An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections

We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm). In particular, the iterates in our method can be infeasible throughout the whole procedure. Nevertheless, we provide conditions which ensure convergence to an optimal feasible point under suitable assumptions. One convergence result deals with step size sequences that are fixed a priori. Two other results handle dynamic Polyak-type step sizes depending on a lower or upper estimate of the optimal objective function value, respectively. Additionally, we briefly sketch two applications: Optimization with convex chance constraints, and finding the minimum l1-norm solution to an underdetermined linear system, an important problem in Compressed Sensing.Comment: 36 pages, 3 figure

Elastic-Net Regularization: Error estimates and Active Set Methods

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are established. Two iterative numerical algorithms of active set type are proposed, and their convergence properties are discussed. Numerical results are presented to illustrate the features of the functional and algorithms

Evolutionary processes in finite populations

We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov-Moran process.We show that toO(1/N), the time-averaged fitness is lower for the finite population than it is for the infinite population.We also showthat fluctuations in the number of individuals for a given genotype can be proportional to a power of the inverse of the mutation rate. Finally, we show that the probability for the system to take a given path through the fitness landscape can be nonmonotonic in system size

Necessary conditions for variational regularization schemes

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

Extracellular matrix and growth factor engineering for controlled angiogenesis in regenerative medicine

Blood vessel growth plays a key role in regenerative medicine, both to restore blood supply to ischemic tissues and to ensure rapid vascularization of clinical-size tissue-engineered grafts. For example, vascular endothelial growth factor (VEGF) is the master regulator of physiological blood vessel growth and is one of the main molecular targets of therapeutic angiogenesis approaches. However, angiogenesis is a complex process and there is a need to develop rational therapeutic strategies based on a firm understanding of basic vascular biology principles, as evidenced by the disappointing results of initial clinical trials of angiogenic factor delivery. In particular, the spatial localization of angiogenic signals in the extracellular matrix (ECM) is crucial to ensure the proper assembly and maturation of new vascular structures. Here, we discuss the therapeutic implications of matrix interactions of angiogenic factors, with a special emphasis on VEGF, as well as provide an overview of current approaches, based on protein and biomaterial engineering that mimic the regulatory functions of ECM to optimize the signaling microenvironment of vascular growth factors

Optical coherence tomography controlled selective retina therapy with a novel microsecond laser

Selective retina therapy (SRT) is a short pulse (μs-regime) alternative to conventional laser photocoagulation (LPC) for treatment of retinal diseases. LPC leads to collateral damage of retinal layers adjacent to the retinal pigment epithelium (RPE), including healthy, non-regenerative photoreceptors due to the high thermal load, whereas in SRT, RPE cells are destroyed by microbubbles without damaging the neuronal retina. A novel experimental SRT laser operating at 532 nm wavelength can deliver 2 – 20 μs pulse sequences. Its tight integration into an upgraded diagnostic SPECTRALIS system combines beam control for treatment planning with real-time optical coherence tomography (OCT) overexposure protection of the photoreceptors. This “Spectralis Centaurus” system, was built and preliminary tested on porcine ex-vivo samples, reaching an unprecedented accuracy with unique planning and follow-up capabilities for upcoming clinical cellular level micro-surgery. The combination of OCT with SRT selectively limits cell death to the RPE by precisely controlling energy deposition while optically monitoring tissue response

Evidence for a dissociation between the control of oculomotor capture and disengagement

The current study investigated whether capture of the eyes by a salient onset distractor and the disengagement of the eyes from that distractor are driven by the same or by different underlying control modes. A variant of the classic oculomotor capture task was used. Observers had to make a saccade to the only gray circle among red background circles. On some trials, a green (novel color), red (placeholder color) or gray (target color) distractor square was presented with sudden onset. Results showed that when participants reacted fast, oculomotor capture was primarily driven by bottom-up pop-out: both types of distractors (green and gray) that popped out among the red background elements showed more capture than a red distractor that did not pop-out. In contrast to initial capture, disengagement of the eyes from the distractor was driven by top-down target–distractor similarity effects. We also examined the time-course of this effect. The distractor could change from green to either the target or placeholder color. When the color change was early in time (30–40 ms after its onset), dwell times were strongly affected by the change, whereas the effect on oculomotor capture was weak. Importantly, a change occurring as early as 60–80 ms after distractor onset did neither affect capture nor dwell times, corroborating the assumption of parallel programming of saccades

