TY - JOUR AB - We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H. AU - Dietlein, Adrian M AU - Gebert, Martin AU - Müller, Peter ID - 10879 IS - 3 JF - Journal of Spectral Theory KW - Random Schrödinger operators KW - spectral shift function KW - Anderson orthogonality SN - 1664-039X TI - Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function VL - 9 ER - TY - JOUR AB - Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles. AU - Flandoli, Franco AU - Priola, Enrico AU - Zanco, Giovanni A ID - 10878 IS - 6 JF - Discrete and Continuous Dynamical Systems KW - Applied Mathematics KW - Discrete Mathematics and Combinatorics KW - Analysis SN - 1553-5231 TI - A mean-field model with discontinuous coefficients for neurons with spatial interaction VL - 39 ER - TY - CONF AB - This paper investigates the power of preprocessing in the CONGEST model. Schmid and Suomela (ACM HotSDN 2013) introduced the SUPPORTED CONGEST model to study the application of distributed algorithms in Software-Defined Networks (SDNs). In this paper, we show that a large class of lower bounds in the CONGEST model still hold in the SUPPORTED model, highlighting the robustness of these bounds. This also raises the question how much does preprocessing help in the CONGEST model. AU - Foerster, Klaus-Tycho AU - Korhonen, Janne AU - Rybicki, Joel AU - Schmid, Stefan ID - 6935 SN - 9781450362177 T2 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing TI - Does preprocessing help under congestion? ER - TY - JOUR AB - Autoregulation is the direct modulation of gene expression by the product of the corresponding gene. Autoregulation of bacterial gene expression has been mostly studied at the transcriptional level, when a protein acts as the cognate transcriptional repressor. A recent study investigating dynamics of the bacterial toxin–antitoxin MazEF system has shown how autoregulation at both the transcriptional and post-transcriptional levels affects the heterogeneity of Escherichia coli populations. Toxin–antitoxin systems hold a crucial but still elusive part in bacterial response to stress. This perspective highlights how these modules can also serve as a great model system for investigating basic concepts in gene regulation. However, as the genomic background and environmental conditions substantially influence toxin activation, it is important to study (auto)regulation of toxin–antitoxin systems in well-defined setups as well as in conditions that resemble the environmental niche. AU - Nikolic, Nela ID - 138 IS - 1 JF - Current Genetics TI - Autoregulation of bacterial gene expression: lessons from the MazEF toxin–antitoxin system VL - 65 ER - TY - JOUR AB - We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2 we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide. AU - Fischer, Julian L AU - Kneuss, Olivier ID - 151 IS - 1 JF - Journal of Differential Equations TI - Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity VL - 266 ER - TY - JOUR AB - The cerebral cortex is composed of a large variety of distinct cell-types including projection neurons, interneurons and glial cells which emerge from distinct neural stem cell (NSC) lineages. The vast majority of cortical projection neurons and certain classes of glial cells are generated by radial glial progenitor cells (RGPs) in a highly orchestrated manner. Recent studies employing single cell analysis and clonal lineage tracing suggest that NSC and RGP lineage progression are regulated in a profound deterministic manner. In this review we focus on recent advances based mainly on correlative phenotypic data emerging from functional genetic studies in mice. We establish hypotheses to test in future research and outline a conceptual framework how epigenetic cues modulate the generation of cell-type diversity during cortical development. This article is protected by copyright. All rights reserved. AU - Amberg, Nicole AU - Laukoter, Susanne AU - Hippenmeyer, Simon ID - 27 IS - 1 JF - Journal of Neurochemistry TI - Epigenetic cues modulating the generation of cell type diversity in the cerebral cortex VL - 149 ER - TY - JOUR AB - Tissue morphogenesis is driven by mechanical forces that elicit changes in cell size, shape and motion. The extent by which forces deform tissues critically depends on the rheological properties of the recipient tissue. Yet, whether and how dynamic changes in tissue rheology affect tissue morphogenesis and how they are regulated within the developing organism remain unclear. Here, we show that blastoderm spreading at the onset of zebrafish morphogenesis relies on a rapid, pronounced and spatially patterned tissue fluidization. Blastoderm fluidization is temporally controlled by mitotic cell rounding-dependent cell–cell contact disassembly during the last rounds of cell cleavages. Moreover, fluidization is spatially restricted to the central blastoderm by local activation of non-canonical Wnt signalling within the blastoderm margin, increasing cell cohesion and thereby counteracting the effect of mitotic rounding on contact disassembly. Overall, our results identify a fluidity transition mediated by loss of cell cohesion as a critical regulator of embryo morphogenesis. AU - Petridou, Nicoletta AU - Grigolon, Silvia AU - Salbreux, Guillaume AU - Hannezo, Edouard B AU - Heisenberg, Carl-Philipp J ID - 5789 JF - Nature Cell Biology SN - 14657392 TI - Fluidization-mediated tissue spreading by mitotic cell rounding and non-canonical Wnt signalling VL - 21 ER - TY - JOUR AB - The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain. AU - Lang, Moritz AU - Shkolnikov, Mikhail ID - 196 IS - 8 JF - Proceedings of the National Academy of Sciences TI - Harmonic dynamics of the Abelian sandpile VL - 116 ER - TY - CONF AB - Learning disentangled representations is considered a cornerstone problem in representation learning. Recently, Locatello et al. (2019) demonstrated that unsupervised disentanglement learning without inductive biases is theoretically impossible and that existing inductive biases and unsupervised methods do not allow to consistently learn disentangled representations. However, in many practical settings, one might have access to a limited amount of supervision, for example through manual labeling of (some) factors of variation in a few training examples. In this paper, we investigate the impact of such supervision on state-of-the-art disentanglement methods and perform a large scale study, training over 52000 models under well-defined and reproducible experimental conditions. We observe that a small number of labeled examples (0.01--0.5\% of the data set), with potentially imprecise and incomplete labels, is sufficient to perform model selection on state-of-the-art unsupervised models. Further, we investigate the benefit of incorporating supervision into the training process. Overall, we empirically validate that with little and imprecise supervision it is possible to reliably learn disentangled representations. AU - Locatello, Francesco AU - Tschannen, Michael AU - Bauer, Stefan AU - Rätsch, Gunnar AU - Schölkopf, Bernhard AU - Bachem, Olivier ID - 14184 T2 - 8th International Conference on Learning Representations TI - Disentangling factors of variation using few labels ER - TY - CONF AB - We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available. AU - Gresele, Luigi AU - Rubenstein, Paul K. AU - Mehrjou, Arash AU - Locatello, Francesco AU - Schölkopf, Bernhard ID - 14189 T2 - Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence TI - The incomplete Rosetta Stone problem: Identifiability results for multi-view nonlinear ICA VL - 115 ER -