Equivariant Neural Networks for Indirect Measurements

In the recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches apply deep neural networks in a post-processing step to the reconstructions obtained by classical reconstruction methods. However, the latter methods can be computationally expensive and introduce artifacts that are not present in the measured data and, in turn, can deteriorate the performance on the given task. To overcome these limitations, we propose a class of equivariant neural networks that can be directly applied to the measurements to solve the desired task. To this end, we build appropriate network structures by developing layers that are equivariant with respect to data transformations induced by well-known symmetries in the domain of the forward operator. We rigorously analyze the relation between the measurement operator and the resulting group representations and prove a representer theorem that characterizes the class of linear operators that translate between a given pair of group actions. Based on this theory, we extend the existing concepts of Lie group equivariant deep learning to inverse problems and introduce new representations that result from the involved measurement operations. This allows us to efficiently solve classification, regression or even reconstruction tasks based on indirect measurements also for very sparse data problems, where a classical reconstruction-based approach may be hard or even impossible. We illustrate the effectiveness of our approach in numerical experiments and compare with existing methods.Comment: 22 pages, 6 figure

Error analysis for filtered back projection reconstructions in Besov spaces

Filtered back projection (FBP) methods are the most widely used reconstruction algorithms in computerized tomography (CT). The ill-posedness of this inverse problem allows only an approximate reconstruction for given noisy data. Studying the resulting reconstruction error has been a most active field of research in the 1990s and has recently been revived in terms of optimal filter design and estimating the FBP approximation errors in general Sobolev spaces. However, the choice of Sobolev spaces is suboptimal for characterizing typical CT reconstructions. A widely used model are sums of characteristic functions, which are better modelled in terms of Besov spaces $\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$. In particular $\mathrm{B}^{\alpha,1}_1(\mathbb{R}^2)$ with $\alpha \approx 1$ is a preferred model in image analysis for describing natural images. In case of noisy Radon data the total FBP reconstruction error $$\|f-f_L^\delta\| \le \|f-f_L\|+ \|f_L - f_L^\delta\|$$ splits into an approximation error and a data error, where $L$ serves as regularization parameter. In this paper, we study the approximation error of FBP reconstructions for target functions $f \in \mathrm{L}^1(\mathbb{R}^2) \cap \mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$ with positive $\alpha \not\in \mathbb{N}$ and $1 \leq p,q \leq \infty$. We prove that the $\mathrm{L}^p$-norm of the inherent FBP approximation error $f-f_L$ can be bounded above by \begin{equation*} \|f - f_L\|_{\mathrm{L}^p(\mathbb{R}^2)} \leq c_{\alpha,q,W} \, L^{-\alpha} \, |f|_{\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)} \end{equation*} under suitable assumptions on the utilized low-pass filter's window function $W$. This then extends by classical methods to estimates for the total reconstruction error.Comment: 32 pages, 8 figure

Fourier-Domain Inversion for the Modulo Radon Transform

Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these approaches inherit the limitations of multiple-exposure fusion strategy. To overcome these disadvantages, the modulo Radon transform (MRT) has been proposed. The MRT is based on a co-design of hardware and algorithms. In the hardware step, Radon transform projections are folded using modulo non-linearities. Thereon, recovery is performed by algorithmically inverting the folding, thus enabling a single-shot, HDR approach to tomography. The first steps in this topic established rigorous mathematical treatment to the problem of reconstruction from folded projections. This paper takes a step forward by proposing a new, Fourier domain recovery algorithm that is backed by mathematical guarantees. The advantages include recovery at lower sampling rates while being agnostic to modulo threshold, lower computational complexity and empirical robustness to system noise. Beyond numerical simulations, we use prototype modulo ADC based hardware experiments to validate our claims. In particular, we report image recovery based on hardware measurements up to 10 times larger than the sensor's dynamic range while benefiting with lower quantization noise ($\sim$12 dB).Comment: 12 pages, submitted for possible publicatio

New Sunscreen Systems For Cosmetic And Pharmaceutical Applications Based On Photochromic Compounds

