An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy - Carlen, Eric; Maas, Jan (Communications in Mathematical Physics)
Let ℭ denote the Clifford algebra over ℝ𝑛, which is the von Neumann algebra generated by n self-adjoint operators Q j , j = 1,…,n satisfying the canonical anticommutation relations, Q i Q j + Q j Q i = 2δ ij I, and let τ denote the normalized trace on ℭ. This algebra arises in quantum mechanics as the algebra of observables generated by n fermionic degrees of freedom. Let 𝔓 denote the set of all positive operators 𝜌∈ℭ such that τ(ρ) = 1; these are the non-commutative analogs of probability densities in the non-commutative probability space (ℭ,𝜏). The fermionic Fokker–Planck equation is a quantum-mechanical analog of the classical Fokker–Planck equation with which it has much in common, such as the same optimal hypercontractivity properties. In this paper we construct a Riemannian metric on 𝔓 that we show to be a natural analog of the classical 2-Wasserstein metric, and we show that, in analogy with the classical case, the fermionic Fokker–Planck equation is gradient flow in this metric for the relative entropy with respect to the ground state. We derive a number of consequences of this, such as a sharp Talagrand inequality for this metric, and we prove a number of results pertaining to this metric. Several open problems are raised.

Dissipative preparation of spatial order in Rydberg-dressed Bose-Einstein condensates - Otterbach, Johannes; Lemeshko, Mikhail (Physical Review Letters)
We propose a technique for engineering momentum-dependent dissipation in Bose-Einstein condensates with non-local interactions. The scheme relies on the use of momentum-dependent dark-states in close analogy to velocity-selective coherent population trapping. During the short-time dissipative dynamics, the system is driven into a particular finite-momentum phonon mode, which in real space corresponds to an ordered structure with non-local density-density correlations. Dissipation-induced ordering can be observed and studied in present-day experiments using cold atoms with dipole-dipole or off-resonant Rydberg interactions. Due to its dissipative nature, the ordering does not require artificial breaking of translational symmetry by an opticallattice or harmonic trap. This opens up a perspective of direct cooling of quantum gases into strongly-interacting phases.

Efficient and dynamic algorithms for alternating Büchi games and maximal end-component decomposition - Chatterjee, Krishnendu; Henzinger, Monika H (Journal of the ACM)
The computation of the winning set for Büchi objectives in alternating games on graphs is a central problem in computer-aided verification with a large number of applications. The long-standing best known upper bound for solving the problem is Õ(n ⋅ m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n ⋅ m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2)-time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n ⋅ m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m>n4/3 an earlier bound of O(m ⋅ √m)). We then show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. Our algorithms are the first dynamic algorithms for this problem. We then consider another core graph theoretic problem in verification of probabilistic systems, namely computing the maximal end-component decomposition of a graph. We present two improved static algorithms for the maximal end-component decomposition problem. Our first algorithm is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm which is obtained using the same technique as for alternating Büchi games. Thus, we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time per edge insertion. Again, our algorithms are the first dynamic algorithms for this problem.

Induced matchings of barcodes and the algebraic stability of persistence - Bauer, Ulrich; Lesnick, Michael (Proceedings of the Annual Symposium on Computational Geometry)
We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s).

On Gromov's method of selecting heavily covered points - Matoušek, Jiří; Wagner, Uli (Discrete & Computational Geometry)
A result of Boros and Füredi (d = 2) and of Bárány (arbitrary d) asserts that for every d there exists cd > 0 such that for every n-point set P ⊂ ℝd, some point of ℝd is covered by at least (Formula presented.) of the d-simplices spanned by the points of P. The largest possible value of cd has been the subject of ongoing research. Recently Gromov improved the existing lower bounds considerably by introducing a new, topological proof method. We provide an exposition of the combinatorial component of Gromov's approach, in terms accessible to combinatorialists and discrete geometers, and we investigate the limits of his method. In particular, we give tighter bounds on the cofilling profiles for the (n - 1)-simplex. These bounds yield a minor improvement over Gromov's lower bounds on cd for large d, but they also show that the room for further improvement through the cofilling profiles alone is quite small. We also prove a slightly better lower bound for c3 by an approach using an additional structure besides the cofilling profiles. We formulate a combinatorial extremal problem whose solution might perhaps lead to a tight lower bound for cd.

The morse theory of Čech and Delaunay filtrations - Bauer, Ulrich; Edelsbrunner, Herbert (Proceedings of the Annual Symposium on Computational Geometry)
Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s).

