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Publications of John Harer    :chronological  alphabetical  combined listing:

%% Books   
@book{fds324398,
   Author = {Edelsbrunner, H and Harer, J},
   Title = {Computational Topology - an Introduction.},
   Publisher = {American Mathematical Society},
   Year = {2010},
   ISBN = {978-0-8218-4925-5},
   Abstract = {This book is an introduction to computational topology for
             students in Computer Science and Mathematics.},
   Key = {fds324398}
}

@book{fds10018,
   Author = {Penner, R. C. and Harer, J. L.},
   Title = {Combinatorics of train tracks},
   Journal = {pp. xii+216, 1992, Princeton University Press, Princeton,
             NJ},
   MRNUMBER = {94b:57018},
   url = {http://www.ams.org/mathscinet-getitem?mr=94b:57018},
   Key = {fds10018}
}


%% Papers Published   
@article{fds324397,
   Author = {Bendich, P and Chin, SP and Clark, J and Desena, J and Harer, J and Munch,
             E and Newman, A and Porter, D and Rouse, D and Strawn, N and Watkins,
             A},
   Title = {Topological and statistical behavior classifiers for
             tracking applications},
   Journal = {IEEE Transactions on Aerospace and Electronic
             Systems},
   Volume = {52},
   Number = {6},
   Pages = {2644-2661},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1109/TAES.2016.160405},
   Abstract = {© 1965-2011 IEEE.This paper introduces a method to
             integrate target behavior into the multiple hypothesis
             tracker (MHT) likelihood ratio. In particular, a periodic
             track appraisal based on behavior is introduced. The track
             appraisal uses elementary topological data analysis coupled
             with basic machine-learning techniques, and it adjusts the
             traditional kinematic data association likelihood (i.e.,
             track score) using an established formulation for
             feature-aided data association. The proposed method is
             tested and demonstrated on synthetic vehicular data
             representing an urban traffic scene generated by the
             Simulation of Urban Mobility package. The vehicles in the
             scene exhibit different driving behaviors. The proposed
             method distinguishes those behaviors and shows improved data
             association decisions relative to a conventional, kinematic
             MHT.},
   Doi = {10.1109/TAES.2016.160405},
   Key = {fds324397}
}

@article{fds321990,
   Author = {Bendich, P and Gasparovic, E and Harer, J and Tralie,
             C},
   Title = {Geometric models for musical audio data},
   Journal = {LIPIcs},
   Volume = {51},
   Pages = {65.1-65.5},
   Year = {2016},
   Month = {June},
   ISBN = {9783959770095},
   url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.65},
   Abstract = {© Paul Bendich, Ellen Gasparovic, John Harer, and
             Christopher Tralie. We study the geometry of sliding window
             embeddings of audio features that summarize perceptual
             information about audio, including its pitch and timbre.
             These embeddings can be viewed as point clouds in high
             dimensions, and we add structure to the point clouds using a
             cover tree with adaptive thresholds based on multi-scale
             local principal component analysis to automatically assign
             points to clusters. We connect neighboring clusters in a
             scaffolding graph, and we use knowledge of stratified space
             structure to refine our estimates of dimension in each
             cluster, demonstrating in our music applications that
             choruses and verses have higher dimensional structure, while
             transitions between them are lower dimensional. We showcase
             our technique with an interactive web-based application
             powered by Javascript and WebGL which plays music
             synchronized with a principal component analysis embedding
             of the point cloud down to 3D. We also render the clusters
             and the scaffolding on top of this projection to visualize
             the transitions between different sections of the
             music.},
   Doi = {10.4230/LIPIcs.SoCG.2016.65},
   Key = {fds321990}
}

@article{fds243563,
   Author = {Perea, JA and Deckard, A and Haase, SB and Harer,
             J},
   Title = {SW1PerS: Sliding windows and 1-persistence scoring;
             discovering periodicity in gene expression time series
             data.},
   Journal = {BMC Bioinformatics},
   Volume = {16},
   Pages = {257},
   Year = {2015},
   Month = {August},
   url = {http://dx.doi.org/10.1186/s12859-015-0645-6},
   Abstract = {Identifying periodically expressed genes across different
             processes (e.g. the cell and metabolic cycles, circadian
             rhythms, etc) is a central problem in computational biology.
             Biological time series may contain (multiple) unknown signal
             shapes of systemic relevance, imperfections like noise,
             damping, and trending, or limited sampling density. While
             there exist methods for detecting periodicity, their design
             biases (e.g. toward a specific signal shape) can limit their
             applicability in one or more of these situations.We present
             in this paper a novel method, SW1PerS, for quantifying
             periodicity in time series in a shape-agnostic manner and
             with resistance to damping. The measurement is performed
             directly, without presupposing a particular pattern, by
             evaluating the circularity of a high-dimensional
             representation of the signal. SW1PerS is compared to other
             algorithms using synthetic data and performance is
             quantified under varying noise models, noise levels,
             sampling densities, and signal shapes. Results on biological
             data are also analyzed and compared.On the task of
             periodic/not-periodic classification, using synthetic data,
             SW1PerS outperforms all other algorithms in the low-noise
             regime. SW1PerS is shown to be the most shape-agnostic of
             the evaluated methods, and the only one to consistently
             classify damped signals as highly periodic. On biological
             data, and for several experiments, the lists of top 10%
             genes ranked with SW1PerS recover up to 67% of those
             generated with other popular algorithms. Moreover, the list
             of genes from data on the Yeast metabolic cycle which are
             highly-ranked only by SW1PerS, contains evidently non-cosine
             patterns (e.g. ECM33, CDC9, SAM1,2 and MSH6) with highly
             periodic expression profiles. In data from the Yeast cell
             cycle SW1PerS identifies genes not preferred by other
             algorithms, hence not previously reported as periodic, but
             found in other experiments such as the universal growth rate
             response of Slavov. These genes are BOP3, CDC10, YIL108W,
             YER034W, MLP1, PAC2 and RTT101.In biological systems with
             low noise, i.e. where periodic signals with interesting
             shapes are more likely to occur, SW1PerS can be used as a
             powerful tool in exploratory analyses. Indeed, by having an
             initial set of periodic genes with a rich variety of signal
             types, pattern/shape information can be included in the
             study of systems and the generation of hypotheses regarding
             the structure of gene regulatory networks.},
   Doi = {10.1186/s12859-015-0645-6},
   Key = {fds243563}
}

@article{fds303544,
   Author = {Munch, E and Turner, K and Bendich, P and Mukherjee, S and Mattingly, J and Harer, J},
   Title = {Probabilistic Fréchet Means for Time Varying Persistence
             Diagrams},
   Volume = {9},
   Number = {1},
   Pages = {1173-1204},
   Year = {2015},
   Month = {January},
   url = {http://arxiv.org/abs/1307.6530v3},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. In 2011, Mileyko and his
             collaborators made the first study of the properties of the
             Fr\'echet mean in $(\mathcal{D}_p,W_p)$, the space of
             persistence diagrams equipped with the p-th Wasserstein
             metric. In particular, they showed that the Fr\'echet mean
             of a finite set of diagrams always exists, but is not
             necessarily unique. The means of a continuously-varying set
             of diagrams do not themselves (necessarily) vary
             continuously, which presents obvious problems when trying to
             extend the Fr\'echet mean definition to the realm of
             vineyards. We fix this problem by altering the original
             definition of Fr\'echet mean so that it now becomes a
             probability measure on the set of persistence diagrams; in a
             nutshell, the mean of a set of diagrams will be a weighted
             sum of atomic measures, where each atom is itself a
             persistence diagram determined using a perturbation of the
             input diagrams. This definition gives for each $N$ a map
             $(\mathcal{D}_p)^N \to \mathbb{P}(\mathcal{D}_p)$. We show
             that this map is H\"older continuous on finite diagrams and
             thus can be used to build a useful statistic on time-varying
             persistence diagrams, better known as vineyards.},
   Doi = {10.1214/15-EJS1030},
   Key = {fds303544}
}

@article{fds321992,
   Author = {Rouse, D and Watkins, A and Porter, D and Harer, J and Bendich, P and Strawn, N and Munch, E and Desena, J and Clarke, J and Gilbert, J and Chin,
             S and Newman, A},
   Title = {Feature-aided multiple hypothesis tracking using topological
             and statistical behavior classifiers},
   Journal = {Proceedings of SPIE - The International Society for Optical
             Engineering},
   Volume = {9474},
   Year = {2015},
   Month = {January},
   ISBN = {9781628415902},
   ISSN = {10.1117/12.2179555},
   url = {http://dx.doi.org/10.1117/12.2179555},
   Abstract = {© 2015 SPIE. This paper introduces a method to integrate
             target behavior into the multiple hypothesis tracker (MHT)
             likelihood ratio. In particular, a periodic track appraisal
             based on behavior is introduced that uses elementary
             topological data analysis coupled with basic machine
             learning techniques. The track appraisal adjusts the
             traditional kinematic data association likelihood (i.e.,
             track score) using an established formulation for
             classification-aided data association. The proposed method
             is tested and demonstrated on synthetic vehicular data
             representing an urban traffic scene generated by the
             Simulation of Urban Mobility package. The vehicles in the
             scene exhibit different driving behaviors. The proposed
             method distinguishes those behaviors and shows improved data
             association decisions relative to a conventional, kinematic
             MHT.},
   Doi = {10.1117/12.2179555},
   Key = {fds321992}
}

