@misc{9932, abstract = {Gene duplication is important in evolution, because it provides new raw material for evolutionary adaptations. Several existing hypotheses about the causes of duplicate retention and diversification differ in their emphasis on gene dosage, sub-functionalization, and neo-functionalization. Little experimental data exists on the relative importance of gene expression changes and changes in coding regions for the evolution of duplicate genes. Furthermore, we do not know how strongly the environment could affect this importance. To address these questions, we performed evolution experiments with the TEM-1 beta lactamase gene in E. coli to study the initial stages of duplicate gene evolution in the laboratory. We mimicked tandem duplication by inserting two copies of the TEM-1 gene on the same plasmid. We then subjected these copies to repeated cycles of mutagenesis and selection in various environments that contained antibiotics in different combinations and concentrations. Our experiments showed that gene dosage is the most important factor in the initial stages of duplicate gene evolution, and overshadows the importance of point mutations in the coding region.}, author = {Dhar, Riddhiman and Bergmiller, Tobias and Wagner, Andreas}, publisher = {Dryad}, title = {{Data from: Increased gene dosage plays a predominant role in the initial stages of evolution of duplicate TEM-1 beta lactamase genes}}, doi = {10.5061/dryad.jc402}, year = {2014}, } @article{350, abstract = {Herein, a colloidal synthetic route to produce highly monodisperse Cu2HgGeSe4 (CHGSe) nanoparticles (NPs) is presented in detail. The high yield of the developed procedure allowed the production of CHGSe NPs at the gram scale. A thorough analysis of their structural and optical properties is shown. CHGSe NPs displayed poly-tetrahedral morphology and narrow size distributions with average size in the range of 10–40 nm and size dispersions below 10 %. A 1.6 eV optical band gap was measured by mean of UV–Vis. By adjusting the cation ratio, an effective control of their electrical conductivity is achieved. The prepared NPs are used as building blocks for the production of CHGSe bulk nanostructured materials. The thermoelectric properties of CHGSe nanomaterials are studied in the temperature range from 300 to 730 K. CHGSe nanomaterials reached electrical conductivities up to 5 × 104 S m−1, Seebeck coefficients above 100 μV K−1, and thermal conductivities below 1.0 W m−1 K−1 which translated into thermoelectric figures of merit up to 0.34 at 730 K.}, author = {Li, Wenhua and Ibáñez, Maria and Cadavid, Doris and Zamani, Reza and Rubio Garcia, Javier and Gorsse, Stéphane and Morante, Joan and Arbiol, Jordi and Cabot, Andreu}, journal = {Journal of Nanoparticle Research}, number = {3}, publisher = {Kluwer}, title = {{Colloidal synthesis and functional properties of quaternary Cu based semiconductors: Cu2HgGeSe4}}, doi = {10.1007/s11051-014-2297-2}, volume = {16}, year = {2014}, } @article{451, abstract = {We introduce algorithms for the computation of homology, cohomology, and related operations on cubical cell complexes, using the technique based on a chain contraction from the original chain complex to a reduced one that represents its homology. This work is based on previous results for simplicial complexes, and uses Serre’s diagonalization for cubical cells. An implementation in C++ of the introduced algorithms is available at http://www.pawelpilarczyk.com/chaincon/ together with some examples. The paper is self-contained as much as possible, and is written at a very elementary level, so that basic knowledge of algebraic topology should be sufficient to follow it.}, author = {Pawel Pilarczyk and Real, Pedro}, journal = {Advances in Computational Mathematics}, number = {1}, pages = {253 -- 275}, publisher = {Kluwer}, title = {{Computation of cubical homology, cohomology, and (co)homological operations via chain contraction}}, doi = {10.1007/s10444-014-9356-1}, volume = {41}, year = {2014}, } @article{468, abstract = {Invasive alien parasites and pathogens are a growing threat to biodiversity worldwide, which can contribute to the extinction of endemic species. On the Galápagos Islands, the invasive parasitic fly Philornis downsi poses a major threat to the endemic avifauna. Here, we investigated the influence of this parasite on the breeding success of two Darwin's finch species, the warbler finch (Certhidea olivacea) and the sympatric small tree finch (Camarhynchus parvulus), on Santa Cruz Island in 2010 and 2012. While the population of the small tree finch appeared to be stable, the warbler finch has experienced a dramatic decline in population size on Santa Cruz Island since 1997. We aimed to identify whether warbler finches are particularly vulnerable during different stages of the breeding