# Publications

## Recent Papers

- E. Brown, J. Moehlis and P. Holmes (2004) Neural Computation 16 (4): 673-715. On phase reduction and response dynamics of neural oscillator populations.
- R. Goodman, P. Holmes, and M.I. Weinstein (2004) Physica D192 (3/4): 215-248. Strong NLS soliton-defect interactions.
- E. Brown, J. Moehlis, P. Holmes, E. Clayton, J. Rajkowski and G. Aston-Jones (2004). J. Comp. Neurosci. 17 (1): 5-21.The influence of spike rate and stimulus duration on brainstem noradrenergic neurons.
- R. Altendorfer, D. Koditschek and P. Holmes (2004) Int. J. Robotics Research 23 (10-11), 979-999. Stability analyisis of legged locomotion by symmetry-factored return maps.
- R. Altendorfer, D. Koditschek and P. Holmes (2004) Int. J. Robotics Research 23 (10-11), 1001-1012. Stability analyisis of a clock-driven rigid-body SLIP model of RHex.
- J. Seipel, P. Holmes and R.J. Full (2004) Biological Cybern., 91: 76-90. Dynamics and stability of insect locomotion: A hexapedal model for horizontal plane motions.
- R. Ghigliazza and P. Holmes (2004) SIAM J. on Applied Dynamical Systems 3 (4), 636-670. Minimal models of bursting neurons: How multiple currents, conductances and timescales affect bifurcation diagrams.
- Raffaele M. Ghigliazza (2004) Ph.D. Dissertation, Neuromechanical models for insect locomotion.
- R. Ghigliazza and P. Holmes (2004) SIAM J. on Applied Dynamical Systems 3 (4), 671-700. A minimal model of a central pattern generator and motoneurons for insect locomotion.
- T.R. Smith, J. Moehlis and P. Holmes (2005) J. Fluid Mech. 538, 71-110. Low-dimensional models for turbulent plane Couette flow in a minimal flow unit.
- T.R. Smith, J. Moehlis and P. Holmes (2005) Nonlinear Dynamics 41, 275-307. Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial.
- J.E. Seipel and P. Holmes (2005) Int. J. Robotics Research 24 (8), 657-674. Running in three dimensions: analysis of a point-mass sprung-leg model.
- T.R. Smith, J. Moehlis and P. Holmes (2005) Physica D211, 347-376. Dynamics of an 0:1:2 0(2)-equivarant system: Heteroclinic cycles and periodic orbits.
- R. Ghigliazza and P. Holmes (2005) Regular and Chaotic Dynamics 10 (2), 193-225. Towards a neuromechanical model for insect locomotion: Hybrid dynamical systems.
- R. M. Ghigliazza, R. Altendorfer, P. Holmes and D. Koditschek (2005) SIAM Review 47 (3), 519-549. A simply stabilized running model.
- P. Holmes (2005) Int. J. Bifurcation and Chaos 15 (9), 2703-2716. Ninety plus thirty years of nonlinear dynamics: More is different and less is more.
- E. Brown, J. Gao, P. Holmes, R. Bogacz, M. Gilzenrat and J.D. Cohen (2005) Int. Jour. Bifurcation and Chaos 15 (3), 803-826. Simple neural networks that optimize decisions.
- R. Bogacz, E. Brown, J. Moehlis, P. Holmes and J.D. Cohen (2006) Psychological Review 113 (4), 700-765. The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced choice tasks.
- P. Holmes, R.J.Full, D. Koditschek and J. Guckenheimer (2006) SIAM Review 48 (2), 207-304. Dynamics of legged locomotion: Models, analyses and challenges.
- T. McMillen and P. Holmes (2006) J. Math. Psych. 50, 30-57. The dynamics of choice among multiple alternatives
- J. E. Seipel and P. Holmes (2006) Int. J. Robotics Research 25 (9), 889-902. Three dimensional translational dynamics and stability of multi-legged runners.
- T. McMillen and P. Holmes (2006) J. Math. Biol. 53, 843-866. An elastic rod model for anguilliform swimming.
- P.A. Simen, J.D. Cohen and P. Holmes (2006) Neural Networks 19, 1013-1026. Rapid decision threshold modulation by reward rate in a neural network.