@article{fds243564,
   Author = {Farr, RS and Harer, JL and Fink, TMA},
   Title = {Easily repairable networks: reconnecting nodes after
             damage.},
   Journal = {Physical Review Letters},
   Volume = {113},
   Number = {13},
   Pages = {138701},
   Year = {2014},
   Month = {September},
   ISSN = {0031-9007},
   url = {http://dx.doi.org/10.1103/physrevlett.113.138701},
   Abstract = {We introduce a simple class of distribution networks that
             withstand damage by being repairable instead of redundant.
             Instead of asking how hard it is to disconnect nodes through
             damage, we ask how easy it is to reconnect nodes after
             damage. We prove that optimal networks on regular lattices
             have an expected cost of reconnection proportional to the
             lattice length, and that such networks have exactly three
             levels of structural hierarchy. We extend our results to
             networks subject to repeated attacks, in which the repairs
             themselves must be repairable. We find that, in exchange for
             a modest increase in repair cost, such networks are able to
             withstand any number of attacks.},
   Doi = {10.1103/physrevlett.113.138701},
   Key = {fds243564}
}

@article{fds323579,
   Author = {Bristow, SL and Leman, AR and Simmons Kovacs and LA and Deckard, A and Harer, J and Haase, SB},
   Title = {Checkpoints couple transcription network oscillator dynamics
             to cell-cycle progression.},
   Journal = {Genome Biology: biology for the post-genomic
             era},
   Volume = {15},
   Number = {9},
   Pages = {446},
   Year = {2014},
   Month = {September},
   url = {http://dx.doi.org/10.1186/preaccept-1107846495134380},
   Abstract = {The coupling of cyclin dependent kinases (CDKs) to an
             intrinsically oscillating network of transcription factors
             has been proposed to control progression through the cell
             cycle in budding yeast, Saccharomyces cerevisiae. The
             transcription network regulates the temporal expression of
             many genes, including cyclins, and drives cell-cycle
             progression, in part, by generating successive waves of
             distinct CDK activities that trigger the ordered program of
             cell-cycle events. Network oscillations continue
             autonomously in mutant cells arrested by depletion of CDK
             activities, suggesting the oscillator can be uncoupled from
             cell-cycle progression. It is not clear what mechanisms, if
             any, ensure that the network oscillator is restrained when
             progression in normal cells is delayed or arrested. A recent
             proposal suggests CDK acts as a master regulator of
             cell-cycle processes that have the potential for autonomous
             oscillatory behavior.Here we find that mitotic CDK is not
             sufficient for fully inhibiting transcript oscillations in
             arrested cells. We do find that activation of the DNA
             replication and spindle assembly checkpoints can fully
             arrest the network oscillator via overlapping but distinct
             mechanisms. Further, we demonstrate that the DNA replication
             checkpoint effector protein, Rad53, acts to arrest a portion
             of transcript oscillations in addition to its role in
             halting cell-cycle progression.Our findings indicate that
             checkpoint mechanisms, likely via phosphorylation of network
             transcription factors, maintain coupling of the network
             oscillator to progression during cell-cycle
             arrest.},
   Doi = {10.1186/preaccept-1107846495134380},
   Key = {fds323579}
}

@article{fds243565,
   Author = {Turner, K and Mileyko, Y and Mukherjee, S and Harer,
             J},
   Title = {Fréchet Means for Distributions of Persistence
             Diagrams},
   Journal = {Discrete & Computational Geometry},
   Volume = {52},
   Number = {1},
   Pages = {44-70},
   Year = {2014},
   Month = {July},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-014-9604-7},
   Abstract = {Given a distribution ρ on persistence diagrams and
             observations X1,...Xn∼iidρ we introduce an algorithm in
             this paper that estimates a Fr\'echet mean from the set of
             diagrams X1,...Xn. If the underlying measure ρ is a
             combination of Dirac masses ρ=1m∑mi=1δZi then we prove
             the algorithm converges to a local minimum and a law of
             large numbers result for a Fr\'echet mean computed by the
             algorithm given observations drawn iid from ρ. We
             illustrate the convergence of an empirical mean computed by
             the algorithm to a population mean by simulations from
             Gaussian random fields.},
   Doi = {10.1007/s00454-014-9604-7},
   Key = {fds243565}
}

@article{fds221199,
   Author = {Elizabeth Munch and Paul Bendich and Katharine Turner and Sayan
             Mukherjee, Jonathan Mattingly and John Harer},
   Title = {Probabilistic Fréchet Means and Statistics on
             Vineyards},
   Year = {2014},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. Mileyko and his
             collaborators made the first study of the properties of the
             Fr\'{e}chet mean in (Dp,Wp), the space of persistence
             diagrams equipped with the p-th Wasserstein metric. In
             particular, they showed that the Fr\'{e}chet mean of a
             finite set of diagrams always exists, but is not necessarily
             unique. As an unfortunate consequence, one sees that the
             means of a continuously-varying set of diagrams do not
             themselves vary continuously, which presents obvious
             problems when trying to extend the Fr\'{e}chet mean
             definition to the realm of vineyards. We fix this problem by
             altering the original definition of Fr\'{e}chet mean so that
             it now becomes a probability measure on the set of
             persistence diagrams; in a nutshell, the mean of a set of
             diagrams will be a weighted sum of atomic measures, where
             each atom is itself the (Fr\'{e}chet mean) persistence
             diagram of a perturbation of the input diagrams. We show
             that this new definition defines a (H\"older) continuous
             map, for each k, from (Dp)k→P(Dp), and we present several
             examples to show how it may become a useful statistic on
             vineyards.},
   Key = {fds221199}
}

@article{fds243562,
   Author = {Perea, JA and Harer, J},
   Title = {Sliding Windows and Persistence: An Application of
             Topological Methods to Signal Analysis},
   Journal = {Foundations of Computational Mathematics},
   Volume = {15},
   Number = {3},
   Pages = {799-838},
   Year = {2014},
   ISSN = {1615-3375},
   url = {http://dx.doi.org/10.1007/s10208-014-9206-z},
   Abstract = {© 2014, SFoCM.We develop in this paper a theoretical
             framework for the topological study of time series data.
             Broadly speaking, we describe geometrical and topological
             properties of sliding window embeddings, as seen through the
             lens of persistent homology. In particular, we show that
             maximum persistence at the point-cloud level can be used to
             quantify periodicity at the signal level, prove structural
             and convergence theorems for the resulting persistence
             diagrams, and derive estimates for their dependency on
             window size and embedding dimension. We apply this
             methodology to quantifying periodicity in synthetic data
             sets and compare the results with those obtained using
             state-of-the-art methods in gene expression analysis. We
             call this new method SW1PerS, which stands for Sliding
             Windows and 1-Dimensional Persistence Scoring.},
   Doi = {10.1007/s10208-014-9206-z},
   Key = {fds243562}
}

@article{fds303543,
   Author = {Perea, J and Harer, J},
   Title = {Sliding Windows and Persistence: An Application of
             Topological Methods to Signal Analysis},
   Year = {2013},
   Month = {July},
   url = {http://arxiv.org/abs/1307.6188v2},
   Abstract = {We develop in this paper a theoretical framework for the
             topological study of time series data. Broadly speaking, we
             describe geometrical and topological properties of sliding
             window (or time-delay) embeddings, as seen through the lens
             of persistent homology. In particular, we show that maximum
             persistence at the point-cloud level can be used to quantify
             periodicity at the signal level, prove structural and
             convergence theorems for the resulting persistence diagrams,
             and derive estimates for their dependency on window size and
             embedding dimension. We apply this methodology to
             quantifying periodicity in synthetic data sets, and compare
             the results with those obtained using state-of-the-art
             methods in gene expression analysis. We call this new method
             SW1PerS which stands for Sliding Windows and 1-dimensional
             Persistence Scoring.},
   Key = {fds303543}
}

@article{fds243566,
   Author = {Topp, CN and Iyer-Pascuzzi, AS and Anderson, JT and Lee, C-R and Zurek,
             PR and Symonova, O and Zheng, Y and Bucksch, A and Mileyko, Y and Galkovskyi, T and Moore, BT and Harer, J and Edelsbrunner, H and Mitchell-Olds, T and Weitz, JS and Benfey, PN},
   Title = {3D phenotyping and quantitative trait locus mapping identify
             core regions of the rice genome controlling root
             architecture.},
   Journal = {Proceedings of the National Academy of Sciences of
             USA},
   Volume = {110},
   Number = {18},
   Pages = {E1695-E1704},
   Year = {2013},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23580618},
   Abstract = {Identification of genes that control root system
             architecture in crop plants requires innovations that enable
             high-throughput and accurate measurements of root system
             architecture through time. We demonstrate the ability of a
             semiautomated 3D in vivo imaging and digital phenotyping
             pipeline to interrogate the quantitative genetic basis of
             root system growth in a rice biparental mapping population,
             Bala × Azucena. We phenotyped >1,400 3D root models and
             >57,000 2D images for a suite of 25 traits that quantified
             the distribution, shape, extent of exploration, and the
             intrinsic size of root networks at days 12, 14, and 16 of
             growth in a gellan gum medium. From these data we identified
             89 quantitative trait loci, some of which correspond to
             those found previously in soil-grown plants, and provide
             evidence for genetic tradeoffs in root growth allocations,
             such as between the extent and thoroughness of exploration.
             We also developed a multivariate method for generating and
             mapping central root architecture phenotypes and used it to
             identify five major quantitative trait loci (r(2) = 24-37%),
             two of which were not identified by our univariate analysis.
             Our imaging and analytical platform provides a means to
             identify genes with high potential for improving root traits
             and agronomic qualities of crops.},
   Doi = {10.1073/pnas.1304354110},
   Key = {fds243566}
}

