@misc{9753,
  abstract     = {Background: The brood of ants and other social insects is highly susceptible to pathogens, particularly those that penetrate the soft larval and pupal cuticle. We here test whether the presence of a pupal cocoon, which occurs in some ant species but not in others, affects the sanitary brood care and fungal infection patterns after exposure to the entomopathogenic fungus Metarhizium brunneum. We use a) a comparative approach analysing four species with either naked or cocooned pupae and b) a within-species analysis of a single ant species, in which both pupal types co-exist in the same colony. Results: We found that the presence of a cocoon did not compromise fungal pathogen detection by the ants and that species with cocooned pupae increased brood grooming after pathogen exposure. All tested ant species further removed brood from their nests, which was predominantly expressed towards larvae and naked pupae treated with the live fungal pathogen. In contrast, cocooned pupae exposed to live fungus were not removed at higher rates than cocooned pupae exposed to dead fungus or a sham control. Consistent with this, exposure to the live fungus caused high numbers of infections and fungal outgrowth in larvae and naked pupae, but not in cocooned pupae. Moreover, the ants consistently removed the brood prior to fungal outgrowth, ensuring a clean brood chamber. Conclusion: Our study suggests that the pupal cocoon has a protective effect against fungal infection, causing an adaptive change in sanitary behaviours by the ants. It further demonstrates that brood removal - originally described for honeybees as “hygienic behaviour” – is a widespread sanitary behaviour in ants, which likely has important implications on disease dynamics in social insect colonies.},
  author       = {Tragust, Simon and Ugelvig, Line V and Chapuisat, Michel and Heinze, Jürgen and Cremer, Sylvia},
  publisher    = {Dryad},
  title        = {{Data from: Pupal cocoons affect sanitary brood care and limit fungal infections in ant colonies}},
  doi          = {10.5061/dryad.nc0gc},
  year         = {2014},
}

@misc{9888,
  abstract     = {Detailed description of the experimental prodedures, data analyses and additional statistical analyses of the results.},
  author       = {Wolf, Stephan and Mcmahon, Dino and Lim, Ka and Pull, Christopher and Clark, Suzanne and Paxton, Robert and Osborne, Juliet},
  publisher    = {Public Library of Science},
  title        = {{Supporting information}},
  doi          = {10.1371/journal.pone.0103989.s003},
  year         = {2014},
}

@article{9931,
  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, subfunctionalization, and neofunctionalization. Little experimental data exist 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 Escherichia 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},
  issn         = {1558-5646},
  journal      = {Evolution},
  number       = {6},
  pages        = {1775--1791},
  publisher    = {Wiley},
  title        = {{Increased gene dosage plays a predominant role in the initial stages of evolution of duplicate TEM-1 beta lactamase genes}},
  doi          = {10.1111/evo.12373},
  volume       = {68},
  year         = {2014},
}

@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},
}

@inbook{10817,
  abstract     = {The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption.},
  author       = {Günther, David and Reininghaus, Jan and Seidel, Hans-Peter and Weinkauf, Tino},
  booktitle    = {Topological Methods in Data Analysis and Visualization III.},
  editor       = {Bremer, Peer-Timo and Hotz, Ingrid and Pascucci, Valerio and Peikert, Ronald},
  isbn         = {9783319040981},
  issn         = {2197-666X},
  pages        = {135--150},
  publisher    = {Springer Nature},
  title        = {{Notes on the simplification of the Morse-Smale complex}},
  doi          = {10.1007/978-3-319-04099-8_9},
  year         = {2014},
}

