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Die in Englisch verfasste Dissertation, die unter der Betreuung von Herrn Prof. Dr. H. F. de Groote, Fachbereich Mathematik, entstand, ist der Mathematischen Physik zuzuordnen. Sie behandelt Stonesche Spektren von Neumannscher Algebren, observable Funktionen sowie einige Anwendungen in der Physik. Das abschließende Kapitel liefert eine Verallgemeinerung des Kochen-Specker-Theorems. Stonesche Spektren und observable Funktionen wurden von de Groote eingeführt. Das Stonesche Spektrum einer von Neumann-Algebra ist eine Verallgemeinerung des Gelfand-Spektrums, die observablen Funktionen verallgemeinern die Gelfand-Transformierten. Da de Grootes Ergebnisse zum großen Teil unveröffentlicht sind, folgt nach dem Einleitungskapitel im zweiten Kapitel eine Übersichtsdarstellung dieser Ergebnisse. Das dritte Kapitel behandelt die Stoneschen Spektren endlicher von Neumann-Algebren. Für Algebren vom Typ In wird eine vollständige Charakterisierung des Stoneschen Spektrums entwickelt. Zu Typ-II1-Algebren werden einige Resultate vorgestellt. Das vierte Kapitel liefert. einige einfache Anwendungen des Formalismus auf die Physik. Das fünfte Kapitel gibt erstmals einen funktionalanalytischen Beweis des Kochen-Specker-Theorems und liefert die Verallgemeinerung dieses Satzes, wobei die Situation für alle von Neumann-Algebren geklärt wird.
The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type I_n factor as algebra of observables, including I_infinity. Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von Neumann algebra R without summands of types I_1 and I_2, using a known result on two-valued measures on the projection lattice P(R). Some connections with presheaf formulations as proposed by Isham and Butterfield are made.
Objectives: To analyze the performance of radiological assessment categories and quantitative computational analysis of apparent diffusion coefficient (ADC) maps using variant machine learning algorithms to differentiate clinically significant versus insignificant prostate cancer (PCa). Methods: Retrospectively, 73 patients were included in the study. The patients (mean age, 66.3 ± 7.6 years) were examined with multiparametric MRI (mpMRI) prior to radical prostatectomy (n = 33) or targeted biopsy (n = 40). The index lesion was annotated in MRI ADC and the equivalent histologic slides according to the highest Gleason Grade Group (GrG). Volumes of interest (VOIs) were determined for each lesion and normal-appearing peripheral zone. VOIs were processed by radiomic analysis. For the classification of lesions according to their clinical significance (GrG ≥ 3), principal component (PC) analysis, univariate analysis (UA) with consecutive support vector machines, neural networks, and random forest analysis were performed. Results: PC analysis discriminated between benign and malignant prostate tissue. PC evaluation yielded no stratification of PCa lesions according to their clinical significance, but UA revealed differences in clinical assessment categories and radiomic features. We trained three classification models with fifteen feature subsets. We identified a subset of shape features which improved the diagnostic accuracy of the clinical assessment categories (maximum increase in diagnostic accuracy ΔAUC = + 0.05, p < 0.001) while also identifying combinations of features and models which reduced overall accuracy. Conclusions: The impact of radiomic features to differentiate PCa lesions according to their clinical significance remains controversial. It depends on feature selection and the employed machine learning algorithms. It can result in improvement or reduction of diagnostic performance.
Background: Due to the difficulties in the definite diagnosis, data on brain imaging in pediatric patients with central nervous system (CNS)-invasive mold infection (IMD) are scarce. Our aim was to describe brain imaging abnormalities seen in immunocompromised children with CNS-IMD, and to analyze retrospectively whether specific imaging findings and sequences have a prognostic value. Methods: In a retrospective study of 19 pediatric patients with proven or probable CNS-IMD, magnetic resonance imaging (MRI)-findings were described and analyzed. The results were correlated with outcome, namely death, severe sequelae, or no neurological sequelae. Results: 11 children and 8 adolescents (11/8 with proven/probable CNS-IMD) were included. Seven of the patients died and 12/19 children survived (63%): seven without major neurological sequelae and five with major neurological sequelae. Multifocal ring enhancement and diffusion restriction were the most common brain MRI changes. Diffusion restriction was mostly seen at the core of the lesion. No patient with disease limited to one lobe died. Perivascular microbleeding seen on susceptibility weighted imaging (SWI) and/or gradient-echo/T2* images, as well as infarction, were associated with poor prognosis. Conclusions: The presence of infarction was related to poor outcome. As early microbleeding seems to be associated with poor prognosis, we suggest including SWI in routine diagnostic evaluation of immunocompromised children with suspected CNS-IMD.
