Estimation of a function of low local dimensionality by deep neural networks

Deep neural networks (DNNs) achieve impressive results for complicated tasks like object detection on images and speech recognition. Motivated by this practical success, there is now a strong interest in showing good theoretical properties of DNNs. To describe for which tasks DNNs perform well and when they fail, it is a key challenge to understand their performance. The aim of this paper is to contribute to the current statistical theory of DNNs. We apply DNNs on high dimensional data and we show that the least squares regression estimates using DNNs are able to achieve dimensionality reduction in case that the regression function has locally low dimensionality. Consequently, the rate of convergence of the estimate does not depend on its input dimension $d$, but on its local dimension $d^*$ and the DNNs are able to circumvent the curse of dimensionality in case that $d^*$ is much smaller than $d$. In our simulation study we provide numerical experiments to support our theoretical result and we compare our estimate with other conventional nonparametric regression estimates. The performance of our estimates is also validated in experiments with real data

The Radial Hedgehog Solution in the Landau-de Gennes Theory: Effects of the Bulk Potentials

We study equilibrium configurations in spherical droplets of nematic liquid crystal with strong radial anchoring, within the Landau-de Gennes theory with a sixth-order bulk potential. The sixth-order potential predicts a bulk biaxial phase for sufficiently low temperatures, which the conventional fourth-order potential cannot predict. We prove the existence of a radial hedgehog solution, which is a uniaxial solution with a single isotropic point defect at the droplet centre, for all temperatures and droplet sizes, and prove that there is a unique radial hedgehog solution for moderately low temperatures, but not deep in the nematic phase. We numerically compute critical points of the Landau-de Gennes free energy with the sixth order bulk potential, with rotational and mirror symmetry, and find at least two competing stable critical points: the biaxial torus and split core solutions, which have biaxial regions around the centre, for low temperatures. The size of the biaxial regions increases with decreasing temperature. We also compare the properties of the radial hedgehog solution with the fourth-order and sixth-order potentials respectively, in terms of the Morse indices as a function of the temperature and droplet radius; the role of the radial hedgehog solution as a transition state in switching processes; and compare the bifurcation plots with temperature, with the fourth- and sixth-order potentials. Overall, the sixth-order potential has a stabilising effect on biaxial critical points and a de-stabilising effect on uniaxial critical points and we discover an altogether novel bulk biaxial critical point of the Landau-de Gennes energy with the sixth-order potential, for which the bulk biaxiality is driven by the sixth-order potential

Kultivierung von Caenorhabditis elegans über Flüssigmedium zur Untersuchung des molekularen Folsäuremetabolismus

Folates play an important role in the human metabolism. They are important for the DNA-formation, as well as for the methyl -transfer, especially for the methylation of homocysteine to methionine. The methylene tetrahydrofolate reductase (MTHFR), the methionine synthase (MS) and the cystathionine beta synthase (CBS) are the central enzymes of the folate metabolism. Due to certain mutations, polymorphism of these enzymes may appear. The two most important polymorphism of the MTHFR are the C677T-polymorphism and the A1298C-polymorphism. For the methionine synthase, the A2756G-polymorphism is one of the most common. Mutations also appear for the CBS. These mutations may result in an increased requirement for folic acid to maintain the enzymatic activity, an increased homocysteine-level and some diseases or even malformation of the embryo. The nematode C. elegans was first discovered 1900 and from the very be-ginning it was in the focus of research- interest. During the 60ies it was es-tablished as a model organism. Since then, the interest it gained increased enormously and it will retain its role as an important research object in the scientific future. Its similarity to the human genome is remarkable. Some homologue genes exist in C. elegans for the MTHFR, the MS and the CBS. An orthologue gene for the folate-transporter folt-1 was also found. During experimental work of this thesis, the bodysize, life-cycles, life-span and progeny were determined and compared with investigations from the literature. Especially the differences between cultivation on NGM-plates and in liquid medium were investigated by comparing the bodysize and the life-cycles. Probable cases of deviations within the present results to the data in the literature are discussed in this work and suggestions for future improve-ments are indicated

Correlation of Matrix Metalloproteinases and Tissue Inhibitors of Matrix Metalloproteinase Expression in Ileal Carcinoids, Lymph Nodes and Liver Metastasis with Prognosis and Survival

Purpose: Ileal carcinoids are gut epithelial tumors originating from serotonin-containing enterochromaffin (EC) cells. Therapeutic options for effectively inhibiting the growth and spread of metastatic carcinoids are still limited. We aimed to identify the role of matrix metalloproteinases (MMPs) and their endogenous tissue inhibitors (TIMPs) during tumor development and metastasis. Patients and Methods: Tissue samples were obtained from surgically treated patients. Expression of the EC-cell marker, vesicular monoamine transporter-1 (VMAT-1), was used to verify ileal carcinoids. We investigated the differential expression of MMP-2, 7, 9, 11, and 13 and their endogenous inhibitors (TIMP-1, 2, and 3) by quantitative real-time RT-PCR in 25 primary tumors, their corresponding lymph node metastases and/or liver metastases and matched normal mucosa. Results: Significantly increased expression of VMAT-1, MMP-2, MMP-11, TIMP-1 and TIMP-3 was determined by quantitative RT-PCR in EC-cell carcinoids compared to normal intestinal mucosa (p < 0.05). In contrast, MMP-2 and MMP-9 as well as TIMP-1, TIMP-2, and TIMP-3 expression in primary tumors of patients with liver metastases (M1) was significantly lower than in patients lacking liver metastases (M0). EC-cell tumors were significantly larger in the M1 group of tumors, while VMAT-1 expression was significantly decreased. We found an inverse correlation between tumor size and prognosis. Univariate analysis further revealed that decreased expression of VMAT-1, MMP-2 and TIMP-3 in primary tumors was significantly associated with a reduced survival time of the patients. Conclusion: Our data reveal that MMP-2 and TIMP-3 expression together with VMAT-1 expression are of potential prognostic and clinical value in ileal carcinoids. Copyright (C) 2008 S. Karger AG, Base

