Endpoint resolvent estimates for compact Riemannian manifolds

We prove $L^p\to L^{p'}$ bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension $n$ in the endpoint case $p=2(n+1)/(n+3)$. It has the same behavior with respect to the spectral parameter $z$ as its Euclidean analogue, due to Kenig-Ruiz-Sogge, provided a parabolic neighborhood of the positive half-line is removed. This is region is optimal, for instance, in the case of a sphere.Comment: 14 page

DeepOBS: A Deep Learning Optimizer Benchmark Suite

Because the choice and tuning of the optimizer affects the speed, and ultimately the performance of deep learning, there is significant past and recent research in this area. Yet, perhaps surprisingly, there is no generally agreed-upon protocol for the quantitative and reproducible evaluation of optimization strategies for deep learning. We suggest routines and benchmarks for stochastic optimization, with special focus on the unique aspects of deep learning, such as stochasticity, tunability and generalization. As the primary contribution, we present DeepOBS, a Python package of deep learning optimization benchmarks. The package addresses key challenges in the quantitative assessment of stochastic optimizers, and automates most steps of benchmarking. The library includes a wide and extensible set of ready-to-use realistic optimization problems, such as training Residual Networks for image classification on ImageNet or character-level language prediction models, as well as popular classics like MNIST and CIFAR-10. The package also provides realistic baseline results for the most popular optimizers on these test problems, ensuring a fair comparison to the competition when benchmarking new optimizers, and without having to run costly experiments. It comes with output back-ends that directly produce LaTeX code for inclusion in academic publications. It supports TensorFlow and is available open source.Comment: Accepted at ICLR 2019. 9 pages, 3 figures, 2 table

Surveying the SO(10) Model Landscape: The Left-Right Symmetric Case

Grand Unified Theories (GUTs) are a very well motivated extensions of the Standard Model (SM), but the landscape of models and possibilities is overwhelming, and different patterns can lead to rather distinct phenomenologies. In this work we present a way to automatise the model building process, by considering a top to bottom approach that constructs viable and sensible theories from a small and controllable set of inputs at the high scale. By providing a GUT scale symmetry group and the field content, possible symmetry breaking paths are generated and checked for consistency, ensuring anomaly cancellation, SM embedding and gauge coupling unification. We emphasise the usefulness of this approach for the particular case of a non-supersymmetric SO(10) model with an intermediate left-right symmetry and we analyse how low-energy observables such as proton decay and lepton flavour violation might affect the generated model landscape.Comment: 36 pages, 6 figure

Perturbing and imaging nuclear compartments to reveal mechanisms of transcription regulation and telomere maintenance