cycle. Contrary to our prediction, breeding success was lower in the small tree finch than in the warbler finch. In both species P. downsi had a strong negative impact on breeding success and our data suggest that heavy rain events also lowered the fledging success. On the one hand parents might be less efficient in compensating their chicks' energy loss due to parasitism as they might be less efficient in foraging on days of heavy rain. On the other hand, intense rainfalls might lead to increased humidity and more rapid cooling of the nests. In the case of the warbler finch we found that the control of invasive plant species with herbicides had a significant additive negative impact on the breeding success. It is very likely that the availability of insects (i.e. food abundance) is lower in such controlled areas, as herbicide usage led to the removal of the entire understory. Predation seems to be a minor factor in brood loss.}, author = {Cimadom, Arno and Ulloa, Angel and Meidl, Patrick and Zöttl, Markus and Zöttl, Elisabet and Fessl, Birgit and Nemeth, Erwin and Dvorak, Michael and Cunninghame, Francesca and Tebbich, Sabine}, journal = {PLoS One}, number = {9}, publisher = {Public Library of Science}, title = {{Invasive parasites habitat change and heavy rainfall reduce breeding success in Darwin's finches}}, doi = {10.1371/journal.pone.0107518}, volume = {9}, year = {2014}, } @inproceedings{475, abstract = {First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard. }, author = {Aminof, Benjamin and Rubin, Sasha}, booktitle = {Electronic Proceedings in Theoretical Computer Science, EPTCS}, location = {Grenoble, France}, pages = {83 -- 90}, publisher = {Open Publishing Association}, title = {{First cycle games}}, doi = {10.4204/EPTCS.146.11}, volume = {146}, year = {2014}, } @article{535, abstract = {Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP∩co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon}, journal = {Algorithmica}, number = {3}, pages = {457 -- 492}, publisher = {Springer}, title = {{Polynomial-time algorithms for energy games with special weight structures}}, doi = {10.1007/s00453-013-9843-7}, volume = {70}, year = {2014}, } @article{537, abstract = {Transgenerational effects are broader than only parental relationships. Despite mounting evidence that multigenerational effects alter phenotypic and life-history traits, our understanding of how they combine to determine fitness is not well developed because of the added complexity necessary to study them. Here, we derive a quantitative genetic model of adaptation to an extraordinary new environment by an additive genetic component, phenotypic plasticity, maternal and grandmaternal effects. We show how, at equilibrium, negative maternal and negative grandmaternal effects maximize expected population mean fitness. We define negative transgenerational effects as those that have a negative effect on trait expression in the subsequent generation, that is, they slow, or potentially reverse, the expected evolutionary dynamic. When maternal effects are positive, negative grandmaternal effects are preferred. As expected under Mendelian inheritance, the grandmaternal effects have a lower impact on fitness than the maternal effects, but this dual inheritance model predicts a more complex relationship between maternal and grandmaternal effects to constrain phenotypic variance and so maximize expected population mean fitness in the offspring.}, author = {Prizak, Roshan and Ezard, Thomas and Hoyle, Rebecca}, journal = {Ecology and Evolution}, number = {15}, pages = {3139 -- 3145}, publisher = {Wiley-Blackwell}, title = {{Fitness consequences of maternal and grandmaternal effects}}, doi = {10.1002/ece3.1150}, volume = {4}, year = {2014}, } @inproceedings{2082, abstract = {NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). Security proofs and attacks for NMAC can typically be lifted to HMAC. NMAC was introduced by Bellare, Canetti and Krawczyk [Crypto'96], who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto'06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. - Our first contribution is a simpler and uniform proof for this fact: If f is an ε-secure PRF (against q queries) and a δ-non-adaptively secure PRF (against q queries), then NMAC f is an (ε+ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. - We then show that this ε+ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(ℓε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. - Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto'99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight ℓq2/2 c bound for this step, improving over the trivial bound of ℓ2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto'05].