Ziel dieser Doktorarbeit war die Entwicklung eines neuartigen, adaptiven Sonnenschutzmittels, dessen Schutzwirkung sich der Intensität der Strahlung anpassen sollte. Das Funktionsprinzip ist von der photochromen Sonnenbrille bekannt. Nach dem Screening der verschiedenen photochromen Substanzklassen in Bezug auf ihr spektrales Verhalten und ihre Sonnenschutzwirkung, wurde die Klasse der Diarylethene, vor allem wegen ihrer hohen Stabilität, zur weiteren Optimierung ausgewählt. Durch synthetische Optimierungen innerhalb dieser Substanzklasse konnte als Zielmolekül, 1,2-Bis(2´-tert-butylbenzo[b]thien-6´-yl)perfluorocyclopenten, erhalten werden. Diese Substanz zeigte die besten Ergebnisse bzgl. Stabilität (durch eine intramolekulare Energieabbaufunktion), einem deutlichen Absorptionsanstieg im UVB-Bereich bei Sonnenlichtbestrahlung, guter Löseeigenschaften und einer fehlenden Thermochromie. Das Zielmolekül lässt sich in einer Drei-Schritt-Synthese (Sonogashira-Kupplung, Friedel-Crafts-Acylierung und McMurry-Reaktion) herstellen. Der Upscale ist unproblematisch. Die Substanz steht nun für weitere Tests (Toxizität, Einarbeitungsversuche in Cremegrundlagen) zur Verfügung.Theme of this thesis was the development of a novel, adaptive sunscreening agent, which protection abilities should adapt to the intensity of radiation. The operating principle is known from the photochromic sunglasses. After screening of the different photochromic substance classes, in relation to their spectral behavior and their sun protection abilities, the class of the diarylethenes were chosen for further optimisation, above all because of their high stability. By synthetic optimisation in this substance class 1,2-Bis(2´-tert-butylbenzo[b]thien-6´-yl)perfluorocyclopentene could be optained as the target-molecule. This substance shows the best results relating to stability (through a intramolecular energy dissipation function), a plain absorption increase in the UVB-range at solar radiation, a good solubility and a lack of thermochromism. The target-molecule could be produced by a three-step-synthesis (a Sonogashira-coupling, a Friedel-Crafts-acylation and a McMurry-reaction). The reaction can easily be upscaled. The substance is now available for other tests (on toxicity, embedding tests in sunscreen-formulations)

Mutations and amplification of oncogenes in endometrial cancer

Alterations in oncogenes are critical steps in the development of endometrial cancer. To investigate the potential clinical relevance of the amplification of the oncogenes c-erbB2, c-myc, and int-2 and the mutation of K-ras in endometrial cancer, 112 tumors were examined using PCR-based fluorescent DNA technology. Amplification of the three oncogenes and the mutation of K-ras were correlated with age, tumor size, lymph node status, metastases, stage, histological types, grade, steroid hormone receptor expression (estrogen receptor, ER; progesterone receptor, PgR), family history of cancer, previous history of cancer or precursor lesions, and previous history of hormone replacement therapy. Oncogene amplification of c-erbB2 was detected in 18.9%, of c-myc in 2.7% and of int-2 in 4.2%, and K-ras mutation in 11.6%. No significant correlations could be detected between amplification of c-erbB2 and any of the other parameters. Mutation of K-ras is associated with positive expression of PgR. This might indicate that mutation and activation of K-ras are involved in the development of hormonal independence in endometrial cancer

Safety and efficacy of intravenously administered tedisamil for rapid conversion of recent-onset atrial fibrillation or atrial flutter

