@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}, } @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 = {EMS Press}, title = {{Persistent homology: Theory and practice}}, doi = {10.4171/120-1/3}, year = {2014}, } @article{1904, abstract = {We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation with a time-dependent potential and we show the existence of the wave operator in Schatten spaces.}, author = {Frank, Rupert and Lewin, Mathieu and Lieb, Élliott and Seiringer, Robert}, journal = {Journal of the European Mathematical Society}, number = {7}, pages = {1507 -- 1526}, publisher = {EMS Press}, title = {{Strichartz inequality for orthonormal functions}}, doi = {10.4171/JEMS/467}, volume = {16}, year = {2014}, } @article{2233, abstract = { A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, valuing a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by λi, where the discount factor λ is a fixed rational number greater than 1. The value of a word is the minimal value of the automaton runs on it. Discounted summation is a common and useful measuring scheme, especially for infinite sequences, reflecting the assumption that earlier weights are more important than later weights. Unfortunately, determinization of NDAs, which is often essential in formal verification, is, in general, not possible. We provide positive news, showing that every NDA with an integral discount factor is determinizable. We complete the picture by proving that the integers characterize exactly the discount factors that guarantee determinizability: for every nonintegral rational discount factor λ, there is a nondeterminizable λ-NDA. We also prove that the class of NDAs with integral discount factors enjoys closure under the algebraic operations min, max, addition, and subtraction, which is not the case for general NDAs nor for deterministic NDAs. For general NDAs, we look into approximate determinization, which is always possible as the influence of a word's suffix decays. We show that the naive approach, of unfolding the automaton computations up to a sufficient level, is doubly exponential in the discount factor. We provide an alternative construction for approximate determinization, which is singly exponential in the discount factor, in the precision, and in the number of states. We also prove matching lower bounds, showing that the exponential dependency on each of these three parameters cannot be avoided. All our results hold equally for automata over finite words and for automata over infinite words. }, author = {Boker, Udi and Henzinger, Thomas A}, issn = {1860-5974}, journal = {Logical Methods in Computer Science}, number = {1}, publisher = {International Federation for Computational Logic}, title = {{Exact and approximate determinization of discounted-sum automata}}, doi = {10.2168/LMCS-10(1:10)2014}, volume = {10}, year = {2014}, } @article{2234, abstract = {We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with κ limit-average functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the case of one limit-average function, both randomization and memory are necessary for strategies even for ε-approximation, and that finite-memory randomized strategies are sufficient for achieving Pareto optimal values. Under the satisfaction objective, in contrast to the case of one limit-average function, infinite memory is necessary for strategies achieving a specific value (i.e. randomized finite-memory strategies are not sufficient), whereas memoryless randomized strategies are sufficient for ε-approximation, for all ε > 0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be ε-approximated in time polynomial in the size of the MDP and 1/ε, and exponential in the number of limit-average functions, for all ε > 0. Our analysis also reveals flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, corrects the flaws, and allows us to obtain improved results.}, author = {Brázdil, Tomáš and Brožek, Václav and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín}, issn = {1860-5974}, journal = {Logical Methods in Computer Science}, number = {1}, publisher = {International Federation for Computational Logic}, title = {{Markov decision processes with multiple long-run average objectives}}, doi = {10.2168/LMCS-10(1:13)2014}, volume = {10}, 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{2027, abstract = {We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the state space. Our framework focuses on probabilistic reachability, which is a core property for verification, and is illustrated through two distinct instantiations. The first assumes that full knowledge of the MDP is available, and performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP, and yields probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. The latter is the first extension of statistical model checking for unbounded properties inMDPs. In contrast with other related techniques, our approach is not restricted to time-bounded (finite-horizon) or discounted properties, nor does it assume any particular properties of the MDP. We also show how our methods extend to LTL objectives. We present experimental results showing the performance of our framework on several examples.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Chmelik, Martin and Forejt, Vojtěch and Kretinsky, Jan and Kwiatkowska, Marta and Parker, David and Ujma, Mateusz}, booktitle = {12th International Symposium on Automated Technology for Verification and Analysis}, location = {Sydney, Australia}, pages = {98 -- 114}, publisher = {Springer}, title = {{Verification of Markov decision processes using learning algorithms}}, doi = {10.1007/978-3-319-11936-6_8}, volume = {8837}, year = {2014}, } @article{2028, abstract = {Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model.