}, author = {Gazi, Peter and Pietrzak, Krzysztof Z and Rybar, Michal}, editor = {Garay, Juan and Gennaro, Rosario}, location = {Santa Barbara, USA}, number = {1}, pages = {113 -- 130}, publisher = {Springer}, title = {{The exact PRF-security of NMAC and HMAC}}, doi = {10.1007/978-3-662-44371-2_7}, volume = {8616}, year = {2014}, } @article{2083, abstract = {Understanding the effects of sex and migration on adaptation to novel environments remains a key problem in evolutionary biology. Using a single-cell alga Chlamydomonas reinhardtii, we investigated how sex and migration affected rates of evolutionary rescue in a sink environment, and subsequent changes in fitness following evolutionary rescue. We show that sex and migration affect both the rate of evolutionary rescue and subsequent adaptation. However, their combined effects change as the populations adapt to a sink habitat. Both sex and migration independently increased rates of evolutionary rescue, but the effect of sex on subsequent fitness improvements, following initial rescue, changed with migration, as sex was beneficial in the absence of migration but constraining adaptation when combined with migration. These results suggest that sex and migration are beneficial during the initial stages of adaptation, but can become detrimental as the population adapts to its environment.}, author = {Lagator, Mato and Morgan, Andrew and Neve, Paul and Colegrave, Nick}, journal = {Evolution}, number = {8}, pages = {2296 -- 2305}, publisher = {Wiley}, title = {{Role of sex and migration in adaptation to sink environments}}, doi = {10.1111/evo.12440}, volume = {68}, year = {2014}, } @article{2084, abstract = {Receptor tyrosine kinases (RTKs) are a large family of cell surface receptors that sense growth factors and hormones and regulate a variety of cell behaviours in health and disease. Contactless activation of RTKs with spatial and temporal precision is currently not feasible. Here, we generated RTKs that are insensitive to endogenous ligands but can be selectively activated by low-intensity blue light. We screened light-oxygen-voltage (LOV)-sensing domains for their ability to activate RTKs by light-activated dimerization. Incorporation of LOV domains found in aureochrome photoreceptors of stramenopiles resulted in robust activation of the fibroblast growth factor receptor 1 (FGFR1), epidermal growth factor receptor (EGFR) and rearranged during transfection (RET). In human cancer and endothelial cells, light induced cellular signalling with spatial and temporal precision. Furthermore, light faithfully mimicked complex mitogenic and morphogenic cell behaviour induced by growth factors. RTKs under optical control (Opto-RTKs) provide a powerful optogenetic approach to actuate cellular signals and manipulate cell behaviour.}, author = {Grusch, Michael and Schelch, Karin and Riedler, Robert and Gschaider-Reichhart, Eva and Differ, Christopher and Berger, Walter and Inglés Prieto, Álvaro and Janovjak, Harald L}, journal = {EMBO Journal}, number = {15}, pages = {1713 -- 1726}, publisher = {Wiley-Blackwell}, title = {{Spatio-temporally precise activation of engineered receptor tyrosine kinases by light}}, doi = {10.15252/embj.201387695}, volume = {33}, year = {2014}, } @article{2086, abstract = {Pathogens may gain a fitness advantage through manipulation of the behaviour of their hosts. Likewise, host behavioural changes can be a defence mechanism, counteracting the impact of pathogens on host fitness. We apply harmonic radar technology to characterize the impact of an emerging pathogen - Nosema ceranae (Microsporidia) - on honeybee (Apis mellifera) flight and orientation performance in the field. Honeybees are the most important commercial pollinators. Emerging diseases have been proposed to play a prominent role in colony decline, partly through sub-lethal behavioural manipulation of their hosts. We found that homing success was significantly reduced in diseased (65.8%) versus healthy foragers (92.5%). Although lost bees had significantly reduced continuous flight times and prolonged resting times, other flight characteristics and navigational abilities showed no significant difference between infected and non-infected bees. Our results suggest that infected bees express normal flight characteristics but are constrained in their homing ability, potentially compromising the colony by reducing its resource inputs, but also counteracting the intra-colony spread of infection. We provide the first high-resolution analysis of sub-lethal effects of an emerging disease on insect flight behaviour. The potential causes and the implications for both host and parasite are discussed.