@article{2253,
  abstract     = {Plant growth is achieved predominantly by cellular elongation, which is thought to be controlled on several levels by apoplastic auxin. Auxin export into the apoplast is achieved by plasma membrane efflux catalysts of the PIN-FORMED (PIN) and ATP-binding cassette protein subfamily B/phosphor- glycoprotein (ABCB/PGP) classes; the latter were shown to depend on interaction with the FKBP42, TWISTED DWARF1 (TWD1). Here by using a transgenic approach in combination with phenotypical, biochemical and cell biological analyses we demonstrate the importance of a putative C-terminal in-plane membrane anchor of TWD1 in the regulation of ABCB-mediated auxin transport. In contrast with dwarfed twd1 loss-of-function alleles, TWD1 gain-of-function lines that lack a putative in-plane membrane anchor (HA-TWD1-Ct) show hypermorphic plant architecture, characterized by enhanced stem length and leaf surface but reduced shoot branching. Greater hypocotyl length is the result of enhanced cell elongation that correlates with reduced polar auxin transport capacity for HA-TWD1-Ct. As a consequence, HA-TWD1-Ct displays higher hypocotyl auxin accumulation, which is shown to result in elevated auxin-induced cell elongation rates. Our data highlight the importance of C-terminal membrane anchoring for TWD1 action, which is required for specific regulation of ABCB-mediated auxin transport. These data support a model in which TWD1 controls lateral ABCB1-mediated export into the apoplast, which is required for auxin-mediated cell elongation.},
  author       = {Bailly, Aurélien and Wang, Bangjun and Zwiewka, Marta and Pollmann, Stephan and Schenck, Daniel and Lüthen, Hartwig and Schulz, Alexander and Friml, Jirí and Geisler, Markus},
  issn         = {09607412},
  journal      = {Plant Journal},
  number       = {1},
  pages        = {108 -- 118},
  publisher    = {Wiley-Blackwell},
  title        = {{Expression of TWISTED DWARF1 lacking its in-plane membrane anchor leads to increased cell elongation and hypermorphic growth}},
  doi          = {10.1111/tpj.12369},
  volume       = {77},
  year         = {2014},
}

@article{2254,
  abstract     = {Theta-gamma network oscillations are thought to represent key reference signals for information processing in neuronal ensembles, but the underlying synaptic mechanisms remain unclear. To address this question, we performed whole-cell (WC) patch-clamp recordings from mature hippocampal granule cells (GCs) in vivo in the dentate gyrus of anesthetized and awake rats. GCs in vivo fired action potentials at low frequency, consistent with sparse coding in the dentate gyrus. GCs were exposed to barrages of fast AMPAR-mediated excitatory postsynaptic currents (EPSCs), primarily relayed from the entorhinal cortex, and inhibitory postsynaptic currents (IPSCs), presumably generated by local interneurons. EPSCs exhibited coherence with the field potential predominantly in the theta frequency band, whereas IPSCs showed coherence primarily in the gamma range. Action potentials in GCs were phase locked to network oscillations. Thus, theta-gamma-modulated synaptic currents may provide a framework for sparse temporal coding of information in the dentate gyrus.},
  author       = {Pernia-Andrade, Alejandro and Jonas, Peter M},
  issn         = {08966273},
  journal      = {Neuron},
  number       = {1},
  pages        = {140 -- 152},
  publisher    = {Elsevier},
  title        = {{Theta-gamma-modulated synaptic currents in hippocampal granule cells in vivo define a mechanism for network oscillations}},
  doi          = {10.1016/j.neuron.2013.09.046},
  volume       = {81},
  year         = {2014},
}

@article{2255,
  abstract     = {Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm.},
  author       = {Edelsbrunner, Herbert and Pausinger, Florian},
  issn         = {09249907},
  journal      = {Journal of Mathematical Imaging and Vision},
  number       = {1},
  pages        = {164 -- 177},
  publisher    = {Springer},
  title        = {{Stable length estimates of tube-like shapes}},
  doi          = {10.1007/s10851-013-0468-x},
  volume       = {50},
  year         = {2014},
}

@article{2257,
  abstract     = {Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such “K-pairwise” models—being systematic extensions of the previously used pairwise Ising models—provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.},
  author       = {Tkacik, Gasper and Marre, Olivier and Amodei, Dario and Schneidman, Elad and Bialek, William and Berry, Michael},
  issn         = {1553734X},
  journal      = {PLoS Computational Biology},
  number       = {1},
  publisher    = {Public Library of Science},
  title        = {{Searching for collective behavior in a large network of sensory neurons}},
  doi          = {10.1371/journal.pcbi.1003408},
  volume       = {10},
  year         = {2014},
}

