@inproceedings{12901, author = {Schlögl, Alois and Kiss, Janos and Elefante, Stefano}, booktitle = {AHPC19 - Austrian HPC Meeting 2019 }, location = {Grundlsee, Austria}, pages = {25}, publisher = {Institut für Mathematik und wissenschaftliches Rechnen der Universität Graz}, title = {{Is Debian suitable for running an HPC Cluster?}}, year = {2019}, } @misc{13067, abstract = {Genetic incompatibilities contribute to reproductive isolation between many diverging populations, but it is still unclear to what extent they play a role if divergence happens with gene flow. In contact zones between the "Crab" and "Wave" ecotypes of the snail Littorina saxatilis divergent selection forms strong barriers to gene flow, while the role of postzygotic barriers due to selection against hybrids remains unclear. High embryo abortion rates in this species could indicate the presence of such barriers. Postzygotic barriers might include genetic incompatibilities (e.g. Dobzhansky-Muller incompatibilities) but also maladaptation, both expected to be most pronounced in contact zones. In addition, embryo abortion might reflect physiological stress on females and embryos independent of any genetic stress. We examined all embryos of >500 females sampled outside and inside contact zones of three populations in Sweden. Females' clutch size ranged from 0 to 1011 embryos (mean 130±123) and abortion rates varied between 0 and100% (mean 12%). We described female genotypes by using a hybrid index based on hundreds of SNPs differentiated between ecotypes with which we characterised female genotypes. We also calculated female SNP heterozygosity and inversion karyotype. Clutch size did not vary with female hybrid index and abortion rates were only weakly related to hybrid index in two sites but not at all in a third site. No additional variation in abortion rate was explained by female SNP heterozygosity, but increased female inversion heterozygosity added slightly to increased abortion. Our results show only weak and probably biologically insignificant postzygotic barriers contributing to ecotype divergence and the high and variable abortion rates were marginally, if at all, explained by hybrid index of females.}, author = {Johannesson, Kerstin and Zagrodzka, Zuzanna and Faria, Rui and Westram, Anja M and Butlin, Roger}, publisher = {Dryad}, title = {{Data from: Is embryo abortion a postzygotic barrier to gene flow between Littorina ecotypes?}}, doi = {10.5061/DRYAD.TB2RBNZWK}, year = {2019}, } @article{138, abstract = {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.}, author = {Nikolic, Nela}, journal = {Current Genetics}, number = {1}, pages = {133--138}, publisher = {Springer}, title = {{Autoregulation of bacterial gene expression: lessons from the MazEF toxin–antitoxin system}}, doi = {10.1007/s00294-018-0879-8}, volume = {65}, year = {2019}, } @inproceedings{14184, abstract = {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.}, author = {Locatello, Francesco and Tschannen, Michael and Bauer, Stefan and Rätsch, Gunnar and Schölkopf, Bernhard and Bachem, Olivier}, booktitle = {8th International Conference on Learning Representations}, location = {Virtual}, title = {{Disentangling factors of variation using few labels}}, year = {2019}, } @inproceedings{14189, abstract = {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.}, author = {Gresele, Luigi and Rubenstein, Paul K. and Mehrjou, Arash and Locatello, Francesco and Schölkopf, Bernhard}, booktitle = {Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence}, location = {Tel Aviv, Israel}, pages = {217--227}, publisher = {ML Research Press}, title = {{The incomplete Rosetta Stone problem: Identifiability results for multi-view nonlinear ICA}}, volume = {115}, year = {2019}, } @inproceedings{14190, abstract = {Learning meaningful and compact representations with disentangled semantic aspects is considered to be of key importance in representation learning. Since real-world data is notoriously costly to collect, many recent state-of-the-art disentanglement models have heavily relied on synthetic toy data-sets. In this paper, we propose a novel data-set which consists of over one million images of physical 3D objects with seven factors of variation, such as object color, shape, size and position. In order to be able to control all the factors of variation precisely, we built an experimental platform where the objects are being moved by a robotic arm. In addition, we provide two more datasets which consist of simulations of the experimental setup. These datasets provide for the first time the possibility to systematically investigate how well different disentanglement methods perform on real data in comparison to simulation, and how simulated data can be leveraged to build better representations of the real world. We provide a first experimental study of these questions and our results indicate that learned models transfer poorly, but that model and hyperparameter selection is an effective means of transferring information to the real world.}, author = {Gondal, Muhammad Waleed and Wüthrich, Manuel and Miladinović, Đorđe and Locatello, Francesco and Breidt, Martin and Volchkov, Valentin and Akpo, Joel and Bachem, Olivier and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, title = {{On the transfer of inductive bias from simulation to the real world: a new disentanglement dataset}}, volume = {32}, year = {2019}, } @inproceedings{14191, abstract = {A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed for the deterministic setting where problem data is readily available. In this setting, generalized conditional gradient methods (aka Frank-Wolfe-type methods) provide scalable solutions by leveraging the so-called linear minimization oracle instead of the projection onto the semidefinite cone. Most problems in machine learning and modern engineering applications, however, contain some degree of stochasticity. In this work, we propose the first conditional-gradient-type method for solving stochastic optimization problems under affine constraints. Our method guarantees O(k−1/3) convergence rate in expectation on the objective residual and O(k−5/12) on the feasibility gap.