@article{fds221197,
   Author = {Christopher N Topp and Anjali S Iyer-Pascuzzi and Jill T Anderson and Cheng-Ruei Lee and Paul R Zurek and Olga Symonova and Ying Zheng and Alexander Bucksch and Yuriy Milyeko and Taras Galkovskyi and Brad
             Moore, John Harer and Herbert Edelsbrunner and Thomas Mitchell
             Olds and Joshua S Weitz and Philip N Benfey},
   Title = {3-dimensional phenotyping of growing root systems combined
             with QTL mapping identifies core regions of the rice genome
             controlling root architecture},
   Journal = {PNAS},
   Year = {2013},
   Abstract = {Identification of genes that control root system
             architecture in crop plants requires innovations that enable
             high-throughput and accurate measurements of root system
             architecture through time. We demonstrate the ability of a
             semiautomated 3D in vivo imaging and digital phenotyping
             pipeline to interrogate the quantitative genetic basis of
             root system growth in a rice biparental mapping population,
             Bala × Azucena. We phenotyped >1,400 3D root models and
             >57,000 2D images for a suite of 25 traits that quantified
             the distribution, shape, extent of exploration, and the
             intrinsic size of root networks at days 12, 14, and 16 of
             growth in a gellan gum medium. From these data we identified
             89 quantitative trait loci, some of which correspond to
             those found previously in soil-grown plants, and provide
             evidence for genetic tradeoffs in root growth allocations,
             such as between the extent and thoroughness of exploration.
             We also developed a multivariate method for generating and
             mapping central root architecture phenotypes and used it to
             identify five major quantitative trait loci (r2 = 24–37%),
             two of which were not identified by our univariate analysis.
             Our imaging and analytical platform provides a means to
             identify genes with high potential for improving root traits
             and agronomic qualities of crops.},
   Key = {fds221197}
}

@article{fds243595,
   Author = {Topp, and CN, and Iyer-Pascuzzi, AS and Anderson, JT and Lee, C-R and Zurek, PR and Symonova, O and Zheng, Y and Bucksch, A and Milyeko, Y and Galkovskyi, T and Moore, BT and Harer, J and Edelsbrunner, H and Mitchell-Olds, T and Weitz, JS and Benfey, PN},
   Title = {3-dimensional phenotyping of growing root systems and QTL
             mapping identifies core regions of the rice genome
             controlling root architecture},
   Journal = {PNAS},
   Volume = {110},
   Pages = {E1695-1704},
   Year = {2013},
   Key = {fds243595}
}

@article{fds243596,
   Author = {Galkovskyi, T and Mileyko, Y and Bucksch, A and Moore, B and Symonova,
             O and Price, CA and Topp, CN and Iyer-Pascuzzi, AS and Zurek, PR and Fang,
             S and Harer, J and Benfey, PN and Weitz, JS},
   Title = {GiA Roots: software for the high throughput analysis of
             plant root system architecture.},
   Journal = {BMC Plant Biology},
   Volume = {12},
   Number = {116},
   Pages = {116},
   Year = {2012},
   Month = {July},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22834569},
   Abstract = {BACKGROUND: Characterizing root system architecture (RSA) is
             essential to understanding the development and function of
             vascular plants. Identifying RSA-associated genes also
             represents an underexplored opportunity for crop
             improvement. Software tools are needed to accelerate the
             pace at which quantitative traits of RSA are estimated from
             images of root networks. RESULTS: We have developed GiA
             Roots (General Image Analysis of Roots), a semi-automated
             software tool designed specifically for the high-throughput
             analysis of root system images. GiA Roots includes
             user-assisted algorithms to distinguish root from background
             and a fully automated pipeline that extracts dozens of root
             system phenotypes. Quantitative information on each
             phenotype, along with intermediate steps for full
             reproducibility, is returned to the end-user for downstream
             analysis. GiA Roots has a GUI front end and a command-line
             interface for interweaving the software into large-scale
             workflows. GiA Roots can also be extended to estimate novel
             phenotypes specified by the end-user. CONCLUSIONS: We
             demonstrate the use of GiA Roots on a set of 2393 images of
             rice roots representing 12 genotypes from the species Oryza
             sativa. We validate trait measurements against prior
             analyses of this image set that demonstrated that RSA traits
             are likely heritable and associated with genotypic
             differences. Moreover, we demonstrate that GiA Roots is
             extensible and an end-user can add functionality so that GiA
             Roots can estimate novel RSA traits. In summary, we show
             that the software can function as an efficient tool as part
             of a workflow to move from large numbers of root images to
             downstream analysis.},
   Doi = {10.1186/1471-2229-12-116},
   Key = {fds243596}
}

@article{fds303545,
   Author = {Turner, K and Mileyko, Y and Mukherjee, S and Harer,
             J},
   Title = {Fréchet Means for Distributions of Persistence
             diagrams},
   Year = {2012},
   Month = {June},
   url = {http://arxiv.org/abs/1206.2790v2},
   Abstract = {Given a distribution $\rho$ on persistence diagrams and
             observations $X_1,...X_n \stackrel{iid}{\sim} \rho$ we
             introduce an algorithm in this paper that estimates a
             Fr\'echet mean from the set of diagrams $X_1,...X_n$. If the
             underlying measure $\rho$ is a combination of Dirac masses
             $\rho = \frac{1}{m} \sum_{i=1}^m \delta_{Z_i}$ then we prove
             the algorithm converges to a local minimum and a law of
             large numbers result for a Fr\'echet mean computed by the
             algorithm given observations drawn iid from $\rho$. We
             illustrate the convergence of an empirical mean computed by
             the algorithm to a population mean by simulations from
             Gaussian random fields.},
   Key = {fds303545}
}

@article{fds243591,
   Author = {Munch, E and Shapiro, M and Harer, J},
   Title = {Failure filtrations for fenced sensor networks},
   Journal = {International Journal of Robotics Research},
   Volume = {31},
   Number = {9},
   Pages = {1044-1056},
   Year = {2012},
   ISSN = {0278-3649},
   url = {http://arxiv.org/abs/1109.6535v1},
   Abstract = {In this paper we consider the question of sensor network
             coverage for a two-dimensional domain. We seek to compute
             the probability that a set of sensors fails to cover given
             only non-metric, local (who is talking to whom) information
             and a probability distribution of failure of each node. This
             builds on the work of de Silva and Ghrist who analyzed this
             problem in the deterministic situation. We first show that
             it is part of a slightly larger class of problems which is
             #P-hard, and thus fast algorithms likely do not exist unless
             P = NP. The question of whether the specific problem is, in
             fact, #P-hard remains open. We then give a deterministic
             algorithm which is feasible in the case of a small set of
             sensors, and give a dynamic algorithm for an arbitrary set
             of sensors failing over time which utilizes a new criterion
             for coverage to give an early warning of potential failure.
             These algorithms build on the theory of topological
             persistence. © The Author(s) 2012.},
   Doi = {10.1177/0278364912451671},
   Key = {fds243591}
}

@article{fds243594,
   Author = {Deckard, A and Anafi, RC and Hogenesch, JB and Haase, SB and Harer,
             J},
   Title = {Design and Analysis of Large-Scale Biological Rhythm
             Studies: A Comparison of Algorithms for Detecting Periodic
             Signals in Biological Data},
   Journal = {PLOS Computational Biology},
   Volume = {29},
   Number = {24},
   Pages = {3174-3180},
   Year = {2012},
   url = {http://dx.doi.org/10.1093/bioinformatics/btt541},
   Abstract = {The results of a major year-long DARPA funded project to
             study the performance of a large collection of algorithms
             for finding periodic gene expression.},
   Doi = {10.1093/bioinformatics/btt541},
   Key = {fds243594}
}

@article{fds311264,
   Author = {Munch, E and Shapiro, M and Harer, J},
   Title = {Failure Filtrations for Fenced Sensor Networks},
   Year = {2011},
   Month = {September},
   url = {http://arxiv.org/abs/1109.6535v1},
   Abstract = {In this paper we consider the question of sensor network
             coverage for a 2-dimensional domain. We seek to compute the
             probability that a set of sensors fails to cover given only
             non-metric, local (who is talking to whom) information and a
             probability distribution of failure of each node. This
             builds on the work of de Silva and Ghrist who analyzed this
             problem in the deterministic situation. We first show that a
             it is part of a slightly larger class of problems which is
             #P-complete, and thus fast algorithms likely do not exist
             unless P$=$NP. We then give a deterministic algorithm which
             is feasible in the case of a small set of sensors, and give
             a dynamic algorithm for an arbitrary set of sensors failing
             over time which utilizes a new criterion for coverage based
             on the one proposed by de Silva and Ghrist. These algorithms
             build on the theory of topological persistence.},
   Doi = {10.1177/0278364912451671},
   Key = {fds311264}
}

@article{fds199103,
   Author = {Anjali S. Iyer-Pascuzzi and Christopher N. Topp and Jill T.
             Anderson and Cheng-Ruei Lee and Olga Symonova and Yuriy Mileyko and Taras Galkovsky and Ying Zheng and Randy Clark and Leon Kochian and Herbert Edelsbrunner and Joshua S. Weitz and Thomas Mitchell-Olds and John Harer and Philip N. Benfey},
   Title = {Quantitative Genetic Analysis of Root System Architecture in
             Rice Plant and Animal Genomes},
   Journal = {XX Genome Conference},
   Year = {2011},
   Key = {fds199103}
}

@article{fds243597,
   Author = {Bendich, P and Harer, J},
   Title = {Persistent Intersection Homology},
   Journal = {Foundations of Computational Mathematics},
   Volume = {11},
   Number = {3},
   Pages = {305-336},
   Year = {2011},
   ISSN = {1615-3375},
   url = {http://dx.doi.org/10.1007/s10208-010-9081-1},
   Abstract = {The theory of intersection homology was developed to study
             the singularities of a topologically stratified space. This
             paper incorporates this theory into the already developed
             framework of persistent homology. We demonstrate that
             persistent intersection homology gives useful information
             about the relationship between an embedded stratified space
             and its singularities. We give an algorithm for the
             computation of the persistent intersection homology groups
             of a filtered simplicial complex equipped with a
             stratification by subcomplexes, and we prove its
             correctness. We also derive, from Poincaré Duality, some
             structural results about persistent intersection homology.
             © 2010 SFoCM.},
   Doi = {10.1007/s10208-010-9081-1},
   Key = {fds243597}
}