- J. Gao and P. Holmes (2007) J. Comp. Neurosci. 22, 39-61. On the dynamics of electrically-coupled neurons with inhibitory synapses.
- R. Kukillaya and P. Holmes (2007) Biological Cybernetics 97 (5-6), 379-395. A hexapedal jointed-leg model for insect locomotion in the horizontal plane.
- Y. Liu, P. Holmes, and J.D. Cohen (2008) Neural Computation 20 (2), 345-373. A neural network model of the Eriksen task: Reduction, analysis, and data-fitting.
- M. Srinivasan and P. Holmes (2008) J. Theoretical Biology 255, 1-7. How well can spring-mass-like telescoping leg models fit multi-pedal locomotion data?
- P. Eckhoff, P. Holmes, C. Law, P.M. Connolly and J.I. Gold (2008) New J. of Physics 10, doi: 1367-2630/10/1/015006. On diffusion processes with variable drift rates as models for decision making during learning.
- P. Varkonyi, P. Holmes, T. Keimel, K. Hoffman and A.H. Cohen (2008) J. Comp. Neurosci. 25 (2) doi: 10.1007/s10827-008-0076-8. On the derivation and tuning of phase oscillator models for lamprey central pattern generators.
- T. McMillen, T.L. Williams and P. Holmes (2008) PLoS Computational Biology 4 (8), e1000157. Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuro-mechanical phase lags in anguilliform swimmers.
- P. Varkonyi and P. Holmes (2008) SIAM J. on Applied Dynamical Systems 7 (3), 766-794. On synchronization and traveling waves in chains of relaxation oscillators with an application to lamprey CPG.
- J. Proctor and P. Holmes (2008) Regular & Chaotic Dynamics 13 (4), 267-282. Steering by transient destabilization in piecewise-holonomic models of legged locomotion.
- Y.S. Liu, A.J. Yu, and P. Holmes (2009) Neural Computation 21 (6), 1520-1553. Dynamical analysis of a Bayesian inference model for the Eriksen task.
- S. Feng, P. Holmes, A. Rorie and W.T. Newsome (2009) PLoS Computational Biology 5 (2), e1000284. Can monkeys choose optimally when faced with noisy stimuli and unequal rewards?
- J. Zhang, R. Bogacz and P. Holmes (2009) J. Math. Psych. 53 (4), 231-241. A comparison of bounded diffusion models forchoice in time controlled tasks.
- J.Gao, K-F. Wong-Lin, P. Holmes, P. Simen and J.D. Cohen (2009) Neural Computation 21 (9), 2407-2436. Sequential effects in two-choice reaction time tasks: Decomposition and synthesis of mechanisms.
- P. Eckhoff, K-F. Wong-Lin and P. Holmes (2009) J. Neurosci. 29 (13), 4301-4311. Optimality and robustness of a biophysical decision-making model under nonepinephrine modulation.
- X. Zhou, K-F. Wong-Lin and P. Holmes (2009) Neural Computation 21 (8), 2336-2362. Time-varying perturbations can distinguish among integrate-to-threshold models for perceptual decision-making in reaction time tasks.
- J. Gao, G. Schwartz, P. Holmes and M. Berry II (2009) Network: Computation in Neural Systems 20 (2), 106-135. An oscillatory circuit underlying the detection of disruptions in temporally-periodic patterns.
- R. Kukillaya, J. Proctor and P. Holmes (2009) CHAOS: An Interdisciplinary Journal of Nonlinear Science 19 (2), 026107.Neuro-mechanical models for insect locomotion: Stability, maneuverability, and proprioceptive feedback.
- R. Kukillaya and P. Holmes (2009) J. Theoretical Biology 261(2), 210-22. A model for insect locomotion in the horizontal plane: Feedforward activation of fast muscles, stability, and robustness.
- P. Simen, D. Contreras, C. Buck, P. Hu, P. Holmes and J.D. Cohen (2009) J. Exp. Psych. Human Perception and Performance 35 (6), 1865-1897. Reward rate optimization in two-alternative decision making: Empirical tests of theoretical predictions.
