The Wiener criterion for the Laplacian and the heat operator

La tesi presenta il criterio di regolarità di Wiener dell’ambito classico dell’operatore di Laplace ed in seguito alcune nozioni di teoria del potenziale e la dimostrazione del criterio nel caso dell’operatore del calore; in questa seconda sezione viene dedicata particolare attenzione alle formule di media e ad una diseguaglianza forte di Harnack, che risultano fondamentali nella trattazione dell’argomento centrale.

How to assess the external validity of therapeutic trials: a conceptual approach

Background External validity of study results is an important issue from a clinical point of view. From a methodological point of view, however, the concept of external validity is more complex than it seems to be at first glance. Methods Methodological review to address the concept of external validity. Results External validity refers to the question whether results are generalizable to persons other than the population in the original study. The only formal way to establish the external validity would be to repeat the study for that specific target population. We propose a three-way approach for assessing the external validity for specified target populations. (i) The study population might not be representative for the eligibility criteria that were intended. It should be addressed whether the study population differs from the intended source population with respect to characteristics that influence outcome. (ii) The target population will, by definition, differ from the study population with respect to geographical, temporal and ethnical conditions. Pondering external validity means asking the question whether these differences may influence study results. (iii) It should be assessed whether the study's conclusions can be generalized to target populations that do not meet all the eligibility criteria. Conclusion Judging the external validity of study results cannot be done by applying given eligibility criteria to a single target population. Rather, it is a complex reflection in which prior knowledge, statistical considerations, biological plausibility and eligibility criteria all have place.

Reproducibility and validity of video screen measurements of gait in children with spastic cerebral palsy

PURPOSE: To determine the reproducibility and validity of video screen measurement (VSM) of sagittal plane joint angles during gait. METHODS: 17 children with spastic cerebral palsy walked on a 10m walkway. Videos were recorded and 3d-instrumented gait analysis was performed. Two investigators measured six sagittal joint/segment angles (shank, ankle, knee, hip, pelvis, and trunk) using a custom-made software package. The intra- and interrater reproducibility were expressed by the intraclass correlation coefficient (ICC), standard error of measurements (SEM) and smallest detectable difference (SDD). The agreement between VSM and 3d joint angles was illustrated by Bland-Altman plots and limits of agreement (LoA). RESULTS: Regarding the intrarater reproducibility of VSM, the ICC ranged from 0.99 (shank) to 0.58 (trunk), the SEM from 0.81 degrees (shank) to 5.97 degrees (trunk) and the SDD from 1.80 degrees (shank) to 16.55 degrees (trunk). Regarding the interrater reproducibility, the ICC ranged from 0.99 (shank) to 0.48 (trunk), the SEM from 0.70 degrees (shank) to 6.78 degrees (trunk) and the SDD from 1.95 degrees (shank) to 18.8 degrees (trunk). The LoA between VSM and 3d data ranged from 0.4+/-13.4 degrees (knee extension stance) to 12.0+/-14.6 degrees (ankle dorsiflexion swing). CONCLUSION: When performed by the same observer, VSM mostly allows the detection of relevant changes after an intervention. However, VSM angles differ from 3d-IGA and do not reflect the real sagittal joint position, probably due to the additional movements in the other planes.

Validity of an automatic measure protocol in distal femur for allograft selection from a three-dimensional virtual bone bank system

Osteoarticular allograft is one possible treatment in wide surgical resections with large defects. Performing best osteoarticular allograft selection is of great relevance for optimal exploitation of the bone databank, good surgery outcome and patient’s recovery. Current approaches are, however, very time consuming hindering these points in practice. We present a validation study of a software able to perform automatic bone measurements used to automatically assess the distal femur sizes across a databank. 170 distal femur surfaces were reconstructed from CT data and measured manually using a size measure protocol taking into account the transepicondyler distance (A), anterior-posterior distance in medial condyle (B) and anterior-posterior distance in lateral condyle (C). Intra- and inter-observer studies were conducted and regarded as ground truth measurements. Manual and automatic measures were compared. For the automatic measurements, the correlation coefficients between observer one and automatic method, were of 0.99 for A measure and 0.96 for B and C measures. The average time needed to perform the measurements was of 16 h for both manual measurements, and of 3 min for the automatic method. Results demonstrate the high reliability and, most importantly, high repeatability of the proposed approach, and considerable speed-up on the planning.

The course of chronic and recurrent low back pain in the general population

Using latent class analysis (LCA), a previous study on patients attending primary care identified four courses of low back pain (LBP) over the subsequent 6 months. To date, no studies have used longitudinal pain recordings to examine the "natural" course of recurrent and chronic LBP in a population-based sample of individuals. This study examines the course of LBP in the general population and elaborates on the stability and criterion-related validity of the clusters derived. A random sample of 400 individuals reporting LBP in a population-based study was asked to complete a comprehensive questionnaire at the start and end of the year's survey, and 52 weekly pain diaries in between. The latter were analyzed using LCA. 305 individuals returned more than 50% of the diaries. Four clusters were identified (severe persistent, moderate persistent, mild persistent, and fluctuating). The clusters differed significantly with regards to pain and disability. Assessment of cluster stability showed that a considerable proportion of patients in the "fluctuating" group changed their classification over time. Three of the four clusters describing the typical course of pain matched the clusters described previously for patients in primary care. Due to the population-based design, this study achieves, for the first time, a close insight into the "natural" course of chronic and recurrent low back pain, including individuals that did not necessarily visit the general practitioner. The findings will help to understand better the nature of this pain in the general population.

Remission in schizophrenia: validity, frequency, predictors, and patients' perspective 5 years later

In March 2005, the Remission in Schizophrenia Working Group (RSWG) proposed a consensus definition of symptomatic remission in schizophrenia and developed specific operational criteria for its assessment. They pointed out, however, that the validity and the relationship to other outcome dimensions required further examination. This article reviews studies on the validity, frequency, and predictors of symptomatic remission in schizophrenia and studies on patients' perspectives. These studies have demonstrated that the RSWG remission criteria appear achievable and sustainable for a significant proportion of patients, and are related to a better overall symptomatic status and functional outcome and, to a less clear extent, to a better quality of life and cognitive performance. However, achieving symptomatic remission is not automatically concurrent with an adequate status in other outcome dimensions. The results of the present review suggest that the RSWG remission criteria are valid and useful. As such, they should be consistently applied in clinical trials. However the lack of consensus definitions of functional remission and adequate quality of life hampers research on their predictive validity on these outcome dimensions. Future research should therefore search for criteria of these dimensions and test whether the RSWG remission criteria consistently predict a "good" outcome with respect to functioning and quality of life.