Horacio Rotstein
Professor, Biological Sciences
CKB 420-D Cullimore Hall
Education
Ph.D.; Technion, Israel Institute of Technology; Applied Mathematics; 1998
M.S.; Technion, Israel Institute of Technology; Applied Mathematics; 1994
Licenciado en Quimica (5 years program); Universidad Nacional del Sur; Icenciado En Quimica (5 Years Program) Chemistry; 1989
M.S.; Technion, Israel Institute of Technology; Applied Mathematics; 1994
Licenciado en Quimica (5 years program); Universidad Nacional del Sur; Icenciado En Quimica (5 Years Program) Chemistry; 1989
Website
Teaching Interests
Applied Mathematics, Mathematical Biology, Dynamical Systems, Computational Neuroscience, Systems Biology
Past Courses
BIOL 432: INTRO TO COMP NEUROSCIENCE
BIOL 436: ADVANCED NEUROSCIENCE MODELING
BIOL 498: SPECIAL TOPICS IN BIOLOGY
BIOL 631: PROPOSAL PREP FOR EXTNL FUNDIN
BIOL 635: INTRO TO COMP NEUROSCIENCE
BIOL 636: ADVANCED COMP NEUROSCIENCE
BIOL 698: ST: COMPUTATIONAL NEUROSCIENCE
BIOL 791: BIOLOGY SEMINAR
MATH 111: CALCULUS I
MATH 111: CALCULUS I - HONORS
MATH 112: CALCULUS II
MATH 112: CALCULUS II - HONORS
MATH 211: CALCULUS IIIA
MATH 222: DIFFERENTIAL EQUATIONS
MATH 337: LINEAR ALGEBRA
MATH 371: PHYSIOLOGY AND MEDICINE
MATH 430: ANALYTICL & COMPUTATNL NEUROSCI
MATH 430: ANALYTICL & COMPUTNL NEUROSCI
MATH 451: METHODS APPL MATH II
MATH 473: INTERMED DIFFEREN EQUATN
MATH 635: ANALYTCL COMPUTATIONAL NEURO
MATH 635: ANALYTICAL COMPUTATIONAL NEUROS
MATH 636: SYSTM COMPUTATNL NEUROSCI
MATH 637: FOUND OF MATHEMATICAL BIOLOGY
BIOL 436: ADVANCED NEUROSCIENCE MODELING
BIOL 498: SPECIAL TOPICS IN BIOLOGY
BIOL 631: PROPOSAL PREP FOR EXTNL FUNDIN
BIOL 635: INTRO TO COMP NEUROSCIENCE
BIOL 636: ADVANCED COMP NEUROSCIENCE
BIOL 698: ST: COMPUTATIONAL NEUROSCIENCE
BIOL 791: BIOLOGY SEMINAR
MATH 111: CALCULUS I
MATH 111: CALCULUS I - HONORS
MATH 112: CALCULUS II
MATH 112: CALCULUS II - HONORS
MATH 211: CALCULUS IIIA
MATH 222: DIFFERENTIAL EQUATIONS
MATH 337: LINEAR ALGEBRA
MATH 371: PHYSIOLOGY AND MEDICINE
MATH 430: ANALYTICL & COMPUTATNL NEUROSCI
MATH 430: ANALYTICL & COMPUTNL NEUROSCI
MATH 451: METHODS APPL MATH II
MATH 473: INTERMED DIFFEREN EQUATN
MATH 635: ANALYTCL COMPUTATIONAL NEURO
MATH 635: ANALYTICAL COMPUTATIONAL NEUROS
MATH 636: SYSTM COMPUTATNL NEUROSCI
MATH 637: FOUND OF MATHEMATICAL BIOLOGY
Research Interests
Mathematical and Computational Neuroscience, Dynamical Systems, Mathematical and Computational Biology and Chemistry, Systems Biology
Journal Article
Tabak , Esteban , & Rotstein, Horacio (2019). Analysis of spike-driven processes through attributable components . Comm Math Sci, 17, 1177-1192.