Measuring distance between Reeb graphs - Bauer, Ulrich; Ge, Xiaoyin; Wang, Yusu (Proceedings of the Annual Symposium on Computational Geometry)
We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).

Embeddability in the 3 sphere is decidable - Matoušek, Jiří; Sedgwick, Eric; Tancer, Martin; Wagner, Uli (Proceedings of the Annual Symposium on Computational Geometry)
We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in ℝ3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S3, then there is also an embedding in which X has a short meridian, i.e., an essential curve in the boundary of X bounding a disk in S3 nX with length bounded by a computable function of the number of tetrahedra of X.

New paradigms in the establishment and maintenance of gradients during directed cell migration - Majumdar, Ritankar; Sixt, Michael K; Parent, Carole (Current Opinion in Cell Biology)
Directional guidance of migrating cells is relatively well explored in the reductionist setting of cell culture experiments. Here spatial gradients of chemical cues as well as gradients of mechanical substrate characteristics prove sufficient to attract single cells as well as their collectives. How such gradients present and act in the context of an organism is far less clear. Here we review recent advances in understanding how guidance cues emerge and operate in the physiological context.

Eliminating Tverberg points, I. An analogue of the Whitney trick - Mabillard, Isaac; Wagner, Uli (Proceedings of the Annual Symposium on Computational Geometry)
Motivated by topological Tverberg-type problems, we consider multiple (double, triple, and higher multiplicity) selfintersection points of maps from finite simplicial complexes (compact polyhedra) into ℝd and study conditions under which such multiple points can be eliminated. The most classical case is that of embeddings (i.e., maps without double points) of a κ-dimensional complex K into ℝ2κ. For this problem, the work of van Kampen, Shapiro, and Wu provides an efficiently testable necessary condition for embeddability (namely, vanishing of the van Kampen ob-struction). For κ ≥ 3, the condition is also sufficient, and yields a polynomial-time algorithm for deciding embeddability: One starts with an arbitrary map f : K→ℝ2κ, which generically has finitely many double points; if k ≥ 3 and if the obstruction vanishes then one can successively remove these double points by local modifications of the map f. One of the main tools is the famous Whitney trick that permits eliminating pairs of double points of opposite intersection sign. We are interested in generalizing this approach to intersection points of higher multiplicity. We call a point y 2 ℝd an r-fold Tverberg point of a map f : Kκ →ℝd if y lies in the intersection f(σ1)∩. ∩f(σr) of the images of r pairwise disjoint simplices of K. The analogue of (non-)embeddability that we study is the problem Tverbergκ r→d: Given a κ-dimensional complex K, does it satisfy a Tverberg-type theorem with parameters r and d, i.e., does every map f : K κ → ℝd have an r-fold Tverberg point? Here, we show that for fixed r, κ and d of the form d = rm and k = (r-1)m, m ≥ 3, there is a polynomial-time algorithm for deciding this (based on the vanishing of a cohomological obstruction, as in the case of embeddings). Our main tool is an r-fold analogue of the Whitney trick: Given r pairwise disjoint simplices of K such that the intersection of their images contains two r-fold Tverberg points y+ and y- of opposite intersection sign, we can eliminate y+ and y- by a local isotopy of f. In a subsequent paper, we plan to develop this further and present a generalization of the classical Haeiger-Weber Theorem (which yields a necessary and sufficient condition for embeddability of κ-complexes into ℝd for a wider range of dimensions) to intersection points of higher multiplicity.

A PAC-Bayesian bound for Lifelong Learning - Pentina, Anastasia; Lampert, Christoph
Transfer learning has received a lot of attention in the machine learning community over the last years, and several effective algorithms have been developed. However, relatively little is known about their theoretical properties, especially in the setting of lifelong learning, where the goal is to transfer information to tasks for which no data have been observed so far. In this work we study lifelong learning from a theoretical perspective. Our main result is a PAC-Bayesian generalization bound that offers a unified view on existing paradigms for transfer learning, such as the transfer of parameters or the transfer of low-dimensional representations. We also use the bound to derive two principled lifelong learning algorithms, and we show that these yield results comparable with existing methods.