@article{fds243598,
   Author = {Bendich, P and Galkovskyi, T and Harer, J},
   Title = {Improving homology estimates with random
             walks},
   Journal = {Inverse Problems},
   Volume = {27},
   Number = {12},
   Pages = {16},
   Year = {2011},
   ISSN = {0266-5611},
   url = {http://dx.doi.org/10.1088/0266-5611/27/12/124002},
   Abstract = {This experimental paper makes the case for a new approach to
             the use of persistent homology in the study of shape and
             feature in datasets. By introducing ideas from diffusion
             geometry and random walks, we discover that homological
             features can be enhanced and more effectively extracted from
             spaces that are sampled densely and evenly, and with a small
             amount of noise. This study paves the way for a more
             theoretical analysis of how random walk metrics affect
             persistence diagrams, and provides evidence that combining
             topological data analysis with techniques inspired by
             diffusion geometry holds great promise for new analyses of a
             wide variety of datasets. © 2011 IOP Publishing
             Ltd.},
   Doi = {10.1088/0266-5611/27/12/124002},
   Key = {fds243598}
}

@article{fds243599,
   Author = {Mileyko, Y and Mukherjee, S and Harer, J},
   Title = {Probability measures on the space of persistence
             diagrams},
   Journal = {Inverse Problems},
   Volume = {27},
   Number = {12},
   Pages = {25},
   Year = {2011},
   ISSN = {0266-5611},
   url = {http://dx.doi.org/10.1088/0266-5611/27/12/124007},
   Abstract = {This paper shows that the space of persistence diagrams has
             properties that allow for the definition of probability
             measures which support expectations, variances, percentiles
             and conditional probabilities. This provides a theoretical
             basis for a statistical treatment of persistence diagrams,
             for example computing sample averages and sample variances
             of persistence diagrams. We first prove that the space of
             persistence diagrams with the Wasserstein metric is complete
             and separable. We then prove a simple criterion for
             compactness in this space. These facts allow us to show the
             existence of the standard statistical objects needed to
             extend the theory of topological persistence to a much
             larger set of applications. © 2011 IOP Publishing
             Ltd.},
   Doi = {10.1088/0266-5611/27/12/124007},
   Key = {fds243599}
}

@article{fds243600,
   Author = {Bini, G and Harer, J},
   Title = {Euler characteristics of moduli spaces of
             curves},
   Journal = {Journal of the European Mathematical Society},
   Volume = {13},
   Number = {2},
   Pages = {487-512},
   Year = {2011},
   ISSN = {1435-9855},
   url = {http://dx.doi.org/10.4171/JEMS/259},
   Abstract = {Let Mng be the moduli space of n-pointed Riemann surfaces of
             genus g. Denote by M̄ng the Deligne-Mumford
             compactification of Mng. In the present paper, we calculate
             the orbifold and the ordinary Euler characteristics of M̄ng
             for any g and n such that n > 2 - 2g. © 2011 European
             Mathematical Society.},
   Doi = {10.4171/JEMS/259},
   Key = {fds243600}
}

@article{fds243602,
   Author = {Iyer-Pascuzzi, AS and Symonova, O and Mileyko, Y and Hao, Y and Belcher,
             H and Harer, J and Weitz, JS and Benfey, PN},
   Title = {Imaging and analysis platform for automatic phenotyping and
             trait ranking of plant root systems.},
   Journal = {Plant physiology},
   Volume = {152},
   Number = {3},
   Pages = {1148-1157},
   Year = {2010},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20107024},
   Abstract = {The ability to nondestructively image and automatically
             phenotype complex root systems, like those of rice (Oryza
             sativa), is fundamental to identifying genes underlying root
             system architecture (RSA). Although root systems are central
             to plant fitness, identifying genes responsible for RSA
             remains an underexplored opportunity for crop improvement.
             Here we describe a nondestructive imaging and analysis
             system for automated phenotyping and trait ranking of RSA.
             Using this system, we image rice roots from 12 genotypes. We
             automatically estimate RSA traits previously identified as
             important to plant function. In addition, we expand the
             suite of features examined for RSA to include traits that
             more comprehensively describe monocot RSA but that are
             difficult to measure with traditional methods. Using 16
             automatically acquired phenotypic traits for 2,297 images
             from 118 individuals, we observe (1) wide variation in
             phenotypes among the genotypes surveyed; and (2) greater
             intergenotype variance of RSA features than variance within
             a genotype. RSA trait values are integrated into a
             computational pipeline that utilizes supervised learning
             methods to determine which traits best separate two
             genotypes, and then ranks the traits according to their
             contribution to each pairwise comparison. This trait-ranking
             step identifies candidate traits for subsequent quantitative
             trait loci analysis and demonstrates that depth and average
             radius are key contributors to differences in rice RSA
             within our set of genotypes. Our results suggest a strong
             genetic component underlying rice RSA. This work enables the
             automatic phenotyping of RSA of individuals within mapping
             populations, providing an integrative framework for
             quantitative trait loci analysis of RSA.},
   Doi = {10.1104/pp.109.150748},
   Key = {fds243602}
}

@article{fds243601,
   Author = {Cohen-Steiner, D and Edelsbrunner, H and Harer, J and Mileyko,
             Y},
   Title = {Lipschitz functions have Lp-stable
             persistence},
   Journal = {Foundations of Computational Mathematics},
   Volume = {10},
   Number = {2},
   Pages = {127-139},
   Year = {2010},
   ISSN = {1615-3375},
   url = {http://www.cs.duke.edu/~edels/Topology/},
   Abstract = {We prove two stability results for Lipschitz functions on
             triangulable, compact metric spaces and consider
             applications of both to problems in systems biology. Given
             two functions, the first result is formulated in terms of
             the Wasserstein distance between their persistence diagrams
             and the second in terms of their total persistence. © 2010
             SFoCM.},
   Doi = {10.1007/s10208-010-9060-6},
   Key = {fds243601}
}

@article{fds243584,
   Author = {Cohen-Steiner, D and Edelsbrunner, H and Harer, J and Morozov,
             D},
   Title = {Persistent homology for kernels, images, and
             cokernels},
   Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete
             Algorithms},
   Pages = {1011-1020},
   Year = {2009},
   url = {http://www.cs.duke.edu/~edels/Topology/},
   Abstract = {Motivated by the measurement of local homology and of
             functions on noisy domains, we extend the notion of
             persistent homology to sequences of kernels, images, and
             cokernels of maps induced by inclusions in a filtration of
             pairs of spaces. Specifically, we note that persistence in
             this context is well defined, we prove that the persistence
             diagrams are stable, and we explain how to compute them.
             Copyright © by SIAM.},
   Key = {fds243584}
}

@article{fds243585,
   Author = {Edelsbrunner, H and Harer, J},
   Title = {The persistent Morse complex segmentation of a
             3-manifold},
   Journal = {Lecture notes in computer science},
   Volume = {5903 LNCS},
   Series = {Lecture Notes Comp. Sci.},
   Pages = {36-50},
   Booktitle = {3D Physiological Human Workshop, 2009},
   Publisher = {Springer-Verlag, Berlin},
   Editor = {N. Magnenat-Thalmann},
   Year = {2009},
   ISSN = {0302-9743},
   url = {http://dx.doi.org/10.1007/978-3-642-10470-1_4},
   Abstract = {We describe an algorithm for segmenting three-dimensional
             medical imaging data modeled as a continuous function on a
             3-manifold. It is related to watershed algorithms developed
             in image processing but is closer to its mathematical roots,
             which are Morse theory and homological algebra. It allows
             for the implicit treatment of an underlying mesh, thus
             combining the structural integrity of its mathematical
             foundations with the computational efficiency of image
             processing. © Springer-Verlag Berlin Heidelberg
             2009.},
   Doi = {10.1007/978-3-642-10470-1_4},
   Key = {fds243585}
}

@article{fds243586,
   Author = {Cohen-Steiner, D and Edelsbrunner, H and Harer,
             J},
   Title = {Extending persistence using poincaré and lefschetz duality
             (Foundations of Computational Mathematics DOI
             10.1007/s10208-008-9027-z)},
   Journal = {Foundations of Computational Mathematics},
   Volume = {9},
   Number = {1},
   Pages = {133-134},
   Year = {2009},
   ISSN = {1615-3375},
   url = {http://dx.doi.org/10.1007/s10208-008-9038-9},
   Doi = {10.1007/s10208-008-9038-9},
   Key = {fds243586}
}

@article{fds243603,
   Author = {Cohen-Steiner, D and Edelsbrunner, H and Harer,
             J},
   Title = {Extending persistence using poincaré and lefschetz
             duality},
   Journal = {Foundations of Computational Mathematics},
   Volume = {9},
   Number = {1},
   Pages = {79-103},
   Year = {2009},
   ISSN = {1615-3375},
   url = {http://dx.doi.org/10.1007/s10208-008-9027-z},
   Abstract = {Persistent homology has proven to be a useful tool in a
             variety of contexts, including the recognition and
             measurement of shape characteristics of surfaces in 3.
             Persistence pairs homology classes that are born and die in
             a filtration of a topological space, but does not pair its
             actual homology classes. For the sublevelset filtration of a
             surface in 3, persistence has been extended to a pairing of
             essential classes using Reeb graphs. In this paper, we give
             an algebraic formulation that extends persistence to
             essential homology for any filtered space, present an
             algorithm to calculate it, and describe how it aids our
             ability to recognize shape features for codimension 1
             submanifolds of Euclidean space. The extension derives from
             Poincaré duality but generalizes to nonmanifold spaces. We
             prove stability for general triangulated spaces and duality
             as well as symmetry for triangulated manifolds. © 2008
             SFoCM.},
   Doi = {10.1007/s10208-008-9027-z},
   Key = {fds243603}
}

