@article{1709,
  abstract     = {The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.},
  author       = {Reiter, Johannes and Kanodia, Ayush and Gupta, Raghav and Nowak, Martin and Chatterjee, Krishnendu},
  journal      = {Proceedings of the Royal Society of London Series B Biological Sciences},
  number       = {1812},
  publisher    = {Royal Society},
  title        = {{Biological auctions with multiple rewards}},
  doi          = {10.1098/rspb.2015.1041},
  volume       = {282},
  year         = {2015},
}

@phdthesis{1400,
  abstract     = {Cancer results from an uncontrolled growth of abnormal cells. Sequentially accumulated genetic and epigenetic alterations decrease cell death and increase cell replication. We used mathematical models to quantify the effect of driver gene mutations. The recently developed targeted therapies can lead to dramatic regressions. However, in solid cancers, clinical responses are often short-lived because resistant cancer cells evolve. We estimated that approximately 50 different mutations can confer resistance to a typical targeted therapeutic agent. We find that resistant cells are likely to be present in expanded subclones before the start of the treatment. The dominant strategy to prevent the evolution of resistance is combination therapy. Our analytical results suggest that in most patients, dual therapy, but not monotherapy, can result in long-term disease control. However, long-term control can only occur if there are no possible mutations in the genome that can cause cross-resistance to both drugs. Furthermore, we showed that simultaneous therapy with two drugs is much more likely to result in long-term disease control than sequential therapy with the same drugs. To improve our understanding of the underlying subclonal evolution we reconstruct the evolutionary history of a patient's cancer from next-generation sequencing data of spatially-distinct DNA samples. Using a quantitative measure of genetic relatedness, we found that pancreatic cancers and their metastases demonstrated a higher level of relatedness than that expected for any two cells randomly taken from a normal tissue. This minimal amount of genetic divergence among advanced lesions indicates that genetic heterogeneity, when quantitatively defined, is not a fundamental feature of the natural history of untreated pancreatic cancers. Our newly developed, phylogenomic tool Treeomics finds evidence for seeding patterns of metastases and can directly be used to discover rules governing the evolution of solid malignancies to transform cancer into a more predictable disease.},
  author       = {Reiter, Johannes},
  issn         = {2663-337X},
  pages        = {183},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{The subclonal evolution of cancer}},
  year         = {2015},
}

@article{1666,
  abstract     = {Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ∼ 10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of “pre-sites” or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genomics.},
  author       = {Tugrul, Murat and Paixao, Tiago and Barton, Nicholas H and Tkacik, Gasper},
  journal      = {PLoS Genetics},
  number       = {11},
  publisher    = {Public Library of Science},
  title        = {{Dynamics of transcription factor binding site evolution}},
  doi          = {10.1371/journal.pgen.1005639},
  volume       = {11},
  year         = {2015},
}

@inproceedings{1633,
  abstract     = {We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front.

Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation.

Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix.},
  author       = {Hahn, David and Wojtan, Christopher J},
  location     = {Los Angeles, CA, United States},
  number       = {4},
  publisher    = {ACM},
  title        = {{High-resolution brittle fracture simulation with boundary elements}},
  doi          = {10.1145/2766896},
  volume       = {34},
  year         = {2015},
}

@article{1830,
  abstract     = {To prevent epidemics, insect societies have evolved collective disease defences that are highly effective at curing exposed individuals and limiting disease transmission to healthy group members. Grooming is an important sanitary behaviour—either performed towards oneself (self-grooming) or towards others (allogrooming)—to remove infectious agents from the body surface of exposed individuals, but at the risk of disease contraction by the groomer. We use garden ants (Lasius neglectus) and the fungal pathogen Metarhizium as a model system to study how pathogen presence affects self-grooming and allogrooming between exposed and healthy individuals. We develop an epidemiological SIS model to explore how experimentally observed grooming patterns affect disease spread within the colony, thereby providing a direct link between the expression and direction of sanitary behaviours, and their effects on colony-level epidemiology. We find that fungus-exposed ants increase self-grooming, while simultaneously decreasing allogrooming. This behavioural modulation seems universally adaptive and is predicted to contain disease spread in a great variety of host–pathogen systems. In contrast, allogrooming directed towards pathogen-exposed individuals might both increase and decrease disease risk. Our model reveals that the effect of allogrooming depends on the balance between pathogen infectiousness and efficiency of social host defences, which are likely to vary across host–pathogen systems.},
  author       = {Theis, Fabian and Ugelvig, Line V and Marr, Carsten and Cremer, Sylvia},
  issn         = {1471-2970},
  journal      = {Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences},
  number       = {1669},
  publisher    = {Royal Society},
  title        = {{Opposing effects of allogrooming on disease transmission in ant societies}},
  doi          = {10.1098/rstb.2014.0108},
  volume       = {370},
  year         = {2015},
}

