@article{73, abstract = {We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y⊆X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest.}, author = {Erbar, Matthias and Maas, Jan and Wirth, Melchior}, issn = {09442669}, journal = {Calculus of Variations and Partial Differential Equations}, number = {1}, publisher = {Springer}, title = {{On the geometry of geodesics in discrete optimal transport}}, doi = {10.1007/s00526-018-1456-1}, volume = {58}, 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}, } @article{6982, abstract = {We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ϕ : G → M of a graph G into a 2-manifold M maps the vertices in V(G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to the same point or overlapping arcs due to data compression or low resolution. This raises the computational problem of deciding whether a given map ϕ : G → M comes from an embedding. A map ϕ : G → M is a weak embedding if it can be perturbed into an embedding ψ ϵ : G → M with ‖ ϕ − ψ ϵ ‖ < ϵ for every ϵ > 0, where ‖.‖ is the unform norm. A polynomial-time algorithm for recognizing weak embeddings has recently been found by Fulek and Kynčl. It reduces the problem to solving a system of linear equations over Z2. It runs in O(n2ω)≤ O(n4.75) time, where ω ∈ [2,2.373) is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler: We perform a sequence of local operations that gradually “untangles” the image ϕ(G) into an embedding ψ(G) or reports that ϕ is not a weak embedding. It combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations. }, author = {Akitaya, Hugo and Fulek, Radoslav and Tóth, Csaba}, journal = {ACM Transactions on Algorithms}, number = {4}, publisher = {ACM}, title = {{Recognizing weak embeddings of graphs}}, doi = {10.1145/3344549}, volume = {15}, year = {2019}, } @phdthesis{6894, abstract = {Hybrid automata combine finite automata and dynamical systems, and model the interaction of digital with physical systems. Formal analysis that can guarantee the safety of all behaviors or rigorously witness failures, while unsolvable in general, has been tackled algorithmically using, e.g., abstraction, bounded model-checking, assisted theorem proving. Nevertheless, very few methods have addressed the time-unbounded reachability analysis of hybrid automata and, for current sound and automatic tools, scalability remains critical. We develop methods for the polyhedral abstraction of hybrid automata, which construct coarse overapproximations and tightens them incrementally, in a CEGAR fashion. We use template polyhedra, i.e., polyhedra whose facets are normal to a given set of directions. While, previously, directions were given by the user, we introduce (1) the first method for computing template directions from spurious counterexamples, so as to generalize and eliminate them. The method applies naturally to convex hybrid automata, i.e., hybrid automata with (possibly non-linear) convex constraints on derivatives only, while for linear ODE requires further abstraction. Specifically, we introduce (2) the conic abstractions, which, partitioning the state space into appropriate (possibly non-uniform) cones, divide curvy trajectories into relatively straight sections, suitable for polyhedral abstractions. Finally, we introduce (3) space-time interpolation, which, combining interval arithmetic and template refinement, computes appropriate (possibly non-uniform) time partitioning and template directions along spurious trajectories, so as to eliminate them. We obtain sound and automatic methods for the reachability analysis over dense and unbounded time of convex hybrid automata and hybrid automata with linear ODE. We build prototype tools and compare—favorably—our methods against the respective state-of-the-art tools, on several benchmarks.}, author = {Giacobbe, Mirco}, issn = {2663-337X}, pages = {132}, publisher = {Institute of Science and Technology Austria}, title = {{Automatic time-unbounded reachability analysis of hybrid systems}}, doi = {10.15479/AT:ISTA:6894}, year = {2019}, } @misc{9805, abstract = {The spread of adaptive alleles is fundamental to evolution, and in theory, this process is well‐understood. However, only rarely can we follow this process—whether it originates from the spread of a new mutation, or by introgression from another population. In this issue of Molecular Ecology, Hanemaaijer et al. (2018) report on a 25‐year long study of the mosquitoes Anopheles gambiae (Figure 1) and Anopheles coluzzi in Mali, based on genotypes at 15 single‐nucleotide polymorphism (SNP). The species are usually reproductively isolated from each other, but in 2002 and 2006, bursts of hybridization were observed, when F1 hybrids became abundant. Alleles backcrossed from A. gambiae into A. coluzzi, but after the first event, these declined over the following years. In contrast, after 2006, an insecticide resistance allele that had established in A. gambiae spread into A. coluzzi, and rose to high frequency there, over 6 years (~75 generations). Whole genome sequences of 74 individuals showed that A. gambiae SNP from across the genome had become common in the A. coluzzi population, but that most of these were clustered in 34 genes around the resistance locus. A new set of SNP from 25 of these genes were assayed over time; over the 4 years since near‐fixation of the resistance allele; some remained common, whereas others declined. What do these patterns tell us about this introgression event?}, author = {Barton, Nicholas H}, publisher = {Dryad}, title = {{Data from: The consequences of an introgression event}}, doi = {10.5061/dryad.2kb6fh4}, year = {2019}, }