The Karhunen-Loève theorem

La trasformata di Karhunen-Loève monodimensionale è la decomposizione di un processo stocastico del secondo ordine a parametrizzazione continua in coefficienti aleatori scorrelati. Nella presente dissertazione, la trasformata è ottenuta per via analitica, proiettando il processo, considerato in un intervallo di tempo limitato [a,b], su una base deterministica ottenuta dalle autofunzioni dell'operatore di Hilbert-Schmidt di covarianza corrispondenti ad autovalori positivi. Fondamentalmente l'idea del metodo è, dal primo, trovare gli autovalori positivi dell'operatore integrale di Hilbert-Schmidt, che ha in Kernel la funzione di covarianza del processo. Ad ogni tempo dell'intervallo, il processo è proiettato sulla base ortonormale dello span delle autofunzioni dell'operatore di Hilbert-Schmidt che corrispondono ad autovalori positivi. Tale procedura genera coefficienti aleatori che si rivelano variabili aleatorie centrate e scorrelate. L'espansione in serie che risulta dalla trasformata è una combinazione lineare numerabile di coefficienti aleatori di proiezione ed autofunzioni convergente in media quadratica al processo, uniformemente sull'intervallo temporale. Se inoltre il processo è Gaussiano, la convergenza è quasi sicuramente sullo spazio di probabilità (O,F,P). Esistono molte altre espansioni in serie di questo tipo, tuttavia la trasformata di Karhunen-Loève ha la peculiarità di essere ottimale rispetto all'errore totale in media quadratica che consegue al troncamento della serie. Questa caratteristica ha conferito a tale metodo ed alle sue generalizzazioni un notevole successo tra le discipline applicate.

Poor performance of microbiological sampling in the prediction of recurrent arthroplasty infection

During a two-stage revision for prosthetic joint infections (PJI), joint aspirations, open tissue sampling and serum inflammatory markers are performed before re-implantation to exclude ongoing silent infection. We investigated the performance of these diagnostic procedures on the risk of recurrence of PJI among asymptomatic patients undergoing a two-stage revision. A total of 62 PJI were found in 58 patients. All patients had intra-operative surgical exploration during re-implantation, and 48 of them had intra-operative microbiological swabs. Additionally, 18 joint aspirations and one open biopsy were performed before second-stage reimplantation. Recurrence or persistence of PJI occurred in 12 cases with a mean delay of 218 days after re-implantation, but only four pre- or intraoperative invasive joint samples had grown a pathogen in cultures. In at least seven recurrent PJIs (58%), patients had a normal C-reactive protein (CRP, < 10 mg/l) level before re-implantation. The sensitivity, specificity, positive predictive and negative predictive values of pre-operative invasive joint aspiration and CRP for the prediction of PJI recurrence was 0.58, 0.88, 0.5, 0.84 and 0.17, 0.81, 0.13, 0.86, respectively. As a conclusion, pre-operative joint aspiration, intraoperative bacterial sampling, surgical exploration and serum inflammatory markers are poor predictors of PJI recurrence. The onset of reinfection usually occurs far later than reimplantation.

Selective inferior petrosal sinus sampling without venous outflow diversion in the detection of a pituitary adenoma in Cushing's syndrome

Conventional MRI may still be an inaccurate method for the non-invasive detection of a microadenoma in adrenocorticotropin (ACTH)-dependent Cushing's syndrome (CS). Bilateral inferior petrosal sinus sampling (BIPSS) with ovine corticotropin-releasing hormone (oCRH) stimulation is an invasive, but accurate, intervention in the diagnostic armamentarium surrounding CS. Until now, there is a continuous controversial debate regarding lateralization data in detecting a microadenoma. Using BIPSS, we evaluated whether a highly selective placement of microcatheters without diversion of venous outflow might improve detection of pituitary microadenoma.

Comparison of gingival crevicular fluid sampling methods in patients with severe chronic periodontitis

The analysis of samplings from periodontal pockets is important in the diagnosis and therapy of periodontitis. In this study, three different sampling techniques were compared to determine whether one method yielded samples suitable for the reproducible and simultaneous determination of bacterial load, cytokines, neutrophil elastase, and arginine-specific gingipains (Rgps). Rgps are an important virulence factor of Porphyromonas gingivalis, the exact concentration of which in gingival crevicular fluid (GCF) has not been quantified.

A syntactic realization theorem for justification logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms \$mathsfd\$, \$mathsft\$, \$mathsfb\$, \$mathsf4\$, and \$mathsf5\$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for \$mathsfKB5\$ and \$mathsfS5\$ by showing that the positive introspection operator is superfluous.

Enhanced Sensitivity by Nonuniform Sampling Enables Multidimensional MAS NMR Spectroscopy of Protein Assemblies

We report dramatic sensitivity enhancements in multidimensional MAS NMR spectra by the use of nonuniform sampling (NUS) and introduce maximum entropy interpolation (MINT) processing that assures the linearity between the time and frequency domains of the NUS acquired data sets. A systematic analysis of sensitivity and resolution in 2D and 3D NUS spectra reveals that with NUS, at least 1.5- to 2-fold sensitivity enhancement can be attained in each indirect dimension without compromising the spectral resolution. These enhancements are similar to or higher than those attained by the newest-generation commercial cryogenic probes. We explore the benefits of this NUS/MaxEnt approach in proteins and protein assemblies using 1-73-(U-C-13,N-15)/74-108-(U-N-15) Escherichia coil thioredoxin reassembly. We demonstrate that in thioredoxin reassembly, NUS permits acquisition of high-quality 3D-NCACX spectra, which are inaccessible with conventional sampling due to prohibitively long experiment times. Of critical importance, issues that hinder NUS-based SNR enhancement in 3D-NMR of liquids are mitigated in the study of solid samples in which theoretical enhancements on the order of 3-4 fold are accessible by compounding the NUS-based SNR enhancement of each indirect dimension. NUS/MINT is anticipated to be widely applicable and advantageous for multidimensional heteronuclear MAS NMR spectroscopy of proteins, protein assemblies, and other biological systems.

On Certain Applications of the Khukhro-Makarenko Theorem

Some recent results of Khukhro and Makarenko on the existence of characteristic X-subgroups of finite index in a group G, for certain varieties X, are used to obtain generalisations of some well-known results in the literature pertaining to groups G, in which all proper subgroups satisfy some condition or other related to the property 'soluble-by-finite'. In addition, a partial generalisation is obtained for the aforementioned results on the existence of characteristic subgroups.

Magnetic resonance imaging based determination of body compartments with the versatile, interactive sparse sampling (VISS) method

To investigate the inhomogeneity of radiofrequency fields at higher field strengths that can interfere with established volumetric methods, in particular for the determination of visceral (VAT) and subcutaneous adipose tissue (SCAT). A versatile, interactive sparse sampling (VISS) method is proposed to determine VAT, SCAT, and also total body volume (TBV).