@misc{9721,
  abstract     = {To prevent epidemics, insect societies have evolved collective disease defences that are highly effective at curing exposed individuals and limiting disease transmission to healthy group members. Grooming is an important sanitary behaviour—either performed towards oneself (self-grooming) or towards others (allogrooming)—to remove infectious agents from the body surface of exposed individuals, but at the risk of disease contraction by the groomer. We use garden ants (Lasius neglectus) and the fungal pathogen Metarhizium as a model system to study how pathogen presence affects self-grooming and allogrooming between exposed and healthy individuals. We develop an epidemiological SIS model to explore how experimentally observed grooming patterns affect disease spread within the colony, thereby providing a direct link between the expression and direction of sanitary behaviours, and their effects on colony-level epidemiology. We find that fungus-exposed ants increase self-grooming, while simultaneously decreasing allogrooming. This behavioural modulation seems universally adaptive and is predicted to contain disease spread in a great variety of host–pathogen systems. In contrast, allogrooming directed towards pathogen-exposed individuals might both increase and decrease disease risk. Our model reveals that the effect of allogrooming depends on the balance between pathogen infectiousness and efficiency of social host defences, which are likely to vary across host–pathogen systems.},
  author       = {Theis, Fabian and Ugelvig, Line V and Marr, Carsten and Cremer, Sylvia},
  publisher    = {Dryad},
  title        = {{Data from: Opposing effects of allogrooming on disease transmission in ant societies}},
  doi          = {10.5061/dryad.dj2bf},
  year         = {2015},
}

@article{1811,
  abstract     = {Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wave functions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.},
  author       = {Safari, Laleh and Santos, José and Amaro, Pedro and Jänkälä, Kari and Fratini, Filippo},
  journal      = {Journal of Mathematical Physics},
  number       = {5},
  publisher    = {AIP Publishing},
  title        = {{Analytical evaluation of atomic form factors: Application to Rayleigh scattering}},
  doi          = {10.1063/1.4921227},
  volume       = {56},
  year         = {2015},
}

@article{1677,
  abstract     = {We consider real symmetric and complex Hermitian random matrices with the additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale.},
  author       = {Alt, Johannes},
  journal      = {Journal of Mathematical Physics},
  number       = {10},
  publisher    = {AIP Publishing},
  title        = {{The local semicircle law for random matrices with a fourfold symmetry}},
  doi          = {10.1063/1.4932606},
  volume       = {56},
  year         = {2015},
}

@article{1587,
  abstract     = {We investigate the quantum interference shifts between energetically close states, where the state structure is observed by laser spectroscopy. We report a compact and analytical expression that models the quantum interference induced shift for any admixture of circular polarization of the incident laser and angle of observation. An experimental scenario free of quantum interference can thus be predicted with this formula. Although this study is exemplified here for muonic deuterium, it can be applied to any other laser spectroscopy measurement of ns-n′p frequencies of a nonrelativistic atomic system, via an ns→n′p→n′′s scheme.},
  author       = {Amaro, Pedro and Fratini, Filippo and Safari, Laleh and Antognini, Aldo and Indelicato, Paul and Pohl, Randolf and Santos, José},
  journal      = {Physical Review A},
  number       = {6},
  publisher    = {American Physical Society},
  title        = {{Quantum interference shifts in laser spectroscopy with elliptical polarization}},
  doi          = {10.1103/PhysRevA.92.062506},
  volume       = {92},
  year         = {2015},
}