}, author = {Locatello, Francesco and Yurtsever, Alp and Fercoq, Olivier and Cevher, Volkan}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, pages = {14291–14301}, title = {{Stochastic Frank-Wolfe for composite convex minimization}}, volume = {32}, year = {2019}, } @inproceedings{14193, abstract = {A disentangled representation encodes information about the salient factors of variation in the data independently. Although it is often argued that this representational format is useful in learning to solve many real-world down-stream tasks, there is little empirical evidence that supports this claim. In this paper, we conduct a large-scale study that investigates whether disentangled representations are more suitable for abstract reasoning tasks. Using two new tasks similar to Raven's Progressive Matrices, we evaluate the usefulness of the representations learned by 360 state-of-the-art unsupervised disentanglement models. Based on these representations, we train 3600 abstract reasoning models and observe that disentangled representations do in fact lead to better down-stream performance. In particular, they enable quicker learning using fewer samples.}, author = {Steenkiste, Sjoerd van and Locatello, Francesco and Schmidhuber, Jürgen and Bachem, Olivier}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, title = {{Are disentangled representations helpful for abstract visual reasoning?}}, volume = {32}, year = {2019}, } @inproceedings{14197, abstract = {Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an \emph{unobserved} sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing the representations of more than \num{12600} trained state-of-the-art disentangled models, we observe that several disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.}, author = {Locatello, Francesco and Abbati, Gabriele and Rainforth, Tom and Bauer, Stefan and Schölkopf, Bernhard and Bachem, Olivier}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, pages = {14611–14624}, title = {{On the fairness of disentangled representations}}, volume = {32}, year = {2019}, } @inproceedings{14200, abstract = {The key idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than 12000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on seven different data sets. We observe that while the different methods successfully enforce properties ``encouraged'' by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.}, author = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Rätsch, Gunnar and Gelly, Sylvain and Schölkopf, Bernhard and Bachem, Olivier}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, location = {Long Beach, CA, United States}, pages = {4114--4124}, publisher = {ML Research Press}, title = {{Challenging common assumptions in the unsupervised learning of disentangled representations}}, volume = {97}, year = {2019}, } @article{151, abstract = {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.}, author = {Fischer, Julian L and Kneuss, Olivier}, journal = {Journal of Differential Equations}, number = {1}, pages = {257 -- 311}, publisher = {Elsevier}, title = {{Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity}}, doi = {10.1016/j.jde.2018.07.045}, volume = {266}, year = {2019}, } @article{175, abstract = {An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.}, author = {Browning, Timothy D and Loughran, Daniel}, issn = {10886850}, journal = {Transactions of the American Mathematical Society}, number = {8}, pages = {5757--5785}, publisher = {American Mathematical Society}, title = {{Sieving rational points on varieties}}, doi = {10.1090/tran/7514}, volume = {371}, year = {2019}, } @article{196, abstract = {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. }, author = {Lang, Moritz and Shkolnikov, Mikhail}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {8}, pages = {2821--2830}, publisher = {National Academy of Sciences}, title = {{Harmonic dynamics of the Abelian sandpile}}, doi = {10.1073/pnas.1812015116}, volume = {116}, year = {2019}, } @article{27, abstract = {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.}, author = {Amberg, Nicole and Laukoter, Susanne and Hippenmeyer, Simon}, journal = {Journal of Neurochemistry}, number = {1}, pages = {12--26}, publisher = {Wiley}, title = {{Epigenetic cues modulating the generation of cell type diversity in the cerebral cortex}}, doi = {10.1111/jnc.14601}, volume = {149}, year = {2019}, } @article{301, abstract = {A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.}, author = {Gerencser, Mate and Gyöngy, István}, journal = {Stochastic Processes and their Applications}, number = {3}, pages = {995--1012}, publisher = {Elsevier}, title = {{A Feynman–Kac formula for stochastic Dirichlet problems}}, doi = {10.1016/j.spa.2018.04.003}, volume = {129}, year = {2019}, } @article{319, abstract = {We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.}, author = {Gerencser, Mate and Hairer, Martin}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {3-4}, pages = {697–758}, publisher = {Springer}, title = {{Singular SPDEs in domains with boundaries}}, doi = {10.1007/s00440-018-0841-1}, volume = {173}, year = {2019}, } @article{405, abstract = {We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.}, author = {Virosztek, Daniel}, journal = {Linear Algebra and Its Applications}, pages = {67--78}, publisher = {Elsevier}, title = {{Jointly convex quantum Jensen divergences}}, doi = {10.1016/j.laa.2018.03.002}, volume = {576}, year = {2019}, } @article{429, abstract = {We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.}, author = {Ajanki, Oskari H and Erdös, László and Krüger, Torben H}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {1-2}, pages = {293–373}, publisher = {Springer}, title = {{Stability of the matrix Dyson equation and random matrices with correlations}}, doi = {10.1007/s00440-018-0835-z}, volume = {173}, year = {2019}, } @article{439, abstract = {We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the possibility of a P = W conjecture for a suitable wild Hitchin system.}, author = {Hausel, Tamas and Mereb, Martin and Wong, Michael}, issn = {1435-9855}, journal = {Journal of the European Mathematical Society}, number = {10}, pages = {2995--3052}, publisher = {European Mathematical Society}, title = {{Arithmetic and representation theory of wild character varieties}}, doi = {10.4171/JEMS/896}, volume = {21}, year = {2019}, } @article{441, author = {Kalinin, Nikita and Shkolnikov, Mikhail}, issn = {2199-6768}, journal = {European Journal of Mathematics}, number = {3}, pages = {909–928}, publisher = {Springer Nature}, title = {{Tropical formulae for summation over a part of SL(2,Z)}}, doi = {10.1007/s40879-018-0218-0}, volume = {5}, year = {2019}, }