@article{fds243583,
   Author = {Edelsbrunner, H and Harer, J and Patel, AK},
   Title = {Reeb spaces of piecewise linear mappings},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {242-250},
   Year = {2008},
   url = {http://dx.doi.org/10.1145/1377676.1377720},
   Abstract = {Generalizing the concept of a Reeb graph, the Reeb space of
             a multivariate continuous mapping identifies points of the
             domain that belong to a common component of the preimage of
             a point in the range. We study the local and global
             structure of this space for generic, piecewise linear
             mappings on a combinatorial manifold. Copyright 2008
             ACM.},
   Doi = {10.1145/1377676.1377720},
   Key = {fds243583}
}

@article{fds243605,
   Author = {Edelsbrunner, H and Harer, J and Mascarenhas, A and Pascucci, V and Snoeyink, J},
   Title = {Time-varying Reeb graphs for continuous space-time
             data},
   Journal = {Computational Geometry},
   Volume = {41},
   Number = {3},
   Pages = {149-166},
   Year = {2008},
   ISSN = {0925-7721},
   url = {http://dx.doi.org/10.1016/j.comgeo.2007.11.001},
   Abstract = {The Reeb graph is a useful tool in visualizing real-valued
             data obtained from computational simulations of physical
             processes. We characterize the evolution of the Reeb graph
             of a time-varying continuous function defined in
             three-dimensional space. We show how to maintain the Reeb
             graph over time and compress the entire sequence of Reeb
             graphs into a single, partially persistent data structure,
             and augment this data structure with Betti numbers to
             describe the topology of level sets and with path seeds to
             assist in the fast extraction of level sets for
             visualization. © 2008 Elsevier B.V.},
   Doi = {10.1016/j.comgeo.2007.11.001},
   Key = {fds243605}
}

@article{fds324399,
   Author = {Edelsbrunner, H and Harer, J},
   Title = {Persistent homology - a survey},
   Journal = {Contemporary Mathematics},
   Volume = {453},
   Pages = {257-282},
   Year = {2008},
   ISBN = {978-0-8218-4239-3},
   url = {http://math.duke.edu/~harer/public_html/papers/survey.pdf},
   Abstract = {This paper surveys the current state of the art in
             computational topology. It is intended for computational
             geometers and combinatorialists.},
   Key = {fds324399}
}

@article{fds243581,
   Author = {Attali, D and Edelsbrunner, H and Harer, J and Mileyko,
             Y},
   Title = {Alpha-beta witness complexes},
   Journal = {Lecture notes in computer science},
   Volume = {4619 LNCS},
   Pages = {386-397},
   Year = {2007},
   ISSN = {0302-9743},
   Abstract = {Building on the work of Martinetz, Schulten and de Silva,
             Carlsson, we introduce a 2-parameter family of witness
             complexes and algorithms for constructing them. This family
             can be used to determine the gross topology of point cloud
             data in ℝ d or other metric spaces. The 2-parameter family
             is sensitive to differences in sampling density and thus
             amenable to detecting patterns within the data set. It also
             lends itself to theoretical analysis. For example, we can
             prove that in the limit, when the witnesses cover the entire
             domain, witness complexes in the family that share the
             first, scale parameter have the same homotopy type. ©
             Springer-Verlag Berlin Heidelberg 2007.},
   Key = {fds243581}
}

@article{fds243582,
   Author = {Bendice, P and Cohen-Steiner, D and Edelsbrunner, H and Harer, J and Morozov, D},
   Title = {Inferring local homology from sampled stratified
             spaces},
   Journal = {Annual Symposium on Foundations of Computer
             Science},
   Pages = {536-546},
   Year = {2007},
   ISSN = {0272-5428},
   url = {http://www.cs.duke.edu/~edels/Topology/},
   Abstract = {We study the reconstruction of a stratified space from a
             possibly noisy point sample. Specifically, we use the
             vineyard of the distance function restricted to a
             1-parameter family of neighborhoods of a point to assess the
             local homology of the stratified space at that point. We
             prove the correctness of this assessment under the
             assumption of a sufficiently dense sample. We also give an
             algorithm that constructs the vineyard and makes the local
             assessment in time at most cubic in the size of the Delaunay
             triangulation of the point sample. © 2007
             IEEE.},
   Doi = {10.1109/FOCS.2007.4389523},
   Key = {fds243582}
}

@article{fds243606,
   Author = {Cohen-Steiner, D and Edelsbrunner, H and Harer,
             J},
   Title = {Stability of persistence diagrams},
   Journal = {Discrete & Computational Geometry},
   Volume = {37},
   Number = {1},
   Pages = {103-120},
   Year = {2007},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-006-1276-5},
   Abstract = {The persistence diagram of a real-valued function on a
             topological space is a multiset of points in the extended
             plane. We prove that under mild assumptions on the function,
             the persistence diagram is stable: small changes in the
             function imply only small changes in the diagram. We apply
             this result to estimating the homology of sets in a metric
             space and to comparing and classifying geometric shapes. ©
             2006 Springer.},
   Doi = {10.1007/s00454-006-1276-5},
   Key = {fds243606}
}

@article{fds324400,
   Author = {Bendich, P and Cohen-Steiner, D and Edelsbrunner, H and Harer, J and Morozov, D},
   Title = {Inferring Local Homology from Sampled Stratified
             Spaces.},
   Journal = {FOCS},
   Pages = {536-546},
   Publisher = {IEEE Computer Society},
   Year = {2007},
   ISBN = {978-0-7695-3010-9},
   url = {http://dx.doi.org/10.1109/FOCS.2007.33},
   Doi = {10.1109/FOCS.2007.33},
   Key = {fds324400}
}

@article{fds324401,
   Author = {Bendich, P and Cohen-Steiner, D and Edelsbrunner, H and Harer, J and Morozov, D},
   Title = {Inferring local homology from sampled stratified
             spaces},
   Journal = {48TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER
             SCIENCE, PROCEEDINGS},
   Pages = {536-546},
   Year = {2007},
   ISBN = {978-0-7695-3010-9},
   url = {http://dx.doi.org/10.1109/FOCS.2007.45},
   Doi = {10.1109/FOCS.2007.45},
   Key = {fds324401}
}

@article{fds243590,
   Author = {Agarwal, PK and Edelsbrunner, H and Harer, J and Wang,
             Y},
   Title = {Extreme elevation on a 2-manifold},
   Journal = {Discrete & Computational Geometry},
   Volume = {36},
   Number = {4},
   Pages = {553-572},
   Year = {2006},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-006-1265-8},
   Abstract = {Given a smoothly embedded 2-manifold in ℝ3, we define the
             elevation of a point as the height difference to a
             canonically defined second point on the same manifold. Our
             definition is invariant under rigid motions and can be used
             to define features such as lines of discontinuous or
             continuous but non-smooth elevation. We give an algorithm
             for finding points of locally maximum elevation, which we
             suggest mark cavities and protrusions and are useful in
             matching shapes as for example in protein docking. ©
             Springer 2006.},
   Doi = {10.1007/s00454-006-1265-8},
   Key = {fds243590}
}

@article{fds243580,
   Author = {Cohen-Steiner, D and Edelsbrunner, H and Harer,
             J},
   Title = {Stability of persistence diagrams},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {263-271},
   Year = {2005},
   url = {http://dx.doi.org/10.1145/1064092.1064133},
   Abstract = {The persistence diagram of a real-valued function on a
             topological space is a multiset of points in the extended
             plane. We prove that under mild assumptions on the function,
             the persistence diagram is stable: small changes in the
             function imply only small changes in the diagram. We apply
             this result to estimating the homology of sets in a metric
             space and to comparing and classifying geometric shapes.
             Copyright 2005 ACM.},
   Doi = {10.1145/1064092.1064133},
   Key = {fds243580}
}

@article{fds243578,
   Author = {J. Harer and Edelsbrunner, H and Harer, J and Mascarenhas, A and Pascucci,
             V},
   Title = {Time-varying Reeb graphs for continuous space-time
             data},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {366-372},
   Year = {2004},
   Abstract = {We study the evolution of the Reeb graph of a time-varying
             continuous function defined in three-dimensional space.
             While maintaining the Reeb graph, we compress the evolving
             sequence into a single, partially persistent data structure.
             We envision this data structure as a useful tool in
             visualizing real-valued space-time data obtained from
             computational simulations of physical processes.},
   Key = {fds243578}
}

@article{fds243579,
   Author = {J. Harer and Edelsbrunner, H and Harer, J and Natarajan, V and Pascucci,
             V},
   Title = {Local and global comparison of continuous
             functions},
   Journal = {IEEE Visualization 2004 - Proceedings, VIS
             2004},
   Pages = {275-280},
   Year = {2004},
   Abstract = {We introduce local and global comparison measures for a
             collection of k ≤ d real-valued smooth functions on a
             common d-dimensional Riemannian manifold. For k = d = 2 we
             relate the measures to the set of critical points of one
             function restricted to the level sets of the other. The
             definition of the measures extends to piecewise linear
             functions for which they are easy to compute. The
             computation of the measures forms the centerpiece of a
             software tool which we use to study scientific datasets. ©
             2004 IEEE.},
   Key = {fds243579}
}

@article{fds243589,
   Author = {J. Harer and Agarwal, PK and Edelsbrunner, H and Harer, J and Wang,
             Y},
   Title = {Extreme elevation on a 2-manifold},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {357-365},
   Year = {2004},
   Abstract = {Given a smoothly embedded 2-manifold in ℝ 3, we define the
             elevation of a point as the height difference to a
             canonically defined second point on the same manifold. Our
             definition is invariant under rigid motions and can be used
             to define features such as lines of discontinuous or
             continuous but non-smooth elevation. We give an algorithm
             for finding points of locally maximum elevation, which we
             suggest mark cavities and protrusions and are useful in
             matching shapes as for example in protein
             docking.},
   Key = {fds243589}
}