The radial hedgehog solution in the Landau–de Gennes theory : effects of the bulk potentials

We study equilibrium configurations in spherical droplets of nematic liquid crystal with strong radial anchoring, within the Landau–de Gennes theory with a sixth-order bulk potential. The sixth-order potential predicts a bulk biaxial phase for sufficiently low temperatures, which the conventional fourth-order potential cannot predict. We prove the existence of a radial hedgehog solution, which is a uniaxial solution with a single isotropic point defect at the droplet centre, for all temperatures and droplet sizes, and prove that there is a unique radial hedgehog solution for moderately low temperatures, but not deep in the nematic phase. We numerically compute critical points of the Landau–de Gennes free energy with the sixth order bulk potential, with rotational and mirror symmetry, and find at least two competing stable critical points: the biaxial torus and split core solutions, which have biaxial regions around the centre, for low temperatures. The size of the biaxial regions increases with decreasing temperature. We also compare the properties of the radial hedgehog solution with the fourth-order and sixth-order potentials respectively, in terms of the Morse indices as a function of the temperature and droplet radius; the role of the radial hedgehog solution as a transition state in switching processes; and compare the bifurcation plots with temperature, with the fourth- and sixth-order potentials. Overall, the sixth-order potential has a stabilising effect on biaxial critical points and a de-stabilising effect on uniaxial critical points and we discover an altogether novel bulk biaxial critical point of the Landau–de Gennes energy with the sixth-order potential, for which the bulk biaxiality is driven by the sixth-order potential

Mammotome: Less Invasive than ABBI with Similar Accuracy for Early Breast Cancer Detection

We performed a prospective analysis of two consecutive biopsy cohorts investigated by the same team to compare the Mammotome system with the ABBI procedure. From April 1997 to August 2003 a series of 413 nonpalpable mammographic lesions in 387 women (median age 56 years, range 30-84 years) were stereotactically biopsied in the University Hospital of Basel, Switzerland. Until October 1999 the ABBI system was applied exclusively, it was subsequently superseded by the Mammotome device in our clinic. Main outcome measures were accuracy, technical demand, and morbidity. Sensitivity (97.3%/96.8%), negative predictive value (99.2%/98.7%), and diagnostic accuracy (99.4%/99.1%) regarding the detection of malignancy were excellent for both techniques (ABBI/Mammotome). The Mammotome procedure was faster and less invasive, thus causing significantly less morbidity. The larger specimen obtained by the ABBI procedure resulted in more detailed histology. In conclusion, recommend the Mammotome system as the method of choice for detecting nonpalpable early breast cance

Oral anticoagulant management of patients with mechanical heart valves at the Salam Centre of Khartoum:Observations on quality of anticoagulation and thrombotic risk

IntroductionRheumatic heart disease with mechanical heart valve (MHV) replacement is common in Africa. However, MHV requires long-life anticoagulation and managing this can be challenging.Methods and resultsWe report data of a prospective observational study conducted between August 2018 and September 2019 in MHV patients in the Salam Centre for Cardiac Surgery built in Khartoum, by Emergency, an Italian Non-Governmental Organization, to evaluate the quality of anticoagulation control and the risk of thrombotic complications.ResultsWe studied 3647 patients (median age 25.1 years; 53.9 % female). Median Time in Therapeutic Range (TTR) was 53 % (interquartile range 37 % to 67 %) and 70 thrombotic events (rate 1.8 × 100 pt-years [95 % CI 1.38-2.23]) were recorded. Among patients in the first quartile of TTR (≤37 %), we recorded 34/70 (48.6 %) of all thrombotic events (rate 3.7 × 100 pt-years [95 % CI 2.5-5.1]), with a high mortality rate (2.2 × 100 pt-years [95 % CI 1.3-3.3]). In patients with guideline-recommended TTR (≥65 %) the event rate was 0.8 × 100 pt-years for thrombotic events [95 % CI 0.3-1.5] and 0.4 × 100 pt-years for mortality [95 % CI 0.1-0.9]. Multivariable analysis showed that having a TTR in the lowest quartile (≤37 %) and being noncompliant are significantly associated with increased thrombotic risk. Aspirin use or different valve type did not influence the thrombotic risk. Almost 40 % of all thromboembolic complications could have been potentially prevented by further improving VKA management to obtain a TTR > 37 %.ConclusionThe thrombotic risk of MHV patients on VKAs living in a low-income country like Sudan is associated with low quality of anticoagulation control. Efforts should be made to decrease the number of non-compliant patients and to reach a guideline-recommended TTR of ≥65 %