Increased grooming after repeated brood care provides sanitary benefits in a clonal ant - Westhus, Claudia; Ugelvig, Line V; Tourdot, Edouard; Heinze, Jürgen; Doums, Claudie; Cremer, Sylvia (Behavioral Ecology and Sociobiology)
Repeated pathogen exposure is a common threat in colonies of social insects, posing selection pressures on colony members to respond with improved disease-defense performance. We here tested whether experience gained by repeated tending of low-level fungus-exposed (Metarhizium robertsii) larvae may alter the performance of sanitary brood care in the clonal ant, Platythyrea punctata. We trained ants individually over nine consecutive trials to either sham-treated or fungus-exposed larvae. We then compared the larval grooming behavior of naive and trained ants and measured how effectively they removed infectious fungal conidiospores from the fungus-exposed larvae. We found that the ants changed the duration of larval grooming in response to both, larval treatment and their level of experience: (1) sham-treated larvae received longer grooming than the fungus-exposed larvae and (2) trained ants performed less self-grooming but longer larval grooming than naive ants, which was true for both, ants trained to fungus-exposed and also to sham-treated larvae. Ants that groomed the fungus-exposed larvae for longer periods removed a higher number of fungal conidiospores from the surface of the fungus-exposed larvae. As experienced ants performed longer larval grooming, they were more effective in fungal removal, thus making them better caretakers under pathogen attack of the colony. By studying this clonal ant, we can thus conclude that even in the absence of genetic variation between colony members, differences in experience levels of brood care may affect performance of sanitary brood care in social insects.

The complexity of ergodic mean payoff games - Chatterjee, Krishnendu; Ibsen-Jensen, Rasmus
We study two-player (zero-sum) concurrent mean-payoff games played on a finite-state graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with probability 1. The algorithmic study of ergodic games was initiated in a seminal work of Hoffman and Karp in 1966, but all basic complexity questions have remained unresolved. Our main results for ergodic games are as follows: We establish (1) an optimal exponential bound on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy); (2) the approximation problem lies in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP ∩ coNP is the long-standing best known bound). We present a variant of the strategy-iteration algorithm by Hoffman and Karp; show that both our algorithm and the classical value-iteration algorithm can approximate the value in exponential time; and identify a subclass where the value-iteration algorithm is a FPTAS. We also show that the exact value can be expressed in the existential theory of the reals, and establish square-root sum hardness for a related class of games.

Games with a weak adversary - Chatterjee, Krishnendu; Doyen, Laurent (Lecture Notes in Computer Science)
We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable in general, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. From our results we derive new complexity results for partial-observation stochastic games.

Epilepsy-induced motility of differentiated neurons - Chai, Xuejun; Münzner, Gert; Zhao, Shanting; Tinnes, Stefanie; Kowalski, Janina; Häussler, Ute; Young, Christina; Haas, Carola; Frotscher, Michael (Cerebral Cortex)
Neuronal ectopia, such as granule cell dispersion (GCD) in temporal lobe epilepsy (TLE), has been assumed to result from a migration defect during development. Indeed, recent studies reported that aberrant migration of neonatal-generated dentate granule cells (GCs) increased the risk to develop epilepsy later in life. On the contrary, in the present study, we show that fully differentiated GCs become motile following the induction of epileptiform activity, resulting in GCD. Hippocampal slice cultures from transgenic mice expressing green fluorescent protein in differentiated, but not in newly generated GCs, were incubated with the glutamate receptor agonist kainate (KA), which induced GC burst activity and GCD. Using real-time microscopy, we observed that KA-exposed, differentiated GCs translocated their cell bodies and changed their dendritic organization. As found in human TLE, KA application was associated with decreased expression of the extracellular matrix protein Reelin, particularly in hilar interneurons. Together these findings suggest that KA-induced motility of differentiated GCs contributes to the development of GCD and establish slice cultures as a model to study neuronal changes induced by epileptiform activity.

Domain Adaptation of Weighted Majority Votes via Perturbed Variation-Based Self-Labeling - Morvant, Emilie (Pattern Recognition Letters)
In machine learning, the domain adaptation problem arrives when the test (tar-get) and the train (source) data are generated from different distributions. A key applied issue is thus the design of algorithms able to generalize on a new distribution, for which we have no label information. We focus on learning classification models defined as a weighted majority vote over a set of real-valued functions. In this context, Germain et al. (2013) have shown that a measure of disagreement between these functions is crucial to control. The core of this measure is a theoretical bound—the C-bound (Lacasse et al., 2007)—which involves the disagreement and leads to a well performing majority vote learn-ing algorithm in usual non-adaptative supervised setting: MinCq. In this work,we propose a framework to extend MinCq to a domain adaptation scenario.This procedure takes advantage of the recent perturbed variation divergence between distributions proposed by Harel and Mannor (2012). Justified by a theoretical bound on the target risk of the vote, we provide to MinCq a tar-get sample labeled thanks to a perturbed variation-based self-labeling focused on the regions where the source and target marginals appear similar. We also study the influence of our self-labeling, from which we deduce an original process for tuning the hyperparameters. Finally, our framework called PV-MinCq shows very promising results on a rotation and translation synthetic problem.