@article{fds243607,
   Author = {J. Harer and Cole-McLaughlin, K and Edelsbrunner, H and Harer, J and Natarajan, V and Pascucci, V},
   Title = {Loops in Reeb graphs of 2-manifolds},
   Journal = {Discrete and Computanional Geometry},
   Volume = {32},
   Number = {2},
   Pages = {231-244},
   Year = {2004},
   Abstract = {Given a Morse function f over a 2-manifold with or without
             boundary, the Reeb graph is obtained by contracting the
             connected components of the level sets to points. We prove
             tight upper and lower bounds on the number of loops in the
             Reeb graph that depend on the genus, the number of boundary
             components, and whether or not the 2-manifold is orientable.
             We also give an algorithm that constructs the Reeb graph in
             time O(n log n), where n is the number of edges in the
             triangulation used to represent the 2-manifold and the Morse
             function.},
   Key = {fds243607}
}

@article{fds243576,
   Author = {J. Harer and Edelsbrunner, H and Harer, J and Natarajan, V and Pascucci,
             V},
   Title = {Morse-Smale complexes for piecewise linear
             3-manifolds},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {361-370},
   Year = {2003},
   Abstract = {We define the Morse-Smale complex of a Morse function over a
             3-manifold as the overlay of the descending and ascending
             manifolds of all critical points. In the generic case, its
             3-dimensional cells are shaped like crystals and are
             separated by quadrangular faces. In this paper, we give a
             combinatorial algorithm for constructing such complexes for
             piecewise linear data.},
   Key = {fds243576}
}

@article{fds243577,
   Author = {Edelsbrunner, H and Harer, J and Zomorodian, A},
   Title = {Hierarchical Morse-Smale complexes for piecewise linear
             2-manifolds},
   Journal = {Discrete & Computational Geometry},
   Volume = {30},
   Number = {1},
   Pages = {87-107},
   Year = {2003},
   ISSN = {0179-5376},
   url = {http://dx.doi.org/10.1007/s00454-003-2926-5},
   Abstract = {We present algorithms for constructing a hierarchy of
             increasingly coarse Morse-Smale complexes that decompose a
             piecewise linear 2-manifold. While these complexes are
             defined only in the smooth category, we extend the
             construction to the piecewise linear category by ensuring
             structural integrity and simulating differentiability. We
             then simplify Morse-Smale complexes by canceling pairs of
             critical points in order of increasing persistence.},
   Doi = {10.1007/s00454-003-2926-5},
   Key = {fds243577}
}

@article{fds318291,
   Author = {Cole-McLaughlin, K and Edelsbrunner, H and Harer, J and Natarajan, V and Pascucci, V},
   Title = {Loops in Reeb graphs of 2-manifolds},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {344-350},
   Year = {2003},
   Abstract = {Given a Morse function f over a 2-manifold with or without
             boundary, the Reeb graph is obtained by contracting the
             connected components of the level sets to points. We prove
             tight upper and lower bounds on the number of loops in the
             Reeb graph that depend on the genus, the number of boundary
             components, and whether or not the 2-manifold is orientable.
             We also give an algorithm that constructs the Reeb graph in
             time O(n log n), where n is the number of edges in the
             triangulation used to represent the 2-manifold and the Morse
             function.},
   Key = {fds318291}
}

@article{fds243588,
   Author = {J. Harer and Collins, AD and Agarwal, PK and Harer, JL},
   Title = {HPRM: A hierarchical PRM},
   Journal = {Proceedings - IEEE International Conference on Robotics and
             Automation},
   Volume = {3},
   Pages = {4433-4438},
   Year = {2003},
   Abstract = {We introduce a hierarchical variant of the probabilistic
             roadmap method for motion planning. By recursively refining
             an initially sparse sampling in neighborhoods of the
             C-obstacle boundary, our algorithm generates a smaller
             roadmap that is more likely to find narrow passages than
             uniform sampling. We analyze the failure probability and
             computation time, relating them to path length, path
             clearance, roadmap size, recursion depth, and a local
             property of the free space. The approach is general, and can
             be tailored to any variety of robots. In particular, we
             describe algorithmic details for a planar articulated
             arm.},
   Key = {fds243588}
}

@article{fds29135,
   Author = {J. Harer and H. Edelsbrunner.},
   Title = {Jacobi sets of multiple Morse functions.},
   Journal = {Foundations of Computational Mathematics, Minneapolis, eds.
             F. Cucker, R. DeVore, P. Olver and E. Sueli, Cambridge Univ.
             Press, England,},
   Pages = {37-57},
   Year = {2002},
   Abstract = {The Jacobi set of two Morse functions defined on a common
             d-manifold is the set of critical points of the restrictions
             of one function to the level sets of the other function.
             Equivalently, it is the set of points where the gradients of
             the functions are parallel. For a generic pair of Morse
             functions, the Jacobi set is a smoothly embedded 1-manifold.
             We give a polynomial-time algorithm that computes the
             piecewise linear analog of the Jacobi set for functions
             specified at the vertices of a triangulation, and we
             generalize all results to more than two but at most d Morse
             functions.},
   Key = {fds29135}
}

@article{fds243573,
   Author = {Goulden, IP and Harer, JL and Jackson, DM},
   Title = {A geometric parametrization for the virtual euler
             characteristics of the moduli spaces of real and complex
             algebraic curves},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {353},
   Number = {11},
   Pages = {4405-4427},
   Year = {2001},
   ISSN = {0002-9947},
   MRNUMBER = {1851176},
   url = {http://www.ams.org/mathscinet-getitem?mr=1851176},
   Abstract = {We determine an expression ξgs(γ) for the virtual Euler
             characteristics of the moduli spaces of s-pointed real (7 =
             1/2) and complex (7 = 1) algebraic curves. In particular,
             for the space of real curves of genus g with a fixed point
             free involution, we find that the Euler characteristic is
             (-2)s-1(1-2q-1)(g+s-2)!Bg/g! where gth is the gth Bernoulli
             number. This complements the result of Harer and Zagier that
             the Euler characteristic of the moduli space of complex
             algebraic curves is (-1)s(g+s-2)!Bg+1/(g+1)(g- 1)! The proof
             uses Strcbel differentials to triangulate the moduli spaces
             and some recent techniques for map enumeration to count
             cells. The approach involves a parameter γ that permits
             specialization of the formula to the real and complex cases.
             This suggests that ξgs(γ) itself may describe the Eulcr
             characteristics of some related moduli spaces, although we
             do not yet know what these spaces might be. ©2001 American
             Mathematical Society.},
   Key = {fds243573}
}

@article{fds243574,
   Author = {Edelsbrunner, H and Harer, J and Zomorodian, A},
   Title = {Hierarchical Morse complexes for piecewise linear
             2-manifolds},
   Journal = {Proceedings of the Annual Symposium on Computational
             Geometry},
   Pages = {70-79},
   Year = {2001},
   Abstract = {We present algorithms for constructing a hierarchy of
             increasingly coarse Morse complexes that decompose a
             piecewise linear 2-manifold. While Morse complexes are
             defined only in the smooth category, we extend the
             construction to the piecewise linear category by ensuring
             structural integrity and simulating differentiability. We
             then simplify Morse complexes by cancelling pairs of
             critical points in order of increasing persistence.},
   Key = {fds243574}
}

@article{fds243587,
   Author = {Agarwal, PK and Collins, AD and Harer, JL},
   Title = {Minimal trap design},
   Journal = {Proceedings - IEEE International Conference on Robotics and
             Automation},
   Volume = {3},
   Pages = {2243-2248},
   Year = {2001},
   Abstract = {This paper addresses the issue of trap design for sensorless
             automated assembly. First, we present a simple algorithm
             that determines in O(nm α(nm) log(nm)) time whether an
             n-sided polygonal part will fall through an m-sided
             polygonal trap. We then introduce the notion of a minimal
             trap for a polygonal part, and develop an algorithm to
             design a family of minimal feeders built from these traps.
             The algorithm runs in O(kn3+ε) time, where k is the number
             of stable orientations of P. Moreover, it is complete in the
             sense that we can always find a feeder, provided that one
             exists that rejects and supports the appropriate poses of
             the part.},
   Key = {fds243587}
}

@article{fds321993,
   Author = {HARER, J},
   Title = {THE 3RD HOMOLOGY GROUP OF THE MODULI SPACE OF
             CURVES},
   Journal = {Duke Mathematical Journal},
   Volume = {63},
   Number = {1},
   Pages = {25-55},
   Year = {1991},
   Month = {June},
   url = {http://dx.doi.org/10.1215/S0012-7094-91-06302-7},
   Doi = {10.1215/S0012-7094-91-06302-7},
   Key = {fds321993}
}

@article{fds243572,
   Author = {Harer, JL},
   Title = {Stability of the homology of the moduli spaces of Riemann
             surfaces with spin structure},
   Journal = {Mathematische Annalen},
   Volume = {287},
   Number = {1},
   Pages = {323-334},
   Year = {1990},
   ISSN = {0025-5831},
   MRNUMBER = {91e:57002},
   url = {http://dx.doi.org/10.1007/BF01446896},
   Doi = {10.1007/BF01446896},
   Key = {fds243572}
}

@article{fds324402,
   Author = {HARER, J and KAS, A and KIRBY, R},
   Title = {HANDLEBODY STRUCTURES FOR COMPLEX-SURFACES},
   Journal = {Memoirs of the American Mathematical Society},
   Volume = {62},
   Number = {350},
   Pages = {1-102},
   Year = {1986},
   Month = {July},
   Key = {fds324402}
}

@article{fds243570,
   Author = {HARER, J},
   Title = {The virtual cohomological dimension of the mapping class
             group of an orientable surface},
   Journal = {Invent. Math.},
   Volume = {84},
   Number = {1},
   Pages = {157-176},
   Year = {1986},
   ISSN = {0020-9910},
   MRNUMBER = {87c:32030},
   url = {http://dx.doi.org/10.1007/BF01388737},
   Doi = {10.1007/BF01388737},
   Key = {fds243570}
}