}, author = {Bodova, Katarina and Paydarfar, David and Forger, Daniel}, journal = {Journal of Theoretical Biology}, pages = {40 -- 54}, publisher = {Academic Press}, title = {{Characterizing spiking in noisy type II neurons}}, doi = {10.1016/j.jtbi.2014.09.041}, volume = {365}, year = {2014}, } @misc{5415, abstract = {Recently there has been a significant effort to add quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, several basic system properties such as average response time cannot be expressed with weighted automata. In this work, we introduce nested weighted automata as a new formalism for expressing important quantitative properties such as average response time. We establish an almost complete decidability picture for the basic decision problems for nested weighted automata, and illustrate its applicability in several domains. }, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, issn = {2664-1690}, pages = {27}, publisher = {IST Austria}, title = {{Nested weighted automata}}, doi = {10.15479/AT:IST-2014-170-v1-1}, year = {2014}, } @article{2038, abstract = {Recently, there has been an effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions. At the heart of quantitative objectives lies the accumulation of values along a computation. It is often the accumulated sum, as with energy objectives, or the accumulated average, as with mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point in time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire infinite computation. We study the border of decidability for such quantitative extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with both prefix-accumulation assertions, or extending LTL with both path-accumulation assertions, results in temporal logics whose model-checking problem is decidable. Moreover, the prefix-accumulation assertions may be generalized with "controlled accumulation," allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that this branching-time logic is, in a sense, the maximal logic with one or both of the prefix-accumulation assertions that permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL, makes the problem undecidable.}, author = {Boker, Udi and Chatterjee, Krishnendu and Henzinger, Thomas A and Kupferman, Orna}, journal = {ACM Transactions on Computational Logic}, number = {4}, publisher = {ACM}, title = {{Temporal specifications with accumulative values}}, doi = {10.1145/2629686}, volume = {15}, year = {2014}, } @inproceedings{1903, abstract = {We consider two-player zero-sum partial-observation stochastic games on graphs. Based on the information available to the players these games can be classified as follows: (a) general partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) perfect-observation (both players have complete view of the game). The one-sided partial-observation games subsumes the important special case of one-player partial-observation stochastic games (or partial-observation Markov decision processes (POMDPs)). Based on the randomization available for the strategies, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. We consider all these classes of games with reachability, and parity objectives that can express all ω-regular objectives. The analysis problems are classified into the qualitative analysis that asks for the existence of a strategy that ensures the objective with probability 1; and the quantitative analysis that asks for the existence of a strategy that ensures the objective with probability at least λ (0,1). In this talk we will cover a wide range of results: for perfect-observation games; for POMDPs; for one-sided partial-observation games; and for general partial-observation games.}, author = {Chatterjee, Krishnendu}, location = {Budapest, Hungary}, number = {PART 1}, pages = {1 -- 4}, publisher = {Springer}, title = {{Partial-observation stochastic reachability and parity games}}, doi = {10.1007/978-3-662-44522-8_1}, volume = {8634}, year = {2014}, } @article{2211, abstract = {In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Our main results for pure strategies are as follows: (1) For one-sided games with player 2 having perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algorithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 having perfect observation we show that nonelementarymemory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least nonelementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibit serious flaws in previous results of the literature: we show a nonelementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, journal = {ACM Transactions on Computational Logic}, number = {2}, publisher = {ACM}, title = {{Partial-observation stochastic games: How to win when belief fails}}, doi = {10.1145/2579821}, volume = {15}, year = {2014}, } @inproceedings{2054, abstract = {We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in (n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.