Invasive mold disease (IMD) of the central nervous system (CNS) is a severe infectious complication in immunocompromised patients, but early microbiological diagnosis is difficult. As data on the value of biomarkers in the CNS are scarce, in particular in children, we retrospectively analyzed the performance of galactomannan (GM) and PCR assays in CNS samples of 15 children with proven and probable CNS IMD and of 32 immunocompromised children without fungal infection. Galactomannan in the cerebrospinal fluid (CSF) was assessed in nine of the 15 pediatric patients and was positive in five of them. Polymerase chain reaction (PCR) was performed in eight of the 15 patients and detected nucleic acids from molds in six patients. Galactomannan and PCR in CNS samples were the only positive microbiologic parameter in the CNS in three and two patients, respectively. In four patients, PCR specified the pathogen detected in microscopy. Galactomannan and PCR results remained negative in the CSF of all immunocompromised children without evidence for CNS IMD. Our data suggest that GM and PCR in CNS specimens are valuable additional tools in diagnosing CNS IMD and should be included in the work up of all pediatric patients with suspected mold disease of the CNS.
The nuclear factor kappa beta (NFκB) signaling pathway plays an important role in liver homeostasis and cancer development. Tax1-binding protein 1 (Tax1BP1) is a regulator of the NFκB signaling pathway, but its role in the liver and hepatocellular carcinoma (HCC) is presently unknown. Here we investigated the role of Tax1BP1 in liver cells and murine models of HCC and liver fibrosis. We applied the diethylnitrosamine (DEN) model of experimental hepatocarcinogenesis in Tax1BP1+/+ and Tax1BP1−/− mice. The amount and subsets of non-parenchymal liver cells in in Tax1BP1+/+ and Tax1BP1−/− mice were determined and activation of NFκB and stress induced signaling pathways were assessed. Differential expression of mRNA and miRNA was determined. Tax1BP1−/− mice showed increased numbers of inflammatory cells in the liver. Furthermore, a sustained activation of the NFκB signaling pathway was found in hepatocytes as well as increased transcription of proinflammatory cytokines in isolated Kupffer cells from Tax1BP1−/− mice. Several differentially expressed mRNAs and miRNAs in livers of Tax1BP1−/− mice were found, which are regulators of inflammation or are involved in cancer development or progression. Furthermore, Tax1BP1−/− mice developed more HCCs than their Tax1BP1+/+ littermates. We conclude that Tax1BP1 protects from liver cancer development by limiting proinflammatory signaling.
The pathogenesis of nodular lymphocyte–predominant Hodgkin lymphoma (NLPHL) and its relationship to other lymphomas are largely unknown. This is partly because of the technical challenge of analyzing its rare neoplastic lymphocytic and histiocytic (L&H) cells, which are dispersed in an abundant nonneoplastic cellular microenvironment. We performed a genome-wide expression study of microdissected L&H lymphoma cells in comparison to normal and other malignant B cells that indicated a relationship of L&H cells to and/or that they originate from germinal center B cells at the transition to memory B cells. L&H cells show a surprisingly high similarity to the tumor cells of T cell–rich B cell lymphoma and classical Hodgkin lymphoma, a partial loss of their B cell phenotype, and deregulation of many apoptosis regulators and putative oncogenes. Importantly, L&H cells are characterized by constitutive nuclear factor {kappa}B activity and aberrant extracellular signal-regulated kinase signaling. Thus, these findings shed new light on the nature of L&H cells, reveal several novel pathogenetic mechanisms in NLPHL, and may help in differential diagnosis and lead to novel therapeutic strategies.
Pathogenic variants in PRRT2, encoding the proline-rich transmembrane protein 2, have been associated with an evolving spectrum of paroxysmal neurologic disorders. Based on a cohort of children with PRRT2-related infantile epilepsy, this study aimed at delineating the broad clinical spectrum of PRRT2-associated phenotypes in these children and their relatives. Only a few recent larger cohort studies are on record and findings from single reports were not confirmed so far. We collected detailed genetic and phenotypic data of 40 previously unreported patients from 36 families. All patients had benign infantile epilepsy and harbored pathogenic variants in PRRT2 (core cohort). Clinical data of 62 family members were included, comprising a cohort of 102 individuals (extended cohort) with PRRT2-associated neurological disease. Additional phenotypes in the cohort of patients with benign sporadic and familial infantile epilepsy consist of movement disorders with paroxysmal kinesigenic dyskinesia in six patients, infantile-onset movement disorders in 2 of 40 individuals, and episodic ataxia after mild head trauma in one girl with bi-allelic variants in PRRT2. The same girl displayed a focal cortical dysplasia upon brain imaging. Familial hemiplegic migraine and migraine with aura were reported in nine families. A single individual developed epilepsy with continuous spikes and waves during sleep. In addition to known variants, we report the novel variant c.843G>T, p.(Trp281Cys) that co-segregated with benign infantile epilepsy and migraine in one family. Our study highlights the variability of clinical presentations of patients harboring pathogenic PRRT2 variants and expands the associated phenotypic spectrum.