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John Harer

Professor Emeritus of Mathematics
Mathematics
Box 90320, Durham, NC 27708-0034
109 Physic Bldg, Durham, NC 27708

Selected Publications


The parasite intraerythrocytic cycle and human circadian cycle are coupled during malaria infection.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · June 2023 During infections with the malaria parasites Plasmodium vivax, patients exhibit rhythmic fevers every 48 h. These fever cycles correspond with the time the parasites take to traverse the intraerythrocytic cycle (IEC). In other Plasmodium spec ... Full text Cite

Assessment of Simulated Surveillance Testing and Quarantine in a SARS-CoV-2-Vaccinated Population of Students on a University Campus.

Journal Article JAMA Health Forum · October 2021 IMPORTANCE: The importance of surveillance testing and quarantine on university campuses to limit SARS-CoV-2 transmission needs to be reevaluated in the context of a complex and rapidly changing environment that includes vaccines, variants, and waning immu ... Full text Open Access Link to item Cite

PERSISTENT OBSTRUCTION THEORY FOR A MODEL CATEGORY OF MEASURES WITH APPLICATIONS TO DATA MERGING

Journal Article Transactions of the American Mathematical Society Series B · February 2, 2021 Collections of measures on compact metric spaces form a model category (“data complexes”), whose morphisms are marginalization integrals. The fibrant objects in this category represent collections of measures in which there is a measure on a product space ... Full text Cite

Implementation of a Pooled Surveillance Testing Program for Asymptomatic SARS-CoV-2 Infections on a College Campus - Duke University, Durham, North Carolina, August 2-October 11, 2020.

Journal Article MMWR Morb Mortal Wkly Rep · November 20, 2020 On university campuses and in similar congregate environments, surveillance testing of asymptomatic persons is a critical strategy (1,2) for preventing transmission of SARS-CoV-2, the virus that causes coronavirus disease 2019 (COVID-19). All students at D ... Full text Open Access Link to item Cite

An intrinsic oscillator drives the blood stage cycle of the malaria parasite Plasmodium falciparum.

Journal Article Science (New York, N.Y.) · May 2020 The blood stage of the infection of the malaria parasite Plasmodium falciparum exhibits a 48-hour developmental cycle that culminates in the synchronous release of parasites from red blood cells, which triggers 48-hour fever cycles in the host. This ... Full text Cite

Multi-Scale Geometric Summaries for Similarity-Based Sensor Fusion

Conference IEEE Aerospace Conference Proceedings · March 1, 2019 In this work, we address fusion of heterogeneous sensor data using wavelet-based summaries of fused self-similarity information from each sensor. The technique we develop is quite general, does not require domain specific knowledge or physical models, and ... Full text Cite

Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration

Conference IEEE Aerospace Conference Proceedings · June 25, 2018 This paper presents a processing pipeline for fusing 'raw' and / or feature-level multi-sensor data - upstream fusion - and initial results from this pipeline using imagery, radar, and radio frequency (RF) signals data to determine which tracked object, am ... Full text Cite

Geometric Cross-Modal Comparison of Heterogeneous Sensor Data

Conference Proceedings of the 39th IEEE Aerospace Conference · March 2018 In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: full-motion video, and radio-frequency (RF) signals received by detectors at va ... Open Access Link to item Cite

Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology

Journal Article · January 1, 2018 We propose a flexible and multi-scale method for organizing, visualizing, and understanding point cloud datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree for a dataset using an adaptive threshold that is ... Full text Cite

Guidelines for Genome-Scale Analysis of Biological Rhythms.

Journal Article Journal of biological rhythms · October 2017 Genome biology approaches have made enormous contributions to our understanding of biological rhythms, particularly in identifying outputs of the clock, including RNAs, proteins, and metabolites, whose abundance oscillates throughout the day. These methods ... Full text Cite

Topological and statistical behavior classifiers for tracking applications

Journal Article IEEE Transactions on Aerospace and Electronic Systems · December 1, 2016 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 analysi ... Full text Cite

The Local Edge Machine: inference of dynamic models of gene regulation.

Journal Article Genome biology · October 2016 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, size ... Full text Cite

Geometric models for musical audio data

Conference Leibniz International Proceedings in Informatics, LIPIcs · June 1, 2016 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 clo ... Full text Open Access Cite

Geometric Models for Musical Audio Data

Conference Proceedings of the 32st International Symposium on Computational Geometry (SOCG) · June 2016 Link to item Cite

Multi-scale local shape analysis and feature selection in machine learning applications

Conference Proceedings of the International Joint Conference on Neural Networks · September 28, 2015 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 ... Full text Open Access Cite

SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data.