- Bogacz, P. Hu, P. Holmes and J.D. Cohen (2010) Quart. J. Exp. Psych. 63 (5), 863-891. Do humans produce the speed-accuracy tradeoff that maximizes reward rate? Online publ. Sept 10th, 2009, DOI: 10.1080/17470210903091643.
- M. Zackenhouse, P. Holmes and R. Bogacz (2010) J. Math. Psych. 54, 230-246. Robust versus optimal strategies for two-alternative forced choice tasks.
- K.F. Wong-Lin, P. Eckhoff, P. Holmes and J.D. Cohen (2010) Brain Research 1318, 178-187. Optimal control of countermanding saccades.
- J. Proctor and P. Holmes (2010) Biological Cybernetics 102, 513-531. Reflexes and preflexes: On the role of sensory feedback on rhythmic patterns in legged locomotion.
- J. Proctor, R.P. Kukillaya and P. Holmes (2010) Phil. Trans. Roy. Soc. Lond. A. (in press). A phase-reduced neuro-mechanical model for insect locomotion: Feedforward stability and proprioceptive feedback. Supplementary Materials
- F. Balci, P. Simen, R. Niyogi, A. Saxe, P. Holmes and J.D. Cohen (2011) Attention, Perception & Psychophysics 73 (2), 640-657. Acquisition of decision making criteria: Reward rate ultimately beats accuracy.Supplementary Materials
- P. Eckhoff, K.F. Wong-Lin and P. Holmes (2011) SIAM J. on Applied Dynamical Systems 10 (1),148-188. Dimension reduction and dynamics of a spiking neuron model for decision making under neuromodulation.
- E. Fuchs, P. Holmes, T. Kiemel and A. Ayali (2011) Frontiers in Neural Circuits 4:125. Intersegmental coordination of cockroach locomotion: Adaptive control of centrally coupled pattern generator circuits.
- P. Simen, F. Balci, L. deSouza, J.D. Cohen and P. Holmes (2011) J. Neurosci. 31 (25), 9238-9253.A model of interval timing by neural integration. Supplementary Materials
- E.D. Tytell, P. Holmes and A.H. Cohen (2011) Current Opinion in Neurobiology 21 (5), 816-822. Spikes alone do not behavior make: Why neuroscience needs biomechanics.
- F. Balci, D. Freestone, P. Simen, L. deSouza, P. Holmes and J.D. Cohen (2011) Frontiers in Integrative Neurosci. 5: 56.Optimal temporal risk assessment.
- A. Nedic, D. Tomlin, P. Holmes, D.A. Prentice and J.D. Cohen (2012) Proc IEEE 100 (3), 713-733. A decision task in a social context: Human experiments, models, and analyses of behavioral data.
- E. Fuchs, P. Holmes, I. David and A. Ayali (2012) J. Exp. Biol. 215, 1884-1891. Proprioceptive feedback reinforces centrally-generated stepping patterns in the cockroach.
- S. Goldfarb, K.F. Wong-Lin, M. Schwemmer, N.E. Leonard and P. Holmes (2012) Frontiers in Psychology 3: 213. Can post-error dynamics explain sequential reaction time patterns?
- M.K. van Vugt, P. Simen, L. Nystrom, P. Holmes and J.D. Cohen (2012) Frontiers in Neurosci. 6: 106. EEG oscillations reveal neural correlates of evidence accumulation.
- D. Tomlin, A. Nedic, D.A. Prentice, P. Holmes and J.D. Cohen (2013) PLoS ONE 8 (1), e52630. The neural substrates of social influence on decision making. Supplementary Information S1. Supplementary Information S2.
- M.K. van Vugt, P. Simen, L.E. Nystrom, P. Holmes and J.D. Cohen (2014) PLoS ONE 9 (3), e90943. Lateralized readiness potentials reveal properties of a neural mechanism for implementing a decision threshold. Supplementary Materials.
- J.I. Tam and P. Holmes (2014) J. Sound Vib. 333 (6), 1767-1780. Revisiting a magnetoelastic strange attractor. J. Sound Vib. 367, 256. Corrigendum.