@article{2261,
  abstract     = {To reveal the full potential of human pluripotent stem cells, new methods for rapid, site-specific genomic engineering are needed. Here, we describe a system for precise genetic modification of human embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs). We identified a novel human locus, H11, located in a safe, intergenic, transcriptionally active region of chromosome 22, as the recipient site, to provide robust, ubiquitous expression of inserted genes. Recipient cell lines were established by site-specific placement of a ‘landing pad’ cassette carrying attP sites for phiC31 and Bxb1 integrases at the H11 locus by spontaneous or TALEN-assisted homologous recombination. Dual integrase cassette exchange (DICE) mediated by phiC31 and Bxb1 integrases was used to insert genes of interest flanked by phiC31 and Bxb1 attB sites at the H11 locus, replacing the landing pad. This system provided complete control over content, direction and copy number of inserted genes, with a specificity of 100%. A series of genes, including mCherry and various combinations of the neural transcription factors LMX1a, FOXA2 and OTX2, were inserted in recipient cell lines derived from H9 ESC, as well as iPSC lines derived from a Parkinson’s disease patient and a normal sibling control. The DICE system offers rapid, efficient and precise gene insertion in ESC and iPSC and is particularly well suited for repeated modifications of the same locus.},
  author       = {Zhu, Fangfang and Gamboa, Matthew and Farruggio, Alfonso and Hippenmeyer, Simon and Tasic, Bosiljka and Schüle, Birgitt and Chen Tsai, Yanru and Calos, Michele},
  journal      = {Nucleic Acids Research},
  number       = {5},
  publisher    = {Oxford University Press},
  title        = {{DICE, an efficient system for iterative genomic editing in human pluripotent stem cells}},
  doi          = {10.1093/nar/gkt1290},
  volume       = {42},
  year         = {2014},
}

@inbook{2265,
  abstract     = {Coordinated migration of newly-born neurons to their target territories is essential for correct neuronal circuit assembly in the developing brain. Although a cohort of signaling pathways has been implicated in the regulation of cortical projection neuron migration, the precise molecular mechanisms and how a balanced interplay of cell-autonomous and non-autonomous functions of candidate signaling molecules controls the discrete steps in the migration process, are just being revealed. In this chapter, I will focally review recent advances that improved our understanding of the cell-autonomous and possible cell-nonautonomous functions of the evolutionarily conserved LIS1/NDEL1-complex in regulating the sequential steps of cortical projection neuron migration. I will then elaborate on the emerging concept that the Reelin signaling pathway, acts exactly at precise stages in the course of cortical projection neuron migration. Lastly, I will discuss how finely tuned transcriptional programs and downstream effectors govern particular aspects in driving radial migration at discrete stages and how they regulate the precise positioning of cortical projection neurons in the developing cerebral cortex.},
  author       = {Hippenmeyer, Simon},
  booktitle    = { Cellular and Molecular Control of Neuronal Migration},
  editor       = {Nguyen, Laurent},
  pages        = {1 -- 24},
  publisher    = {Springer},
  title        = {{Molecular pathways controlling the sequential steps of cortical projection neuron migration}},
  doi          = {10.1007/978-94-007-7687-6_1},
  volume       = {800},
  year         = {2014},
}

@inproceedings{2275,
  abstract     = {Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. 
This partial enumeration technique reduces complex high-order energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. 
Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach.
},
  author       = {Olsson, Carl and Ulen, Johannes and Boykov, Yuri and Kolmogorov, Vladimir},
  location     = {Sydney, Australia},
  pages        = {2936 -- 2943},
  publisher    = {IEEE},
  title        = {{Partial enumeration and curvature regularization}},
  doi          = {10.1109/ICCV.2013.365},
  year         = {2014},
}

@article{2281,
  abstract     = {We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies {Mathematical expression}, where Q is the unique positive radial solution of {Mathematical expression} in {Mathematical expression}. We present a detailed analysis of the behavior of minimizers as a approaches a*, where all the mass concentrates at a global minimum of the trapping potential.},
  author       = {Guo, Yujin and Seiringer, Robert},
  journal      = {Letters in Mathematical Physics},
  number       = {2},
  pages        = {141 -- 156},
  publisher    = {Springer},
  title        = {{On the mass concentration for Bose-Einstein condensates with attractive interactions}},
  doi          = {10.1007/s11005-013-0667-9},
  volume       = {104},
  year         = {2014},
}