@article{fds243571,
   Author = {Harer, J and Zagier, D},
   Title = {The Euler characteristic of the moduli space of
             curves},
   Journal = {Inventiones mathematicae},
   Volume = {85},
   Number = {3},
   Pages = {457-485},
   Year = {1986},
   ISSN = {0020-9910},
   MRNUMBER = {87i:32031},
   url = {http://dx.doi.org/10.1007/BF01390325},
   Doi = {10.1007/BF01390325},
   Key = {fds243571}
}

@article{fds243569,
   Author = {Harer, J},
   Title = {The second homology group of the mapping class group of an
             orientable surface},
   Journal = {Inventiones mathematicae},
   Volume = {72},
   Number = {2},
   Pages = {221-239},
   Year = {1983},
   ISSN = {0020-9910},
   MRNUMBER = {84g:57006},
   url = {http://dx.doi.org/10.1007/BF01389321},
   Doi = {10.1007/BF01389321},
   Key = {fds243569}
}

@article{fds324403,
   Author = {HARER, JL},
   Title = {The second homology group of the mapping class group of an
             orientable surface},
   Journal = {Invent.Math.},
   Volume = {72},
   Pages = {221-239},
   Year = {1983},
   url = {http://dx.doi.org/10.1007/BF01389321},
   Doi = {10.1007/BF01389321},
   Key = {fds324403}
}

@article{fds243567,
   Author = {HARER, J},
   Title = {How to construct all fibered knots and links},
   Journal = {Topology},
   Volume = {21},
   Number = {3},
   Pages = {263-280},
   Year = {1982},
   ISSN = {0040-9383},
   MRNUMBER = {83e:57007},
   url = {http://dx.doi.org/10.1016/0040-9383(82)90009-X},
   Doi = {10.1016/0040-9383(82)90009-X},
   Key = {fds243567}
}

@article{fds324404,
   Author = {HARER, J},
   Title = {REPRESENTING ELEMENTS OF PI-1M3 BY FIBERED
             KNOTS},
   Journal = {Cambridge Philosophical Society: Mathematical
             Proceedings},
   Volume = {92},
   Number = {JUL},
   Pages = {133-138},
   Year = {1982},
   url = {http://dx.doi.org/10.1017/S030500410005979X},
   Doi = {10.1017/S030500410005979X},
   Key = {fds324404}
}

@article{fds321994,
   Author = {Casson, A and Harer, J},
   Title = {Some homology lens spaces which bound rational homology
             balls},
   Journal = {Pacific Journal of Mathematics},
   Volume = {96},
   Number = {1},
   Pages = {23-36},
   Year = {1981},
   Month = {September},
   MRNUMBER = {83h:57013},
   url = {http://dx.doi.org/10.2140/pjm.1981.96.23},
   Doi = {10.2140/pjm.1981.96.23},
   Key = {fds321994}
}

@article{fds243568,
   Author = {Harer, J},
   Title = {On handlebody structures for hypersurfaces in
             ℂ3 and ℂP3},
   Journal = {Mathematische Annalen},
   Volume = {238},
   Number = {1},
   Pages = {51-58},
   Year = {1978},
   ISSN = {0025-5831},
   MRNUMBER = {80d:57020},
   url = {http://dx.doi.org/10.1007/BF01351453},
   Doi = {10.1007/BF01351453},
   Key = {fds243568}
}

@article{fds10017,
   Author = {Harer, John L.},
   Title = {The rational Picard group of the moduli space of Riemann
             surfaces with spin structure},
   Journal = {Mapping class groups and moduli spaces of Riemann surfaces
             (Gottingen, 1991/Seattle, WA, 1991), pp. 107--136, 1993,
             Amer. Math. Soc., Providence, RI},
   MRNUMBER = {94h:14008},
   url = {http://www.ams.org/mathscinet-getitem?mr=94h:14008},
   Key = {fds10017}
}

@article{fds10019,
   Author = {Harer, John},
   Title = {The third homology group of the moduli space of
             curves},
   Journal = {Duke Math. J., vol. 63, no. 1, pp. 25--55,
             1991},
   MRNUMBER = {92d:57012},
   url = {http://www.ams.org/mathscinet-getitem?mr=92d:57012},
   Key = {fds10019}
}

@article{fds10021,
   Author = {Harer, John L.},
   Title = {The cohomology of the moduli space of curves},
   Journal = {Theory of moduli (Montecatini Terme, 1985), pp. 138--221,
             1988, Springer, Berlin},
   MRNUMBER = {90a:32026},
   url = {http://www.ams.org/mathscinet-getitem?mr=90a:32026},
   Key = {fds10021}
}

@article{fds10022,
   Author = {Harer, John and Kas, Arnold and Kirby, Robion},
   Title = {Handlebody decompositions of complex surfaces},
   Journal = {Mem. Amer. Math. Soc., vol. 62, no. 350, pp. iv+102,
             1986},
   MRNUMBER = {88e:57030},
   url = {http://www.ams.org/mathscinet-getitem?mr=88e:57030},
   Key = {fds10022}
}

@article{fds10024,
   Author = {Harer, John L.},
   Title = {Stability of the homology of the mapping class groups of
             orientable surfaces},
   Journal = {Ann. of Math. (2), vol. 121, no. 2, pp. 215--249,
             1985},
   MRNUMBER = {87f:57009},
   url = {http://www.ams.org/mathscinet-getitem?mr=87f:57009},
   Key = {fds10024}
}

@article{fds10026,
   Title = {Geometry and topology},
   Journal = {Proceedings of the special year held at the University of
             Maryland, College Park, Md., 1983/84, edited by Alexander,
             J. and Harer, J., pp. vi+292, 1985, Springer-Verlag,
             Berlin},
   MRNUMBER = {87a:57003},
   url = {http://www.ams.org/mathscinet-getitem?mr=87a:57003},
   Key = {fds10026}
}

@article{fds10027,
   Author = {Harer, John},
   Title = {The homology of the mapping class group and its connection
             to surface bundles over surfaces},
   Journal = {Four-manifold theory (Durham, N.H., 1982), pp. 311--314,
             1984, Amer. Math. Soc., Providence, RI},
   MRNUMBER = {86c:57010},
   url = {http://www.ams.org/mathscinet-getitem?mr=86c:57010},
   Key = {fds10027}
}

@article{fds10029,
   Author = {Harer, John},
   Title = {Representing elements of pi1(M3)
             by fibred knots},
   Journal = {Math. Proc. Cambridge Philos. Soc., vol. 92, no. 1, pp.
             133--138, 1982},
   MRNUMBER = {83j:57005},
   url = {http://www.ams.org/mathscinet-getitem?mr=83j:57005},
   Key = {fds10029}
}


%% Papers Accepted   
@article{fds321991,
   Author = {Bendich, P and Gasparovic, E and Harer, J and Izmailov, R and Ness,
             L},
   Title = {Multi-scale local shape analysis and feature selection in
             machine learning applications},
   Journal = {Proceedings of the International Joint Conference on Neural
             Networks},
   Volume = {2015-September},
   Year = {2015},
   Month = {September},
   url = {http://dx.doi.org/10.1109/IJCNN.2015.7280428},
   Abstract = {© 2015 IEEE. We introduce a method called multi-scale local
             shape analysis for extracting features that describe the
             local structure of points within a dataset. The method uses
             both geometric and topological features at multiple levels
             of granularity to capture diverse types of local information
             for subsequent machine learning algorithms operating on the
             dataset. Using synthetic and real dataset examples, we
             demonstrate significant performance improvement of
             classification algorithms constructed for these datasets
             with correspondingly augmented features.},
   Doi = {10.1109/IJCNN.2015.7280428},
   Key = {fds321991}
}

@article{fds225825,
   Author = {E. Munch and P. Bendich and K. Turner and S. Mukherjee and J. Mattingly and J. Harer},
   Title = {Probabilistic Frechet Means and Statistics on
             Vineyards},
   Journal = {Foundations of Computational Math},
   Year = {2014},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. In [21], Mileyko and his
             collaborators made the first study of the properties of the
             Fr ́echet mean in (Dp,Wp), the space of persistence
             diagrams equipped with the p-th Wasserstein metric. In
             particular, they showed that the Fr ́echet mean of a finite
             set of diagrams always exists, but is not necessarily
             unique. As an unfortunate consequence, one sees that the
             means of a continuously-varying set of diagrams do not
             themselves vary continuously, which presents obvious
             problems when trying to extend the Fr ́echet mean
             definition to the realm of vineyards. We fix this problem by
             altering the original definition of Fr ́echet mean so that
             it now becomes a probability measure on the set of
             persistence diagrams; in a nutshell, the mean of a set of
             diagrams will be a weighted sum of atomic measures, where
             each atom is itself the (Fr ́echet mean) persistence
             diagram of a perturbation of the input diagrams. We show
             that this new definition defines a (H ̈older) continuous
             map, for each k, from (Dp)k → P(Dp), and we present
             several examples to show how it may become a useful
             statistic on vineyards.},
   Key = {fds225825}
}


%% Papers Submitted   
@article{fds321989,
   Author = {McGoff, KA and Guo, X and Deckard, A and Kelliher, CM and Leman, AR and Francey, LJ and Hogenesch, JB and Haase, SB and Harer,
             JL},
   Title = {The Local Edge Machine: inference of dynamic models of gene
             regulation.},
   Journal = {Genome Biology: biology for the post-genomic
             era},
   Volume = {17},
   Number = {1},
   Pages = {214},
   Year = {2016},
   Month = {October},
   Abstract = {We present a novel approach, the Local Edge Machine, for the
             inference of regulatory interactions directly from
             time-series gene expression data. We demonstrate its
             performance, robustness, and scalability on in silico
             datasets with varying behaviors, sizes, and degrees of
             complexity. Moreover, we demonstrate its ability to
             incorporate biological prior information and make
             informative predictions on a well-characterized in vivo
             system using data from budding yeast that have been
             synchronized in the cell cycle. Finally, we use an atlas of
             transcription data in a mammalian circadian system to
             illustrate how the method can be used for discovery in the
             context of large complex networks.},
   Key = {fds321989}
}