- P. Holmes and J.D. Cohen (2014) Topics in Cog. Sci. 6 (2), 258-278. Optimality and some of its discontents: Successes and shortcomings of existing models for binary decisions.
- P. Holmes (2014) J. Nonlinear Sci. 24 (2), 201-242 and 243-244. Some joys and trials of mathematical neuroscience.Erratum.
- S. Goldfarb, P. Simen, N.E. Leonard and P. Holmes (2014) Frontiers in Neurosci. 8: 148. A comparative study of drift-diffusion and leaky ballistic accumulator models in a reward-maximization perceptual choice task. Supplementary Materials
- A. Ayali, E. Couzin-Fuchs, I. David, O. Gal, P. Holmes and D. Knebel (2014) J. Comparative Physiol. A201, 841-850. Sensory feedback in cockroach locomotion: current knowledge and open questions.
- E. Couzin-Fuchs, T. Kiemel, O. Gal, P. Holmes and A. Ayali (2015) J. Exp. Biol. 218, 285-297. Intersegmental coupling and recovery from perturbations in freely-running cockroaches.
- E. Couzin-Fuchs, O. Gal, P. Holmes and A. Ayali (2015) J. Insect Physiol. 79, 96-104. Differential control of temporal and spatial aspects of cockroach leg coordination.
- D.Y. Takahashi, A.R. Fenley, Y. Teramoto, D.Z. Narayanan, J.I. Borjon, P. Holmes and A.A. Ghazanfar (2015) Science 349 (6249), 734-738. The developmental dynamics of marmoset monkey vocal production. Supplementary Materials.
- M. Schwemmer, S. Feng, P. Holmes, J. Gottlieb and J.D. Cohen (2015) PLoS ONE 10 (8), e136097. A multi-area stochastic model for a covert visual search task. Supplementary Text.
- A.Ayali, A. Borgmann, A. Bueschges, E. Couzin-Fuchs, S. Daun-Gruhn and P. Holmes (2015) Current Opinion in Insect Science 12, 1-10. The comparative investigation of the stick insect and cockroach models in the study of insect locomotion.
- G. Domokos, P. Holmes and Z. Langi (2016) J. Nonlinear Sci. 26 (6),1789-1815. A genealogy of convex solids via local and global bifurcations of gradient vector fields.
- S. Feng and P. Holmes (2016) IMA J. Applied Math. 81, 432-456. Will big data yield new mathematics? An evolving synergy with neuroscience.
- I. David, P. Holmes and A. Ayali (2016) Biology Open 5, 1229-1240. Endogenous rhythm and pattern generating circuit interactions in cockroach motor centers.
- V. Srivastava, P. Holmes and P. Simen (2016) J. Math. Psychol. 75, 96-109. Explicit moments of decision times for single-and double-threshold drift-diffusion processes.
- P. Kreuger, M.K. van Vugt, P. Simen, L. Nystrom, P. Holmes and J.D. Cohen (2017) J. Neurosci. Methods 281, 21-32. Evidence accumulation detected in BOLD signal using slow perceptual decision making. Supplementary Materials.
- Y. Teramoto, D.Y. Takahashi, P. Holmes and A.A. Ghazanfar (2017) eLife 2017;6:e20782. Vocal development in a Waddington landscape.
- D. Tomlin, A. Nedic, D. Prentice, P. Holmes and J.D. Cohen (2017) Cognitive, Affective and Behavioral Neuroscience 17 (4), 784-808. The integration of social influence and reward: Computational approaches and neural evidence. Supplementary Information.
- C. Mantziaris, T. Bockemuehl, P. Holmes, A. Borgmann, S. Daun and A. Bueschges (2017) J. Neurophysiol. 118, 2296-2307. Intra- and intersegmental influences among central pattern generating networks in the walking system of the stick insect.
- Z. Aminzare, V. Srivastava and P. Holmes (2018) SIAM J. on Appl. Dyn. Systems 17 (1), 626-671. Gait transitions in a phase oscillator model of an insect central pattern generator.
- J.L. Proctor and P. Holmes (2018) Biological Cybernetics 112(4),387-401. The effects of feedback on stability and maneuverability of a phase-reduced model for cockroach locomotion.