@inproceedings{10884,
  abstract     = {We revisit the parameterized model checking problem for token-passing systems and specifications in indexed CTL  ∗ \X. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed CTL  ∗ \X in uni-directional token rings can be reduced to checking rings up to some cutoff size. Clarke et al. (2004) have shown a similar result for general topologies and indexed LTL \X, provided processes cannot choose the directions for sending or receiving the token.
We unify and substantially extend these results by systematically exploring fragments of indexed CTL  ∗ \X with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.},
  author       = {Aminof, Benjamin and Jacobs, Swen and Khalimov, Ayrat and Rubin, Sasha},
  booktitle    = {Verification, Model Checking, and Abstract Interpretation},
  isbn         = {9783642540127},
  issn         = {1611-3349},
  location     = {San Diego, CA, United States},
  pages        = {262--281},
  publisher    = {Springer Nature},
  title        = {{Parameterized model checking of token-passing systems}},
  doi          = {10.1007/978-3-642-54013-4_15},
  volume       = {8318},
  year         = {2014},
}

@inproceedings{10885,
  abstract     = {Two-player games on graphs provide the theoretical framework for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of equilibria, they are decidable only for perfect-information games, whereas several applications require imperfect-information games.
In this paper we propose a new notion of equilibria, called doomsday equilibria, which is a strategy profile such that all players satisfy their own objective, and if any coalition of players deviates and violates even one of the players objective, then the objective of every player is violated.
We present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of ω-regular objectives, both for imperfect-information games, and for perfect-information games.We provide optimal complexity bounds for imperfect-information games, and in most cases for perfect-information games.},
  author       = {Chatterjee, Krishnendu and Doyen, Laurent and Filiot, Emmanuel and Raskin, Jean-François},
  booktitle    = {VMCAI 2014: Verification, Model Checking, and Abstract Interpretation},
  isbn         = {9783642540127},
  issn         = {1611-3349},
  location     = {San Diego, CA, United States},
  pages        = {78--97},
  publisher    = {Springer Nature},
  title        = {{Doomsday equilibria for omega-regular games}},
  doi          = {10.1007/978-3-642-54013-4_5},
  volume       = {8318},
  year         = {2014},
}

@inproceedings{10886,
  abstract     = {We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set.},
  author       = {Zobel, Valentin and Reininghaus, Jan and Hotz, Ingrid},
  booktitle    = {Topological Methods in Data Analysis and Visualization III },
  isbn         = {9783319040981},
  issn         = {2197-666X},
  pages        = {249--262},
  publisher    = {Springer},
  title        = {{Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature}},
  doi          = {10.1007/978-3-319-04099-8_16},
  year         = {2014},
}

@inproceedings{10892,
  abstract     = {In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.
Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings.},
  author       = {Biedl, Therese and Huber, Stefan and Palfrader, Peter},
  booktitle    = {25th International Symposium, ISAAC 2014},
  isbn         = {9783319130743},
  issn         = {1611-3349},
  location     = {Jeonju, Korea},
  pages        = {117--127},
  publisher    = {Springer Nature},
  title        = {{Planar matchings for weighted straight skeletons}},
  doi          = {10.1007/978-3-319-13075-0_10},
  volume       = {8889},
  year         = {2014},
}

@inbook{10893,
  abstract     = {Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data.},
  author       = {Kasten, Jens and Reininghaus, Jan and Reich, Wieland and Scheuermann, Gerik},
  booktitle    = {Topological Methods in Data Analysis and Visualization III },
  editor       = {Bremer, Peer-Timo and Hotz, Ingrid and Pascucci, Valerio and Peikert, Ronald},
  isbn         = {9783319040981},
  issn         = {2197-666X},
  pages        = {55--69},
  publisher    = {Springer},
  title        = {{Toward the extraction of saddle periodic orbits}},
  doi          = {10.1007/978-3-319-04099-8_4},
  volume       = {1},
  year         = {2014},
}

@inproceedings{10894,
  abstract     = {PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations.},
  author       = {Bauer, Ulrich and Kerber, Michael and Reininghaus, Jan and Wagner, Hubert},
  booktitle    = {ICMS 2014: International Congress on Mathematical Software},
  isbn         = {9783662441985},
  issn         = {1611-3349},
  location     = {Seoul, South Korea},
  pages        = {137--143},
  publisher    = {Springer Berlin Heidelberg},
  title        = {{PHAT – Persistent Homology Algorithms Toolbox}},
  doi          = {10.1007/978-3-662-44199-2_24},
  volume       = {8592},
  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{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},
}