Dihydropyrimidine Dehydrogenase Testing prior to Treatment with 5-Fluorouracil, Capecitabine, and Tegafur: A Consensus Paper

Background: 5-Fluorouracil (FU) is one of the most commonly used cytostatic drugs in the systemic treatment of cancer. Treatment with FU may cause severe or life-threatening side effects and the treatment-related mortality rate is 0.2–1.0%. Summary: Among other risk factors associated with increased toxicity, a genetic deficiency in dihydropyrimidine dehydrogenase (DPD), an enzyme responsible for the metabolism of FU, is well known. This is due to variants in the DPD gene (DPYD). Up to 9% of European patients carry a DPD gene variant that decreases enzyme activity, and DPD is completely lacking in approximately 0.5% of patients. Here we describe the clinical and genetic background and summarize recommendations for the genetic testing and tailoring of treatment with 5-FU derivatives. The statement was developed as a consensus statement organized by the German Society for Hematology and Medical Oncology in cooperation with 13 medical associations from Austria, Germany, and Switzerland. Key Messages: (i) Patients should be tested for the 4 most common genetic DPYD variants before treatment with drugs containing FU. (ii) Testing forms the basis for a differentiated, risk-adapted algorithm with recommendations for treatment with FU-containing drugs. (iii) Testing may optionally be supplemented by therapeutic drug monitorin

The spike gene is a major determinant for the SARS-CoV-2 Omicron-BA.1 phenotype.

Variant of concern (VOC) Omicron-BA.1 has achieved global predominance in early 2022. Therefore, surveillance and comprehensive characterization of Omicron-BA.1 in advanced primary cell culture systems and animal models are urgently needed. Here, we characterize Omicron-BA.1 and recombinant Omicron-BA.1 spike gene mutants in comparison with VOC Delta in well-differentiated primary human nasal and bronchial epithelial cells in vitro, followed by in vivo fitness characterization in hamsters, ferrets and hACE2-expressing mice, and immunized hACE2-mice. We demonstrate a spike-mediated enhancement of early replication of Omicron-BA.1 in nasal epithelial cultures, but limited replication in bronchial epithelial cultures. In hamsters, Delta shows dominance over Omicron-BA.1, and in ferrets Omicron-BA.1 infection is abortive. In hACE2-knock-in mice, Delta and a Delta spike clone also show dominance over Omicron-BA.1 and an Omicron-BA.1 spike clone, respectively. Interestingly, in naïve K18-hACE2 mice, we observe Delta spike-mediated increased replication and pathogenicity and Omicron-BA.1 spike-mediated reduced replication and pathogenicity, suggesting that the spike gene is a major determinant of replication and pathogenicity. Finally, the Omicron-BA.1 spike clone is less well-controlled by mRNA-vaccination in K18-hACE2-mice and becomes more competitive compared to the progenitor and Delta spike clones, suggesting that spike gene-mediated immune evasion is another important factor that led to Omicron-BA.1 dominance

The spike gene is a major determinant for the SARS-CoV-2 Omicron-BA. 1 phenotype

Variant of concern (VOC) Omicron-BA.1 has achieved global predominance in early 2022. Therefore, surveillance and comprehensive characterization of Omicron-BA.1 in advanced primary cell culture systems and animal models are urgently needed. Here, we characterize Omicron-BA.1 and recombinant Omicron-BA.1 spike gene mutants in comparison with VOC Delta in well-differentiated primary human nasal and bronchial epithelial cells in vitro, followed by in vivo fitness characterization in hamsters, ferrets and hACE2-expressing mice, and immunized hACE2-mice. We demonstrate a spike-mediated enhancement of early replication of Omicron-BA.1 in nasal epithelial cultures, but limited replication in bronchial epithelial cultures. In hamsters, Delta shows dominance over Omicron-BA.1, and in ferrets Omicron-BA.1 infection is abortive. In hACE2-knock-in mice, Delta and a Delta spike clone also show dominance over Omicron-BA.1 and an Omicron-BA.1 spike clone, respectively. Interestingly, in naïve K18-hACE2 mice, we observe Delta spike-mediated increased replication and pathogenicity and Omicron-BA.1 spike-mediated reduced replication and pathogenicity, suggesting that the spike gene is a major determinant of replication and pathogenicity. Finally, the Omicron-BA.1 spike clone is less well-controlled by mRNA-vaccination in K18-hACE2-mice and becomes more competitive compared to the progenitor and Delta spike clones, suggesting that spike gene-mediated immune evasion is another important factor that led to Omicron-BA.1 dominance