}, author = {Wolf, Stephan and Mcmahon, Dino and Lim, Ka and Pull, Christopher and Clark, Suzanne and Paxton, Robert and Osborne, Juliet}, journal = {PLoS One}, number = {8}, publisher = {Public Library of Science}, title = {{So near and yet so far: Harmonic radar reveals reduced homing ability of Nosema infected honeybees}}, doi = {10.1371/journal.pone.0103989}, volume = {9}, year = {2014}, } @article{2131, abstract = {We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in Probability Theory Related Fields by Hairer and Weber. The key idea was to use the theory of controlled rough paths to give definitions of weak/mild solutions and to set up a Picard iteration argument. In this article the limiting behavior of a rather large class of (spatial) approximations to these equations is studied. These approximations are shown to converge and convergence rates are given, but the limit may depend on the particular choice of approximation. This effect is a spatial analogue to the Itô-Stratonovich correction in the theory of stochastic ordinary differential equations, where it is well known that different approximation schemes may converge to different solutions.}, author = {Hairer, Martin M and Jan Maas and Weber, Hendrik}, journal = {Communications on Pure and Applied Mathematics}, number = {5}, pages = {776 -- 870}, publisher = {Wiley-Blackwell}, title = {{Approximating Rough Stochastic PDEs}}, doi = {10.1002/cpa.21495}, volume = {67}, year = {2014}, } @article{2132, abstract = {We consider discrete porous medium equations of the form ∂tρt=Δϕ(ρt), where Δ is the generator of a reversible continuous time Markov chain on a finite set χ, and ϕ is an increasing function. We show that these equations arise as gradient flows of certain entropy functionals with respect to suitable non-local transportation metrics. This may be seen as a discrete analogue of the Wasserstein gradient flow structure for porous medium equations in ℝn discovered by Otto. We present a one-dimensional counterexample to geodesic convexity and discuss Gromov-Hausdorff convergence to the Wasserstein metric.}, author = {Erbar, Matthias and Jan Maas}, journal = {Discrete and Continuous Dynamical Systems- Series A}, number = {4}, pages = {1355 -- 1374}, publisher = {Southwest Missouri State University}, title = {{Gradient flow structures for discrete porous medium equations}}, doi = {10.3934/dcds.2014.34.1355 }, volume = {34}, year = {2014}, } @article{2133, abstract = {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.}, author = {Carlen, Eric and Maas, Jan}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {887 -- 926}, publisher = {Springer}, title = {{An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy}}, doi = {10.1007/s00220-014-2124-8}, volume = {331}, year = {2014}, } @article{2140, abstract = {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.}, author = {Otterbach, Johannes and Lemeshko, Mikhail}, journal = {Physical Review Letters}, number = {7}, publisher = {American Physical Society}, title = {{Dissipative preparation of spatial order in Rydberg-dressed Bose-Einstein condensates}}, doi = {10.1103/PhysRevLett.113.070401}, volume = {113}, year = {2014}, } @article{2141, abstract = {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.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H}, journal = {Journal of the ACM}, number = {3}, publisher = {ACM}, title = {{Efficient and dynamic algorithms for alternating Büchi games and maximal end-component decomposition}}, doi = {10.1145/2597631}, volume = {61}, year = {2014}, } @inproceedings{2153, abstract = {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).}, author = {Bauer, Ulrich and Lesnick, Michael}, booktitle = {Proceedings of the Annual Symposium on Computational Geometry}, location = {Kyoto, Japan}, pages = {355 -- 364}, publisher = {ACM}, title = {{Induced matchings of barcodes and the algebraic stability of persistence}}, doi = {10.1145/2582112.2582168}, year = {2014}, } @article{2154, abstract = {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.}, author = {Matoušek, Jiří and Wagner, Uli}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {1 -- 33}, publisher = {Springer}, title = {{On Gromov's method of selecting heavily covered points}}, doi = {10.1007/s00454-014-9584-7}, volume = {52}, year = {2014}, } @inproceedings{2155, abstract = {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).}, author = {Bauer, Ulrich and Edelsbrunner, Herbert}, booktitle = {Proceedings of the Annual Symposium on Computational Geometry}, location = {Kyoto, Japan}, pages = {484 -- 490}, publisher = {ACM}, title = {{The morse theory of Čech and Delaunay filtrations}}, doi = {10.1145/2582112.2582167}, year = {2014}, } @inproceedings{2156, abstract = {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).}, author = {Bauer, Ulrich and Ge, Xiaoyin and Wang, Yusu}, booktitle = {Proceedings of the Annual Symposium on Computational Geometry}, location = {Kyoto, Japan}, pages = {464 -- 473}, publisher = {ACM}, title = {{Measuring distance between Reeb graphs}}, doi = {10.1145/2582112.2582169}, year = {2014}, }