@article{1940,
  abstract     = {We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the "input") by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively new regulatory strategy emerges where individual cells respond to the input in a nearly step-like fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.},
  author       = {Sokolowski, Thomas R and Tkacik, Gasper},
  journal      = {Physical Review E},
  number       = {6},
  publisher    = {American Physical Society},
  title        = {{Optimizing information flow in small genetic networks. IV. Spatial coupling}},
  doi          = {10.1103/PhysRevE.91.062710},
  volume       = {91},
  year         = {2015},
}

@article{1883,
  abstract     = {We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.
},
  author       = {Keller-Schmidt, Stephanie and Tugrul, Murat and Eguíluz, Víctor and Hernandez Garcia, Emilio and Klemm, Konstantin},
  journal      = {Physical Review E},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Anomalous scaling in an age-dependent branching model}},
  doi          = {10.1103/PhysRevE.91.022803},
  volume       = {91},
  year         = {2015},
}

@inproceedings{1820,
  abstract     = {We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objec- tive we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present ap- proximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst- case running time of our algorithm is double exponential, we present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples.},
  author       = {Chatterjee, Krishnendu and Chmelik, Martin and Gupta, Raghav and Kanodia, Ayush},
  booktitle    = {Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence },
  location     = {Austin, TX, USA},
  pages        = {3496--3502},
  publisher    = {AAAI Press},
  title        = {{Optimal cost almost-sure reachability in POMDPs}},
  doi          = {10.1609/aaai.v29i1.9683},
  volume       = {5},
  year         = {2015},
}

@article{1619,
  abstract     = {The emergence of drug resistant pathogens is a serious public health problem. It is a long-standing goal to predict rates of resistance evolution and design optimal treatment strategies accordingly. To this end, it is crucial to reveal the underlying causes of drug-specific differences in the evolutionary dynamics leading to resistance. However, it remains largely unknown why the rates of resistance evolution via spontaneous mutations and the diversity of mutational paths vary substantially between drugs. Here we comprehensively quantify the distribution of fitness effects (DFE) of mutations, a key determinant of evolutionary dynamics, in the presence of eight antibiotics representing the main modes of action. Using precise high-throughput fitness measurements for genome-wide Escherichia coli gene deletion strains, we find that the width of the DFE varies dramatically between antibiotics and, contrary to conventional wisdom, for some drugs the DFE width is lower than in the absence of stress. We show that this previously underappreciated divergence in DFE width among antibiotics is largely caused by their distinct drug-specific dose-response characteristics. Unlike the DFE, the magnitude of the changes in tolerated drug concentration resulting from genome-wide mutations is similar for most drugs but exceptionally small for the antibiotic nitrofurantoin, i.e., mutations generally have considerably smaller resistance effects for nitrofurantoin than for other drugs. A population genetics model predicts that resistance evolution for drugs with this property is severely limited and confined to reproducible mutational paths. We tested this prediction in laboratory evolution experiments using the “morbidostat”, a device for evolving bacteria in well-controlled drug environments. Nitrofurantoin resistance indeed evolved extremely slowly via reproducible mutations—an almost paradoxical behavior since this drug causes DNA damage and increases the mutation rate. Overall, we identified novel quantitative characteristics of the evolutionary landscape that provide the conceptual foundation for predicting the dynamics of drug resistance evolution.},
  author       = {Chevereau, Guillaume and Dravecka, Marta and Batur, Tugce and Guvenek, Aysegul and Ayhan, Dilay and Toprak, Erdal and Bollenbach, Mark Tobias},
  journal      = {PLoS Biology},
  number       = {11},
  publisher    = {Public Library of Science},
  title        = {{Quantifying the determinants of evolutionary dynamics leading to drug resistance}},
  doi          = {10.1371/journal.pbio.1002299},
  volume       = {13},
  year         = {2015},
}

@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},
}