Compositional specifications for IOCO testing - Daca, Przemyslaw; Henzinger, Thomas A; Krenn, Willibald; Nickovic, Dejan (IEEE 7th International Conference on Software Testing, Verification and Validation)
Model-based testing is a promising technology for black-box software and hardware testing, in which test cases are generated automatically from high-level specifications. Nowadays, systems typically consist of multiple interacting components and, due to their complexity, testing presents a considerable portion of the effort and cost in the design process. Exploiting the compositional structure of system specifications can considerably reduce the effort in model-based testing. Moreover, inferring properties about the system from testing its individual components allows the designer to reduce the amount of integration testing. In this paper, we study compositional properties of the ioco-testing theory. We propose a new approach to composition and hiding operations, inspired by contract-based design and interface theories. These operations preserve behaviors that are compatible under composition and hiding, and prune away incompatible ones. The resulting specification characterizes the input sequences for which the unit testing of components is sufficient to infer the correctness of component integration without the need for further tests. We provide a methodology that uses these results to minimize integration testing effort, but also to detect potential weaknesses in specifications. While we focus on asynchronous models and the ioco conformance relation, the resulting methodology can be applied to a broader class of systems.

Coalescent simulation in continuous space: Algorithms for large neighbourhood size - Kelleher, Jerome; Etheridge, Alison; Barton, Nicholas H (Theoretical Population Biology)
Many species have an essentially continuous distribution in space, in which there are no natural divisions between randomly mating subpopulations. Yet, the standard approach to modelling these populations is to impose an arbitrary grid of demes, adjusting deme sizes and migration rates in an attempt to capture the important features of the population. Such indirect methods are required because of the failure of the classical models of isolation by distance, which have been shown to have major technical flaws. A recently introduced model of extinction and recolonisation in two dimensions solves these technical problems, and provides a rigorous technical foundation for the study of populations evolving in a spatial continuum. The coalescent process for this model is simply stated, but direct simulation is very inefficient for large neighbourhood sizes. We present efficient and exact algorithms to simulate this coalescent process for arbitrary sample sizes and numbers of loci, and analyse these algorithms in detail.

Diverse forms of selection in evolution and computer science - Barton, Nicholas H; Novak, Sebastian; Paixao, Tiago (PNAS)

Likelihood-based inference of population history from low-coverage de novo genome assemblies - Hearn, Jack; Stone, Graham; Bunnefeld, Lynsey; Nicholls, James; Barton, Nicholas H; Lohse, Konrad (Molecular Ecology)
Short-read sequencing technologies have in principle made it feasible to draw detailed inferences about the recent history of any organism. In practice, however, this remains challenging due to the difficulty of genome assembly in most organisms and the lack of statistical methods powerful enough to discriminate between recent, nonequilibrium histories. We address both the assembly and inference challenges. We develop a bioinformatic pipeline for generating outgroup-rooted alignments of orthologous sequence blocks from de novo low-coverage short-read data for a small number of genomes, and show how such sequence blocks can be used to fit explicit models of population divergence and admixture in a likelihood framework. To illustrate our approach, we reconstruct the Pleistocene history of an oak-feeding insect (the oak gallwasp Biorhiza pallida), which, in common with many other taxa, was restricted during Pleistocene ice ages to a longitudinal series of southern refugia spanning the Western Palaearctic. Our analysis of sequence blocks sampled from a single genome from each of three major glacial refugia reveals support for an unexpected history dominated by recent admixture. Despite the fact that 80% of the genome is affected by admixture during the last glacial cycle, we are able to infer the deeper divergence history of these populations. These inferences are robust to variation in block length, mutation model and the sampling location of individual genomes within refugia. This combination of de novo assembly and numerical likelihood calculation provides a powerful framework for estimating recent population history that can be applied to any organism without the need for prior genetic resources.