The cell nucleus is organized into functional domains that form around chromatin, which serves as a scaffold composed of DNA, proteins, and associated RNAs. On the 0.1-1 µm mesoscale these domains can form spatially defined compartments with distinct composition and properties that enrich specific genomic activities like transcription, chromatin modification or DNA repair. In addition, extrachromosomal DNA elements and RNAs can separate from the chromatin template and assemble with proteins into nuclear bodies. The resulting accumulations of proteins and nucleic acids in the nucleus modulate chromatin-templated processes and their organization. The assembly of these compartments occurs in a self-organizing manner via direct and indirect binding of proteins to DNA and/or RNA. Recently, it has been proposed that multivalent interactions drive compartmentalization by inducing phase separation with a non-stoichiometric accumulation of factors into biomolecular condensates. Despite the importance of compartments for genome regulation, insights into their structure and material properties and how these affect their function is limited. To address this issue, it is important to devise approaches that can perturb nuclear compartments in a targeted manner, while also measuring changes in genome activities within the same cell. In this thesis, the methodology to reveal the underlying structure-function relationships of nuclear compartments has been advanced and applied to compartments involved in activation and silencing of chromatin, and telomere maintenance in cancer cells. I first established a toolbox of chromatin effector constructs to probe and perturb properties of nuclear compartments in living cells that comprised different combinations of DNA binding, transcription activation and light-dependent interaction domains. In addition, I developed workflows to quantitatively assess relevant compartment features by fluorescence microscopy. These methods were employed to study the compaction mechanism of mouse pericentric heterochromatin (PCH) foci and to investigate the interplay between transcriptional co-activators, phase separation and transcription at an inducible reporter gene cluster. It revealed determinants of PCH compaction and identified differential co-activator usage and multivalent interactions as contributors to transcription factor (TF) strength. The results furthermore challenged the model of TF phase separation as a general positive driver of gene transcription. In the second part, I focused on exploiting the detection of compartments for measuring activity of the alternative lengthening of telomeres (ALT) pathway used by cancer cells to extend their telomeres in absence of telomerase. I developed ALT-FISH, a scalable and quantitative imaging assay that detects ALT pathway-specific compartments containing large amounts of single-stranded telomeric nucleic acids. I applied the method to cell line models from different cancer entities and to tumor tissue from leiomyosarcoma and neuroblastoma patients. By devising automated ALT-FISH data acquisition and analysis IV workflows, I implemented an approach, which enabled ALT activity measurements in hundreds of thousands of single cells. These technological advancements provided a quantitative description of ALT activity at single cell resolution and were used to characterize the spatial distribution of ALT activity in relation to other biological features and in response to perturbations. Finally, a novel approach for studying the regulation of ALT in tumors could be established by integrating the method with the spatially resolved detection of single cell transcriptomes. In summary, this thesis introduced and utilized several methods to establish connections between nuclear compartment organization, chromatin features, transcription regulation, and telomere maintenance. These perturbation and imaging techniques are versatile and may be applied to dissect nuclear activities related to other compartments and biological model systems. Furthermore, the detection of ALT activity has demonstrated that compartments can offer valuable biological insights into how phenotypic cellular heterogeneity is encoded and linked to diseases such as cancer

Probing weak dipole-dipole interaction using phase-modulated non-linear spectroscopy

Phase-modulated non-linear spectroscopy with higher harmonic demodulation has recently been suggested to provide information on many-body excitations. In the present work we theoretically investigate the application of this method to infer the interaction strength between two particles that interact via weak dipole-dipole interaction. To this end we use full numerical solution of the Schr\"odinger equation with time-dependent pulses. For interpretation purpose we also derive analytical expressions in perturbation theory. We find one can detect dipole-dipole interaction via peak intensities (in contrast to line-shifts which typically are used in conventional spectroscopy). We provide a detailed study on the dependence of these intensities on the parameters of the laser pulse and the dipole-dipole interaction strength. Interestingly, we find that there is a phase between the first and second harmonic demodulated signal, whose value depends on the sign of the dipole-dipole interaction.Comment: 12 pages, 8 figures, Supporting information provided with the source file

Coherent multidimensional spectroscopy in the gas phase

Recent work applying multidimentional coherent electronic spectroscopy at dilute samples in the gas phase is reviewed. The development of refined phase-cycling approaches with improved sensitivity has opened-up new opportunities to probe even dilute gas-phase samples. In this context, first results of 2-dimensional spectroscopy performed at doped helium droplets reveal the femtosecond dynamics upon electronic excitation of cold, weakly-bound molecules, and even the induced dynamics from the interaction with the helium environment. Such experiments, offering well-defined conditions at low temperatures, are potentially enabling the isolation of fundamental processes in the excitation and charge transfer dynamics of molecular structures which so far have been masked in complex bulk environments.Comment: Invited Review Articl

Efficient deep CNNs for cross-modal automated computer vision under time and space constraints

We present an automated computer vision architecture to handle video and image data using the same backbone networks. We show empirical results that lead us to adopt MOBILENETV2 as this backbone architecture. The paper demonstrates that neural architectures are transferable from images to videos through suitable preprocessing and temporal information fusion