}, author = {Chatterjee, Krishnendu}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, editor = {Baldan, Paolo and Gorla, Daniele}, location = {Rome, Italy}, pages = {544 -- 559}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Qualitative concurrent parity games: Bounded rationality}}, doi = {10.1007/978-3-662-44584-6_37}, volume = {8704}, year = {2014}, } @article{535, abstract = {Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP∩co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon}, journal = {Algorithmica}, number = {3}, pages = {457 -- 492}, publisher = {Springer}, title = {{Polynomial-time algorithms for energy games with special weight structures}}, doi = {10.1007/s00453-013-9843-7}, volume = {70}, year = {2014}, } @inproceedings{1872, abstract = {Extensionality axioms are common when reasoning about data collections, such as arrays and functions in program analysis, or sets in mathematics. An extensionality axiom asserts that two collections are equal if they consist of the same elements at the same indices. Using extensionality is often required to show that two collections are equal. A typical example is the set theory theorem (∀x)(∀y)x∪y = y ∪x. Interestingly, while humans have no problem with proving such set identities using extensionality, they are very hard for superposition theorem provers because of the calculi they use. In this paper we show how addition of a new inference rule, called extensionality resolution, allows first-order theorem provers to easily solve problems no modern first-order theorem prover can solve. We illustrate this by running the VAMPIRE theorem prover with extensionality resolution on a number of set theory and array problems. Extensionality resolution helps VAMPIRE to solve problems from the TPTP library of first-order problems that were never solved before by any prover.}, author = {Gupta, Ashutosh and Kovács, Laura and Kragl, Bernhard and Voronkov, Andrei}, booktitle = {12th International Symposium on Automated Technology for Verification and Analysis}, location = {Sydney, Australia}, pages = {185 -- 200}, publisher = {Springer}, title = {{Extensional crisis and proving identity}}, doi = {10.1007/978-3-319-11936-6_14}, volume = {8837}, year = {2014}, } @article{1999, abstract = {Selection for disease control is believed to have contributed to shape the organisation of insect societies — leading to interaction patterns that mitigate disease transmission risk within colonies, conferring them ‘organisational immunity’. Recent studies combining epidemiological models with social network analysis have identified general properties of interaction networks that may hinder propagation of infection within groups. These can be prophylactic and/or induced upon pathogen exposure. Here we review empirical evidence for these two types of organisational immunity in social insects and describe the individual-level behaviours that underlie it. We highlight areas requiring further investigation, and emphasise the need for tighter links between theory and empirical research and between individual-level and collective-level analyses.}, author = {Stroeymeyt, Nathalie and Casillas Perez, Barbara E and Cremer, Sylvia}, journal = {Current Opinion in Insect Science}, number = {1}, pages = {1 -- 15}, publisher = {Elsevier}, title = {{Organisational immunity in social insects}}, doi = {10.1016/j.cois.2014.09.001}, volume = {5}, year = {2014}, } @article{10895, abstract = {Due to their sessile lifestyles, plants need to deal with the limitations and stresses imposed by the changing environment. Plants cope with these by a remarkable developmental flexibility, which is embedded in their strategy to survive. Plants can adjust their size, shape and number of organs, bend according to gravity and light, and regenerate tissues that were damaged, utilizing a coordinating, intercellular signal, the plant hormone, auxin. Another versatile signal is the cation, Ca2+, which is a crucial second messenger for many rapid cellular processes during responses to a wide range of endogenous and environmental signals, such as hormones, light, drought stress and others. Auxin is a good candidate for one of these Ca2+-activating signals. However, the role of auxin-induced Ca2+ signaling is poorly understood. Here, we will provide an overview of possible developmental and physiological roles, as well as mechanisms underlying the interconnection of Ca2+ and auxin signaling. }, author = {Vanneste, Steffen and Friml, Jiří}, issn = {2223-7747}, journal = {Plants}, keywords = {Plant Science, Ecology, Ecology, Evolution, Behavior and Systematics}, number = {4}, pages = {650--675}, publisher = {MDPI}, title = {{Calcium: The missing link in auxin action}}, doi = {10.3390/plants2040650}, volume = {2}, year = {2013}, } @inproceedings{10897, abstract = {Taking images is an efficient way to collect data about the physical world. It can be done fast and in exquisite detail. By definition, image processing is the field that concerns itself with the computation aimed at harnessing the information contained in images [10]. This talk is concerned with topological information. Our main thesis is that persistent homology [5] is a useful method to quantify and summarize topological information, building a bridge that connects algebraic topology with applications. We provide supporting evidence for this thesis by touching upon four technical developments in the overlap between persistent homology and image processing.}, author = {Edelsbrunner, Herbert}, booktitle = {Graph-Based Representations in Pattern Recognition}, isbn = {9783642382208}, issn = {1611-3349}, location = {Vienna, Austria}, pages = {182--183}, publisher = {Springer Nature}, title = {{Persistent homology in image processing}}, doi = {10.1007/978-3-642-38221-5_19}, volume = {7877}, year = {2013}, }