Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space

Dancing with death. A historical perspective on coping with covid-19

In this paper, we address the question on how societies coped with pandemic crises, how they tried to control or adapt to the disease, or even managed to overcome the death trap in history. On the basis of historical research, we describe how societies in the western world accommodated to or exited hardship and restrictive measures over the course of the last four centuries. In particular, we are interested in how historically embedded citizens' resources were directed towards living with and to a certain extent accepting the virus. Such an approach of “applied history” to the management of crises and public hazards, we believe, helps address today's pressing question of what adaptive strategies can be adopted to return to a normalized life, including living with socially acceptable medical, hygienic and other pandemic‐related measures

Profound variation in dihydropyrimidine dehydrogenase activity in human blood cells: major implications for the detection of partly deficient patients

Dihydropyrimidine dehydrogenase (DPD) is responsible for the breakdown of the widely used antineoplastic agent 5-fluorouracil (5FU), thereby limiting the efficacy of the therapy. To identify patients suffering from a complete or partial DPD deficiency, the activity of DPD is usually determined in peripheral blood mononuclear cells (PBM cells). In this study, we demonstrated that the highest activity of DPD was found in monocytes followed by that of lymphocytes, granulocytes and platelets, whereas no significant activity of DPD could be detected in erythrocytes. The activity of DPD in PBM cells proved to be intermediate compared with the DPD activity observed in monocytes and lymphocytes. The mean percentage of monocytes in the PBM cells obtained from cancer patients proved to be significantly higher than that observed in PBM cells obtained from healthy volunteers. Moreover, a profound positive correlation was observed between the DPD activity of PBM cells and the percentage of monocytes, thus introducing a large inter- and intrapatient variability in the activity of DPD and hindering the detection of patients with a partial DPD deficiency. © 1999 Cancer Research Campaig

Dihydropyrimidine Dehydrogenase Deficiency: Metabolic Disease or Biochemical Phenotype?

Dihydropyrimidine dehydrogenase (DPD) deficiency is an autosomal recessive disorder of pyrimidine metabolism that impairs the first step of uracil und thymine degradation. The spectrum of clinical presentations in subjects with the full biochemical phenotype of DPD deficiency ranges from asymptomatic individuals to severely affected patients suffering from seizures, microcephaly, muscular hypotonia, developmental delay and eye abnormalities.We report on a boy with intellectual disability, significant impairment of speech development, highly active epileptiform discharges on EEG, microcephaly and impaired gross-motor development. This clinical presentation triggered metabolic workup that demonstrated the biochemical phenotype of DPD deficiency, which was confirmed by enzymatic and molecular genetic studies. The patient proved to be homozygous for a novel c.2059-22T>G mutation which resulted in an in-frame insertion of 21 base pairs (c.2059-21_c.2059-1) of intron 16 of DPYD. Family investigation showed that the asymptomatic father was also homozygous for the same mutation and enzymatic and biochemical findings were similar to his severely affected son. When the child deteriorated clinically, exome sequencing was initiated under the hypothesis that DPD deficiency did not explain the phenotype completely. A deletion of the maternal allele on chromosome 15q11.2-13-1 was identified allowing the diagnosis of Angelman syndrome (AS). This diagnosis explains the patient's clinical presentation sufficiently; the influence of DPD deficiency on the phenotype, however, remains uncertain

Beta-ureidopropionase deficiency presenting with congenital anomalies of the urogenital and colorectal systems

Beta-ureidopropionase deficiency (McKusick 606673) is an autosomal recessive condition caused by mutations in the UPB1 gene. To date, five patients have been reported, including one putative case detected through newborn screening. Clinical presentation includes neurological and developmental problems. Here, we report another case of beta-ureidopropionase deficiency who presented with congenital anomalies of the urogenital and colorectal systems and with normal neurodevelopmental milestones. Analysis of a urine sample, because of the suspicion of renal stones on ultrasound, showed strongly elevated levels of the characteristic metabolites, N-carbamyl-beta-amino acids. Subsequent analysis of UPB1 identified a novel mutation 209 G>C (R70P) in exon 2 and a previously reported splice receptor mutation IVS1-2A>G. Expression studies of the R70P mutant enzyme showed that the mutant enzyme did not possess any residual activity. Long-term follow-up is required to determine the clinical significance of the beta-ureidopropionase deficiency in our patien