Journal Article BMC bioinformatics · August 2015 BackgroundIdentifying 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 ... Full text Cite

Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis

Journal Article Foundations of Computational Mathematics · June 27, 2015 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 particula ... Full text Cite

Feature-aided multiple hypothesis tracking using topological and statistical behavior classifiers

Conference Proceedings of SPIE - The International Society for Optical Engineering · January 1, 2015 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 b ... Full text Cite

Probabilistic Fréchet means for time varying persistence diagrams

Journal Article Electronic Journal of Statistics · January 1, 2015 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 [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in ... Full text Open Access Cite

Easily repairable networks: reconnecting nodes after damage.

Journal Article Physical review letters · September 2014 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 o ... Full text Cite

The parasite intraerythrocytic cycle and human circadian cycle are coupled during malaria infection.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · June 2023 During infections with the malaria parasites Plasmodium vivax, patients exhibit rhythmic fevers every 48 h. These fever cycles correspond with the time the parasites take to traverse the intraerythrocytic cycle (IEC). In other Plasmodium spec ... Full text Cite

Assessment of Simulated Surveillance Testing and Quarantine in a SARS-CoV-2-Vaccinated Population of Students on a University Campus.

Journal Article JAMA Health Forum · October 2021 IMPORTANCE: The importance of surveillance testing and quarantine on university campuses to limit SARS-CoV-2 transmission needs to be reevaluated in the context of a complex and rapidly changing environment that includes vaccines, variants, and waning immu ... Full text Open Access Link to item Cite

PERSISTENT OBSTRUCTION THEORY FOR A MODEL CATEGORY OF MEASURES WITH APPLICATIONS TO DATA MERGING

Journal Article Transactions of the American Mathematical Society Series B · February 2, 2021 Collections of measures on compact metric spaces form a model category (“data complexes”), whose morphisms are marginalization integrals. The fibrant objects in this category represent collections of measures in which there is a measure on a product space ... Full text Cite

Implementation of a Pooled Surveillance Testing Program for Asymptomatic SARS-CoV-2 Infections on a College Campus - Duke University, Durham, North Carolina, August 2-October 11, 2020.

Journal Article MMWR Morb Mortal Wkly Rep · November 20, 2020 On university campuses and in similar congregate environments, surveillance testing of asymptomatic persons is a critical strategy (1,2) for preventing transmission of SARS-CoV-2, the virus that causes coronavirus disease 2019 (COVID-19). All students at D ... Full text Open Access Link to item Cite

An intrinsic oscillator drives the blood stage cycle of the malaria parasite Plasmodium falciparum.

Journal Article Science (New York, N.Y.) · May 2020 The blood stage of the infection of the malaria parasite Plasmodium falciparum exhibits a 48-hour developmental cycle that culminates in the synchronous release of parasites from red blood cells, which triggers 48-hour fever cycles in the host. This ... Full text Cite

Multi-Scale Geometric Summaries for Similarity-Based Sensor Fusion

Conference IEEE Aerospace Conference Proceedings · March 1, 2019 In this work, we address fusion of heterogeneous sensor data using wavelet-based summaries of fused self-similarity information from each sensor. The technique we develop is quite general, does not require domain specific knowledge or physical models, and ... Full text Cite

Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration

Conference IEEE Aerospace Conference Proceedings · June 25, 2018 This paper presents a processing pipeline for fusing 'raw' and / or feature-level multi-sensor data - upstream fusion - and initial results from this pipeline using imagery, radar, and radio frequency (RF) signals data to determine which tracked object, am ... Full text Cite

Geometric Cross-Modal Comparison of Heterogeneous Sensor Data

Conference Proceedings of the 39th IEEE Aerospace Conference · March 2018 In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: full-motion video, and radio-frequency (RF) signals received by detectors at va ... Open Access Link to item Cite

Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology

Journal Article · January 1, 2018 We propose a flexible and multi-scale method for organizing, visualizing, and understanding point cloud datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree for a dataset using an adaptive threshold that is ... Full text Cite

Guidelines for Genome-Scale Analysis of Biological Rhythms.