@article{2285,
  abstract     = {GABAergic inhibitory interneurons control fundamental aspects of neuronal network function. Their functional roles are assumed to be defined by the identity of their input synapses, the architecture of their dendritic tree, the passive and active membrane properties and finally the nature of their postsynaptic targets. Indeed, interneurons display a high degree of morphological and physiological heterogeneity. However, whether their morphological and physiological characteristics are correlated and whether interneuron diversity can be described by a continuum of GABAergic cell types or by distinct classes has remained unclear. Here we perform a detailed morphological and physiological characterization of GABAergic cells in the dentate gyrus, the input region of the hippocampus. To achieve an unbiased and efficient sampling and classification we used knock-in mice expressing the enhanced green fluorescent protein (eGFP) in glutamate decarboxylase 67 (GAD67)-positive neurons and performed cluster analysis. We identified five interneuron classes, each of them characterized by a distinct set of anatomical and physiological parameters. Cross-correlation analysis further revealed a direct relation between morphological and physiological properties indicating that dentate gyrus interneurons fall into functionally distinct classes which may differentially control neuronal network activity.},
  author       = {Hosp, Jonas and Strüber, Michael and Yanagawa, Yuchio and Obata, Kunihiko and Vida, Imre and Jonas, Peter M and Bartos, Marlene},
  journal      = {Hippocampus},
  number       = {2},
  pages        = {189 -- 203},
  publisher    = {Wiley-Blackwell},
  title        = {{Morpho-physiological criteria divide dentate gyrus interneurons into classes}},
  doi          = {10.1002/hipo.22214},
  volume       = {23},
  year         = {2014},
}

@article{2699,
  abstract     = {We prove the universality of the β-ensembles with convex analytic potentials and for any β &gt;
0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles.},
  author       = {Erdös, László and Bourgade, Paul and Yau, Horng},
  journal      = {Duke Mathematical Journal},
  number       = {6},
  pages        = {1127 -- 1190},
  publisher    = {Duke University Press},
  title        = {{Universality of general β-ensembles}},
  doi          = {10.1215/00127094-2649752},
  volume       = {163},
  year         = {2014},
}

@article{2716,
  abstract     = {Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω ω -regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on vector addition systems with states. Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.},
  author       = {Chatterjee, Krishnendu and Randour, Mickael and Raskin, Jean},
  journal      = {Acta Informatica},
  number       = {3-4},
  pages        = {129 -- 163},
  publisher    = {Springer},
  title        = {{Strategy synthesis for multi-dimensional quantitative objectives}},
  doi          = {10.1007/s00236-013-0182-6},
  volume       = {51},
  year         = {2014},
}

@article{2852,
  abstract     = {A robust combiner for hash functions takes two candidate implementations and constructs a hash function which is secure as long as at least one of the candidates is secure. So far, hash function combiners only aim at preserving a single property such as collision-resistance or pseudorandomness. However, when hash functions are used in protocols like TLS they are often required to provide several properties simultaneously. We therefore put forward the notion of robust multi-property combiners and elaborate on different definitions for such combiners. We then propose a combiner that provably preserves (target) collision-resistance, pseudorandomness, and being a secure message authentication code. This combiner satisfies the strongest notion we propose, which requires that the combined function satisfies every security property which is satisfied by at least one of the underlying hash function. If the underlying hash functions have output length n, the combiner has output length 2 n. This basically matches a known lower bound for black-box combiners for collision-resistance only, thus the other properties can be achieved without penalizing the length of the hash values. We then propose a combiner which also preserves the property of being indifferentiable from a random oracle, slightly increasing the output length to 2 n+ω(log n). Moreover, we show how to augment our constructions in order to make them also robust for the one-wayness property, but in this case require an a priory upper bound on the input length.},
  author       = {Fischlin, Marc and Lehmann, Anja and Pietrzak, Krzysztof Z},
  journal      = {Journal of Cryptology},
  number       = {3},
  pages        = {397 -- 428},
  publisher    = {Springer},
  title        = {{Robust multi-property combiners for hash functions}},
  doi          = {10.1007/s00145-013-9148-7},
  volume       = {27},
  year         = {2014},
}

@inproceedings{2905,
  abstract     = {Persistent homology is a recent grandchild of homology that has found use in
science and engineering as well as in mathematics. This paper surveys the method as well
as the applications, neglecting completeness in favor of highlighting ideas and directions.},
  author       = {Edelsbrunner, Herbert and Morozovy, Dmitriy},
  location     = {Kraków, Poland},
  pages        = {31 -- 50},
  publisher    = {European Mathematical Society Publishing House},
  title        = {{Persistent homology: Theory and practice}},
  doi          = {10.4171/120-1/3},
  year         = {2014},
}

@article{3263,
  abstract     = {Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.},
  author       = {Tkacik, Gasper and Ghosh, Anandamohan and Schneidman, Elad and Segev, Ronen},
  journal      = {PLoS One},
  number       = {1},
  publisher    = {Public Library of Science},
  title        = {{Adaptation to changes in higher-order stimulus statistics in the salamander retina}},
  doi          = {10.1371/journal.pone.0085841},
  volume       = {9},
  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},
}

