensive mobilization of the hip joint using a continuous passive motion machine with a maximum flexion of 90 degrees . No active abduction and passive adduction over the body's midline, if a surgical dislocation was performed. Maximum weight bearing 10-15 kg for 8 weeks. Then, first clinical and radiographic follow-up. Deep venous thrombosis prophylaxis for 8 weeks postoperatively. RESULTS: 17 patients with a mean follow-up of 3.2 years. Ten patients were operated via surgical hip dislocation, two patients with a Stoppa approach, and five using a combined or alternative approach. Anatomic reduction was achieved in ten of the twelve patients (83%) without primary total hip arthroplasty. Mean operation time 3.3 h for surgical hip dislocation and 4.2 h for the Stoppa approach. Complications comprised one delayed trochanteric union, one heterotopic ossification, and one loss of reduction. There were no cases of avascular necrosis. In two patients, a total hip arthroplasty was performed due to the development of secondary hip osteoarthritis.

Impact of B-type natriuretic peptide on short-term clinical outcomes following transcatheter aortic valve implantation

Aims: We aimed to assess the impact of B-type natriuretic peptide (BNP) on short-term outcomes in patients undergoing transcatheter aortic valve implantation (TAVI). Methods and results: Of 500 consecutive patients with severe aortic stenosis undergoing TAVI at our institution, we studied 340 patients who had a BNP assessment prior to TAVI. Patients were divided into tertiles - low: BNP ≤201 pg/mL (n=114), mid: BNP 202-595 pg/mL (n=113) and high: BNP ≥596 pg/mL (n=113). The primary endpoint was all-cause mortality, cardiac death and major adverse cardiac and cerebrovascular events (MACCE; death, major stroke and myocardial infarction) at 30 days. Compared with low tertile, high tertile patients were at higher baseline surgical risk (STS score 5.5±3.0 vs. 7.4±4.1, p=0.002). On echocardiography, high tertile patients had smaller valve areas (0.74±0.21 vs. 0.66±0.23 cm2, p=0.008), higher left ventricular (LV) mass indices (123.40±33.66 vs. 168.22±47.96 g/m2, p<0.001) and lower LV ejection fractions (61.59±7.18 vs. 42.65±15.41%, p<0.001) as compared with low tertile patients. At 30 days, a significantly higher incidence of death (hazard ratio [HR] 7.41, p=0.001) cardiac death (HR 5.82, p=0.006) and MACCE (HR 9.04, p<0.001) was observed among high as compared to low tertile patients. Conclusions: In TAVI patients, higher BNP values at baseline are associated with an increased risk for an adverse event periprocedurally and after 30 days, respectively.

Effect of B-type Natriuretic Peptides on Long-Term Outcomes After Transcatheter Aortic Valve Implantation.

B-type natriuretic peptide (BNP) levels are elevated in patients with aortic stenosis (AS) and decrease acutely after replacement of the stenotic valve. The long-term prognostic value of BNP after transcatheter aortic valve implantation (TAVI) and the relative prognostic utility of single versus serial peri-interventional measurements of BNP and N-terminal prohormone BNP (NT-pro-BNP) are unknown. This study sought to determine the impact of BNP levels on long-term outcomes after TAVI and to compare the utility of BNP versus NT-pro-BNP measured before and after intervention. We analyzed 340 patients with severe AS and baseline pre-TAVI assessment of BNP. In 219 patients, BNP and NT-pro-BNP were measured serially before and after intervention. Clinical outcomes over 2 years were recorded. Patients with high baseline BNP (higher tertile ≥591 pg/ml) had increased risk of all-cause mortality (adjusted hazard ratio 3.16, 95% confidence interval 1.84 to 5.42; p <0.001) and cardiovascular death at 2 years (adjusted hazard ratio 3.37, 95% confidence interval 1.78 to 6.39; p <0.001). Outcomes were most unfavorable in patients with persistently high BNP before and after intervention. Comparing the 2 biomarkers, NT-pro-BNP levels measured after TAVI showed the highest prognostic discrimination for 2-year mortality (area under the curve 0.75; p <0.01). Baseline-to-discharge reduction, but not baseline levels of BNP, was related to New York Heart Association functional improvement. In conclusion, high preintervention BNP independently predicts 2-year outcomes after TAVI, particularly when elevated levels persist after the intervention. BNP and NT-pro-BNP and their serial periprocedural changes provide complementary prognostic information for symptomatic improvement and survival.

Effect of cage type on the behaviour pattern of rabbit does at different physiological stages

Interest in commercially farmed rabbit welfare has increased in recent years. As a result, new alternative housing systems have been developed, although they require evaluation in order to demonstrate their potential for improving welfare. The aim of this trial was to study the behavioural traits of rabbit does housed in 2 different types of cage (TC): conventional vs. alternative with an elevated platform, at different physiological stages (PS); lactation and gestation. Behavioural observations were carried out on 12 rabbit commercial does using continuous 24 h video recording. Independently of PS and TC, rabbit does spent most of their time on foot mats (on av. 57.7%). However, due to the use of platforms (on av. 23.0% of time), lactating does spent 36.6% less time on foot mats (P<0.001) and gestating does spent 27.0% less time on wire mesh (P<0.001) in alternative cages than in conventional cages. Alternative cages allowed for standing posture, but this behaviour was only observed in gestating does (on av. 4.6 times a day). Frequency of drinking was higher in conventional than in alternative cages (24.6 vs. 19.1 times a day; P<0.05). Gestating does housed in conventional cages reached the highest duration and frequency of interacting with neighbours (276 s/d and 4.6 times/d; P<0.05). The frequency of interacting with kits was lower in alternative than in conventional cages (2.4 vs. 8.6 times a day; P<0.01). Doe behaviour was influenced by the time of day, with less activity during the midday hours. During dark hours, rabbit does more frequently performed restless behaviour such as hyperactivity or nursing, matching the time at which rabbit does spent more time on the platform. The platform was frequently used by rabbit does, regardless of their physiological stage, and during late lactation phase, when mothers were not receptive to nursing, does housed in alternative cages used the platform as a mean to flee from kits trying to suckle. Use of the platform might lead to hygienic problems due to retained faeces on the platform and faeces and urine falling onto animals located in the lower part of the cage. The absence of stereotypies in rabbit does of this trial, suggested that animal welfare was not compromised by the type of housing (conventional or alternative cages).

Postwar problems of agriculture; report of the Council of state governments: farm tenure problems, soil conservation, price and production control, surplus war property, forestry problems. State plans for postwar agriculture; reports on what midwestern states are doing now in preparation for the postwar period, including résumé and recommendations of Midwest conference on agricultural problems of ten midwestern states, held in Chicago on June 9-10, 1944, under the auspices of the Council of state governments ....

"BX-240."

On the use of likert-type scales in multilevel data:Influence on aggregate variables

In multilevel analyses, problems may arise when using Likert-type scales at the lowest level of analysis. Specifically, increases in variance should lead to greater censoring for the groups whose true scores fall at either end of the distribution. The current study used simulation methods to examine the influence of single-item Likert-type scale usage on ICC(1), ICC(2), and group-level correlations. Results revealed substantial underestimation of ICC(1) when using Likert-type scales with common response formats (e.g., 5 points). ICC(2) and group-level correlations were also underestimated, but to a lesser extent. Finally, the magnitude of underestimation was driven in large part to an interaction between Likert-type scale usage and the amounts of within- and between-group variance. © Sage Publications.

The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.