AbstractObjectivesThe goal of the present study was to assess the efficacy and safety of intravenous tedisamil, a new antiarrhythmic compound, for conversion of recent-onset atrial fibrillation (AF) or atrial flutter (AFL) to normal sinus rhythm (NSR).BackgroundTedisamil is a novel antiarrhythmic drug with predominantly class III activity. Its efficacy and safety for conversion of recent onset AF or AFL to NSR is not known.MethodsThis was a multicenter, double-blind, randomized, placebo-controlled, sequential ascending dose-group trial. A total of 201 patients with symptomatic AF or AFL of 3 to 48 h duration were enrolled in a two-stage study. During stage 1, patients were randomized to receive tedisamil at 0.4 mg/kg body weight or matching placebo; during stage 2, patients received tedisamil at 0.6 mg/kg body weight or matching placebo. Treatments were given as single intravenous infusions. The primary study end point consisted of the percentage of patients converting to NSR for at least 60 s within 2.5 h.ResultsOf 175 patients representing the intention-to-treat sample, conversion to NSR was observed in 41% (25/61) of the tedisamil 0.4 mg/kg group, 51% (27 of 53) of the tedisamil 0.6 mg/kg group, and 7% (4/59) of the placebo group (p < 0.001 for both tedisamil groups vs. placebo). Average time to conversion was 35 min in patients receiving tedisamil. There were two instances of self-terminating ventricular tachycardia: one episode of torsade de pointes and one of monomorphic ventricular tachycardia, both in patients receiving 0.6 mg/kg tedisamil.ConclusionsTedisamil at dosages of 0.4 and 0.6 mg/kg was superior to placebo in converting AF or AFL. Tedisamil has a rapid onset of action leading to conversion within 30 to 40 min in the majority of responders

Interactive Visual Explanation of Incremental Data Labeling

We present a visual analytics approach for the in-depth analysis and explanation of incremental machine learning processes that are based on data labeling. Our approach offers multiple perspectives to explain the process, i.e., data characteristics, label distribution, class characteristics, and classifier characteristics. Additionally, we introduce metrics from which we derive novel aggregated analytic views that enable the analysis of the process over time. We demonstrate the capabilities of our approach in a case study and thereby demonstrate how our approach improves the transparency of the iterative learning process

The Fossil Phase in the Life of a Galaxy Group

We investigate the origin and evolution of fossil groups in a concordance LCDM cosmological simulation. We consider haloes with masses between (1-5)\times10^{13} \hMsun and study the physical mechanisms that lead to the formation of the large gap in magnitude between the brightest and the second most bright group member, which is typical for these fossil systems. Fossil groups are found to have high dark matter concentrations, which we can relate to their early formation time. The large magnitude-gaps arise after the groups have build up half of their final mass, due to merging of massive group members. We show that the existence of fossil systems is primarily driven by the relatively early infall of massive satellites, and that we do not find a strong environmental dependence for these systems. In addition, we find tentative evidence for fossil group satellites falling in on orbits with typically lower angular momentum, which might lead to a more efficient merger onto the host. We find a population of groups at higher redshifts that go through a ``fossil phase'': a stage where they show a large magnitude-gap, which is terminated by renewed infall from their environment.Comment: 9 pages and 8 figures, submitted to MNRA

Acceptability, Appropriateness and Feasibility of a Nurse-Led Integrated Care Intervention for Patients with Severe Exacerbation of COPD from the Healthcare Professional’s Perspective – A Mixed Method Study

Purpose: To improve inpatient care and self-management in patients with severe acute exacerbations of COPD, we implemented a nurse-led behavioral intervention. This study aimed to assess implementation outcomes from the perspective of the healthcare professionals (HCP) who delivered it. Methods: Using an explanatory sequential mixed method approach, we conducted an online questionnaire and two small group interviews. We applied descriptive statistics for quantitative data, a framework analysis for qualitative data, and a mixed methods matrix to integrate the results. Results: A total of 19 of 27 invited participants answered the online questionnaire; 9 of 19 participated in the group interviews. The intervention's overall acceptability, appropriateness, and feasibility was rated high to very high (median 5/5; 4/5 and 4/5). Enablers to implementation included general recognition of the need for specialized care, sufficient knowledge of the intervention by HCP, and strong interprofessional collaboration. Main barriers included the lack of resident physician's resources and difficulties in adaptability. Conclusion: While the acceptance of the intervention was very high, the perceived appropriateness and feasibility were affected by its complexity. The availability of a knowledgeable interprofessional core team is a strategy that supports the implementation of complex interventions