@article{fds225821,
   Author = {J. Perea and A. Deckard and S. Haase and J. Harer},
   Title = {Sliding Windows and 1-Persistence Scoring; Discovering
             Periodicity in Gene Expression Time Series
             Data},
   Journal = {BMC Bioinformatics},
   Year = {2014},
   Abstract = {Motivation: Identifying periodically expressed genes across
             different processes such as the cell cy- cle, circadian
             rhythms, and metabolic cycles, is a central problem in
             computational biology. Biological time series data may
             contain (multiple) unknown sig- nal shapes, have
             imperfections such as noise, damp- ing, and trending, or
             have limited sampling density. While many methods exist for
             detecting periodicity, their design biases can limit their
             applicability in one or more of these situations. Methods:
             We present in this paper a novel method, SW1PerS, for
             quantifying periodicity in time se- ries data. The
             measurement is performed directly, without presupposing a
             particular shape or pattern, by evaluating the circularity
             of a high-dimensional representation of the signal. SW1PerS
             is compared to other algorithms using synthetic data and
             perfor- mance is quantified under varying noise levels, sam-
             pling densities, and signal shapes. Results on biolog- ical
             data are also analyzed and compared; this data includes
             different periodic processes from various or- ganisms: the
             cell and metabolic cycles in S. cere- visiae, and the
             circadian rhythms in M. musculus. ∗Department of
             Mathematics, Duke University, USA and Institute for
             Mathematics and its Applications, University of Minnesota,
             USA. †Program in Computational Biology and Bioinformatics,
             Duke University, USA. ‡Center for Systems Biology,
             Institute for Genome Sciences & Policy, Duke University,
             USA. §Departments of Mathematics, Computer Science and
             Elec- trical and Computer Engineering, Duke University, USA.
             Results: On the task of periodic/not-periodic clas-
             sification, using synthetic data, SW1PerS performs on par
             with successful methods in periodicity detec- tion.
             Moreover, it outperforms Lomb-Scargle and JTK CYCLE in the
             high-noise/low-sampling range. SW1PerS is shown to be the
             most shape-agnostic of the evaluated methods, and the only
             one to consis- tently classify damped signals as highly
             periodic. On biological data, and for several experiments,
             the lists of top 10% genes ranked with SW1PerS recover up to
             67% of those generated with other popular algo- rithms.
             Moreover, lists of genes which are highly- ranked only by
             SW1PerS contain non-cosine patterns (e.g. ECM33, CDC9,
             SAM1,2 and MSH6 in the Yeast metabolic cycle data of Tu et
             al. (2005)) which are highly periodic. In the Yeast cell
             cycle data SW1PerS identifies genes not preferred by other
             algorithms, not previously reported in Orlando et al.
             (2008); Spell- man et al. (1998), but found in other
             experiments such as the universal growth rate response of
             Slavov and Botstein (2011). These genes are BOP3, CDC10,
             YIL108W, YER034W, MLP1, PAC2 and RTT101.},
   Key = {fds225821}
}

@article{fds225822,
   Author = {K.A. McGoff and X. Guo and A. Deckard and A.R. Leman and C.M. Kelliher and S.B. Haase and J.L. Harer},
   Title = {The Local Edge Machine: Inference of dynamic models of gene
             regulation},
   Journal = {Nature Methods},
   Year = {2014},
   Abstract = {This paper develops the state of the art methodology for
             inferring gene regulatory networks from gene expression data
             for periodic processes. Application is made to finding
             networks for cell cycle and circadian clocks.},
   Key = {fds225822}
}

@article{fds225823,
   Author = {P. Bendich and S. Chin and J. Clarke and J. deSena, J. Harer and E.
             Munch, A. Newman and D. Porter and D. Rouse and N. Strawn and A.
             Watkins},
   Title = {Topological and Statistical Behavior Classifiers for
             Tracking Applications},
   Journal = {IEEE Trans. on Aerospace and Electronic Systems},
   Year = {2014},
   Abstract = {We introduce the first unified theory for target tracking
             using Multiple Hypothesis Tracking, Topological Data
             Analysis, and machine learning. Our string of innovations
             are 1) robust topological features are used to encode
             behavioral information, 2) statistical models are fitted to
             distributions over these topological features, and 3) the
             target type classification methods of Wigren and Bar Shalom
             et al. are employed to exploit the resulting likelihoods for
             topological features inside of the tracking procedure. To
             demonstrate the efficacy of our approach, we test our
             procedure on synthetic vehicular data generated by the
             Simulation of Urban Mobility package.},
   Key = {fds225823}
}

@article{fds225826,
   Author = {P. Bendich and Jacob Harer and John Harer},
   Title = {A Persistent Homology Based Geodesic Distance
             Estimator},
   Journal = {Journal of Machine Learning Research},
   Year = {2014},
   Key = {fds225826}
}

@article{fds221211,
   Author = {J. Perea and A. Deckard and S. Haase and J. Harer},
   Title = {Applications of SWiPerS to the discovery of periodic
             genes},
   Year = {2013},
   Key = {fds221211}
}

@article{fds221202,
   Author = {Sara Bristow and Laura A. Simmons Kovacs and Anastasia Deckard and John Harer and Steven B. Haase},
   Title = {Checkpoint Pathways Couple the CDK-Independent
             Transcriptional Oscillations to Cell Cycle
             Progression},
   Year = {2013},
   Abstract = {A study of how checkpoint pathways control the yeast cell
             cycle, derived from methods of finding periodic genes and
             cell cycle experiments from the Haase Lab.},
   Key = {fds221202}
}

@article{fds243592,
   Author = {Bendich, P and Harer, J and Harer, J},
   Title = {Persistent Homology Enhanced Dimension Reduction},
   Journal = {Foundations of Computational Mathematics},
   Year = {2012},
   Key = {fds243592}
}

@article{fds243593,
   Author = {Michael Jenista},
   Title = {Realizing Boolean Dynamics in Switching Networks},
   Journal = {Siam Journal of Applied Dynamical Systems},
   Pages = {12},
   Year = {2012},
   Abstract = {Switching networks are a common model for biological
             systems, especially for genetic transcription networks.
             Stuart Kaufman originally proposed the usefulness of the
             Boolean framework, but much of the dynamical features there
             are not realizable in a continuous analogue. We introduce
             the notion of braid-like dynamics as a bridge between
             Boolean and continuous dynamics and study its importance in
             the local dynamics of ring and ring-like networks. We
             discuss a near-theorem on the global dynamics of general
             feedback networks, and in the nal chapter study the main
             ideas of this thesis in models of a yeast cell transcription
             network.},
   Key = {fds243593}
}

@article{fds166039,
   Author = {P. Bendich and J. Harer},
   Title = {Elevation for singular spaces using persistent intersection
             homology},
   Year = {2009},
   Key = {fds166039}
}

@article{fds166033,
   Author = {Mehak Aziz and Siobhan M. Brady and David Orlando and Appu Kuruvilla and Scott Spillias and José R. Dinneny and Terri A. Long and John Harer and Uwe Ohler and Philip N. Benfey},
   Title = {Gene Expression Clustering Analysis: How to Choose the Best
             Parameters and Clustering Algorithm},
   Year = {2008},
   Abstract = {This paper is the result of a summer research project
             supported by the Howard Hughes summer program in systems
             biology.},
   Key = {fds166033}
}


%% Preprints   
@article{fds243604,
   Author = {Fink, T and Ahnert, S and Bar On and R and Harer, J},
   Title = {Exact dynamics of Boolean networks with connectivity
             one},
   Journal = {PRL},
   Year = {2009},
   Abstract = {We study boolean dynamics on the simplest class of network
             topologies: those in which each node has a single input (K =
             1). Despite their simplicity, they exhibit highly intricate
             bahaviour. We give the exact solution for the size and
             number of attractors on a loop and multiple loops of the
             same size. By expressing the dynamics of a network as a
             composition of the dynamics of its modules, we give a
             detailed solution to the critical K = 1 Kauffman model, and
             show that the minimum number of attractors scales as
             2n−√2n log2 √2n , where n is the number of nodes in
             loops.},
   Key = {fds243604}
}

@article{fds8935,
   Author = {John Harer},
   Title = {Algorithms for Enumerating Triangulations and Other Maps in
             Surfaces},
   Journal = {1998},
   Key = {fds8935}
}

@article{fds8938,
   Author = {John Harer},
   Title = {An Alternative Approach to Trap Design for Vibratory Bowl
             Feeders},
   Journal = {1998},
   Key = {fds8938}
}

@article{fds8940,
   Author = {John Harer},
   Title = {The Euler Characteristic of the Deligne-Mumford
             Compactification of the Moduli Space of Curves},
   Journal = {1996},
   Key = {fds8940}
}


%% Other   
@misc{fds29132,
   Author = {J. Harer and H. Edelsbrunner},
   Title = {Persistent Morse Complex Segmentation of a
             3-Manifold},
   Journal = {Raindrop Geomagic Technical Report},
   Volume = {066},
   Year = {2004},
   Abstract = {We describe a new algorithm for segmenting 3-dimensional
             medical imaging data, which we abstract as continuous
             functions on 3-manifolds. The algorithm is related to
             watershed algorithms developed in image processing but is
             closer to its mathematical roots, which are Morse theory and
             homological algebra. It allows for the implicit treatment of
             its mathematical foundations with the computational
             efficiency of image processing.},
   Key = {fds29132}
}

 

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