Journal Article Journal of biological rhythms · October 2017 Genome biology approaches have made enormous contributions to our understanding of biological rhythms, particularly in identifying outputs of the clock, including RNAs, proteins, and metabolites, whose abundance oscillates throughout the day. These methods ... Full text Cite

Topological and statistical behavior classifiers for tracking applications

Journal Article IEEE Transactions on Aerospace and Electronic Systems · December 1, 2016 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 analysi ... Full text Cite

The Local Edge Machine: inference of dynamic models of gene regulation.

Journal Article Genome biology · October 2016 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, size ... Full text Cite

Geometric models for musical audio data

Conference Leibniz International Proceedings in Informatics, LIPIcs · June 1, 2016 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 clo ... Full text Open Access Cite

Geometric Models for Musical Audio Data

Conference Proceedings of the 32st International Symposium on Computational Geometry (SOCG) · June 2016 Link to item Cite

Multi-scale local shape analysis and feature selection in machine learning applications

Conference Proceedings of the International Joint Conference on Neural Networks · September 28, 2015 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 ... Full text Open Access Cite

SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data.

Journal Article BMC bioinformatics · August 2015 BackgroundIdentifying 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 ... Full text Cite

Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis

Journal Article Foundations of Computational Mathematics · June 27, 2015 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 particula ... Full text Cite

Feature-aided multiple hypothesis tracking using topological and statistical behavior classifiers

Conference Proceedings of SPIE - The International Society for Optical Engineering · January 1, 2015 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 b ... Full text Cite

Probabilistic Fréchet means for time varying persistence diagrams

Journal Article Electronic Journal of Statistics · January 1, 2015 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 [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in ... Full text Open Access Cite

Easily repairable networks: reconnecting nodes after damage.

Journal Article Physical review letters · September 2014 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 o ... Full text Cite

Checkpoints couple transcription network oscillator dynamics to cell-cycle progression.

Journal Article Genome biology · September 2014 BackgroundThe 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 transcriptio ... Full text Cite

Fréchet Means for Distributions of Persistence Diagrams

Journal Article Discrete and Computational Geometry · January 1, 2014 Given a distribution ρ on persistence diagrams and observations (Formula presented.) we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1,...,Xn. If the underlying measure ρ is a combination of Dirac masses (For ... Full text Cite

Fréchet Means for Distributions of Persistence Diagrams

Journal Article Discrete & Computational Geometry · 2014 Open Access Cite

3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · April 2013 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 imagi ... Full text Cite

Failure filtrations for fenced sensor networks

Journal Article International Journal of Robotics Research · August 1, 2012 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 dist ... Full text Cite

GiA Roots: software for the high throughput analysis of plant root system architecture.

Journal Article BMC plant biology · July 2012 BackgroundCharacterizing 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 too ... Full text Cite

Design and Analysis of Large-Scale Biological Rhythm Studies: A Comparison of Algorithms for Detecting Periodic Signals in Biological Data

Journal Article PLOS Computational Biology · 2012 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. ... Cite

Realizing Boolean Dynamics in Switching Networks

Journal Article Siam Journal of Applied Dynamical Systems · 2012 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 contin ... Cite

Persistent Homology Enhanced Dimension Reduction

Journal Article Foundations of Computational Mathematics · 2012 Cite

Probability measures on the space of persistence diagrams

Journal Article Inverse Problems · December 1, 2011 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 statistic ... Full text Cite

Improving homology estimates with random walks

Journal Article Inverse Problems · December 1, 2011 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 ... Full text Cite

Persistent Intersection Homology

Journal Article Foundations of Computational Mathematics · June 1, 2011 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 h ... Full text Cite

Euler characteristics of moduli spaces of curves

Journal Article Journal of the European Mathematical Society · December 15, 2010 Full text Cite

Lipschitz functions have Lp-stable persistence

Journal Article Foundations of Computational Mathematics · April 1, 2010 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 ... Full text Cite

Imaging and analysis platform for automatic phenotyping and trait ranking of plant root systems.

Journal Article Plant physiology · March 2010 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, id ... Full text Cite

The persistent Morse complex segmentation of a 3-manifold

Journal Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) · December 1, 2009 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 th ... Full text Cite

Exact dynamics of Boolean networks with connectivity one

Journal Article PRL · 2009 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 attractor ... Cite

Extending persistence using poincaré and lefschetz duality

Journal Article Foundations of Computational Mathematics · January 1, 2009 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 spac ... Full text Cite

Persistent homology for kernels, images, and cokernels

Journal Article Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms · January 1, 2009 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 ... Full text Cite

Reeb spaces of piecewise linear mappings

Journal Article Proceedings of the Annual Symposium on Computational Geometry · December 12, 2008 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 f ... Full text Cite

Time-varying Reeb graphs for continuous space-time data

Journal Article Computational Geometry: Theory and Applications · November 1, 2008 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 ... Full text Cite

Persistent homology - a survey

Conference SURVEYS ON DISCRETE AND COMPUTATIONAL GEOMETRY: TWENTY YEARS LATER · January 1, 2008 Link to item Cite

Inferring local homology from sampled stratified spaces

Journal Article Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS · December 1, 2007 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 s ... Full text Cite

Testing Expansion in Bounded-Degree Graphs

Conference 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) · October 2007 Full text Cite

Inferring Local Homology from Sampled Stratified Spaces

Conference 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) · October 2007 Full text Cite

Stability of persistence diagrams

Journal Article Discrete and Computational Geometry · January 1, 2007 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 ... Full text Cite

Alpha-beta witness complexes

Journal Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) · January 1, 2007 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 ℝd or other metr ... Full text Cite

Extreme elevation on a 2-manifold

Journal Article Discrete and Computational Geometry · January 1, 2006 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 l ... Full text Cite

Stability of persistence diagrams

Journal Article Proceedings of the Annual Symposium on Computational Geometry · December 1, 2005 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 ... Full text Cite

Local and global comparison of continuous functions

Journal Article IEEE Visualization 2004 - Proceedings, VIS 2004 · December 1, 2004 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 lev ... Cite

Loops in Reeb graphs of 2-manifolds

Journal Article Discrete and Computational Geometry · January 1, 2004 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 ... Full text Cite

Extreme elevation on a 2-manifold

Journal Article Proceedings of the Annual Symposium on Computational Geometry · January 1, 2004 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 l ... Full text Cite

Time-varying Reeb graphs for continuous space-time data

Journal Article Proceedings of the Annual Symposium on Computational Geometry · January 1, 2004 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 ... Full text Cite

HPRM: A hierarchical PRM

Journal Article Proceedings - IEEE International Conference on Robotics and Automation · December 9, 2003 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 ... Cite

Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds

Journal Article Discrete and Computational Geometry · January 1, 2003 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 ... Full text Cite

Morse-Smale complexes for piecewise linear 3-manifolds

Journal Article Proceedings of the Annual Symposium on Computational Geometry · January 1, 2003 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 ... Full text Cite

Loops in Reeb graphs of 2-manifolds

Journal Article Proceedings of the Annual Symposium on Computational Geometry · January 1, 2003 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 ... Full text Cite

Minimal trap design

Journal Article Proceedings - IEEE International Conference on Robotics and Automation · January 1, 2001 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 introdu ... Full text Cite

Hierarchical Morse complexes for piecewise linear 2-manifolds

Journal Article Proceedings of the Annual Symposium on Computational Geometry · January 1, 2001 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 catego ... Full text Cite

A geometric parametrization for the virtual euler characteristics of the moduli spaces of real and complex algebraic curves

Journal Article Transactions of the American Mathematical Society · January 1, 2001 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 fin ... Full text Cite

Emerging Challenges in Computational Topology

Journal Article · September 1, 1999 Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology. ... Link to item Cite

The third homology group of the moduli space of curves

Journal Article Duke Mathematical Journal · January 1, 1991 Full text Cite

The Euler characteristic of the moduli space of curves

Journal Article Inventiones Mathematicae · October 1, 1986 Full text Cite

HANDLEBODY STRUCTURES FOR COMPLEX-SURFACES

Journal Article MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY · 1986 Cite

How to construct all fibered knots and links

Journal Article Topology · January 1, 1982 Full text Cite

On Almost-Everywhere Convergent Eigenfunction Expansions of the Laplace-Beltrami Operator

Journal Article Mathematical Proceedings of the Cambridge Philosophical Society · January 1, 1982 Full text Cite

Some homology lens spaces which bound rational homology balls

Journal Article Pacific Journal of Mathematics · January 1, 1981 A homology lens space is a smooth closed 3-manif old M3with Hk(M3) = Hk(L(p, l)) for all k (p some nonnegative integer). When p= 1 M3is a homology 3-sphere. It is an open question which of these homology lens spaces bound rational homology balls and of spe ... Full text Cite

On handlebody structures for hypersurfaces in ℂ3 and ℂP3

Journal Article Mathematische Annalen · February 1, 1978 Full text Cite