Rotstein, Horacio, & Nadim, Farzan (2019). Membrane potential resonance arising from responses of neuronal models to oscillatory inputs in current versus voltage clamp. Biological Cybernetics, 113, 373–395.
Bel, Andrea, , & Rotstein, Horacio (2019). Resonance-based mechanisms of generation of relaxation oscillations in networks of non-oscillatory neurons. Trends in Mathematics: Research Perspectives (CRM Barcelona, Summer 2018), 2018,
Bel, Andrea , & Torresi, Ana, & Rotstein, Horacio (2019). Inhibition-based relaxation oscillations emerge in resonator networks. Mathematical Modeling of Natural Phenomena, 14, 405 (article number).
Leiser, Randolph , & Rotstein, Horacio (2019). Network resonance: impedance interactions via a frequency response alternating map (FRAM). SIAM Journal of Applied Dynamical Systems (SIADS), 18, 769-807.
Rotstein, Horacio, & Nadim, Farzan (2019). Membrane potential resonance arising from responses of neuronal models to oscillatory inputs in current versus voltage clamp. Biological Cybernetics, 113, 373–395.
Bel, Andrea, , & Rotstein, Horacio (2019). Resonance-based mechanisms of generation of relaxation oscillations in networks of non-oscillatory neurons. Trends in Mathematics: Research Perspectives (CRM Barcelona, Summer 2018), 2018,
Bel, Andrea , & Torresi, Ana, & Rotstein, Horacio (2019). Inhibition-based relaxation oscillations emerge in resonator networks. Mathematical Modeling of Natural Phenomena, 14, 405 (article number).
Leiser, Randolph , & Rotstein, Horacio (2019). Network resonance: impedance interactions via a frequency response alternating map (FRAM). SIAM Journal of Applied Dynamical Systems (SIADS), 18, 769-807.
SHOW MORE
Bel, Andrea, & Rotstein, Horacio (2019). Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations . Journal of Computational Neuroscience, 46, 169-195.
Tran, Trinh, & Unal, Cagri, & Zaborszky, Laszlo, & Kirkwood, Alfredo, & Rotstein, Horacio, & Golowasch, Jorge (2019). Ionic current correlations are ubiquitous across phyla. Scientific Reports, 9, 1687.
Rotstein, Horacio (2018). Subthreshold amplitude and phase resonance in single neurons: 2D models. Encyclopedia of Computational Neuroscience,
Rotstein, Horacio (2018). Subthreshold antiresonance and antiphasonance in single neurons: 3D models . Encyclopedia of Computational Neuroscience,
Turnquist, Axel, & Rotstein, Horacio (2018). Quadratization: From conductance-based models to caricature models with parabolic nonlinearities. Encyclopedia of Computational Neuroscience,
Kass, Robert, & Amari, Shun-ichi, & Arai, Kensuke, & Brown, Emery, & Diekman, Casey, & Diesmann, Markus, & Doiron, Brent, & Eden, Uri, & Fairhall, Adrienne, & Fiddyment, Grant, & Fukai, Tomoki, & Grun, Sonja, & Harrison, Matthew, & Helias, Moritz, & Nakahara, Hiroyuki, & Teramae, Jun-nosuke, & Thomas, Peter, & Reimers, Mark, & Rodu, Jordan, & Rotstein, Horacio, & Shea-Brown, Eric, & Shimazaki, Hideaki, & Shinomoto, Shigeru, & Yu, Byron, & Kramer, Mark (2018). Computational neuroscience: mathematical and statistical perspectives. Annual Review of Statistics and its Applications, 5(1), 183-214.
Burke, Dennis, & Rotstein, Horacio, & Álvarez, Verónica (2017). Striatal local circuitry: a new framework for lateral inhibition . Neuron,
Rotstein, Horacio (2017). Spiking resonances in models with the same slow resonant and fast amplifying ionic currents but different subthreshold dynamic properties. Journal of Computational Neuroscience,
Rotstein, Horacio, & Schneider, Elisa , & Szczupak, Lidia (2017). Feedback signal from motoneurons influences a rhythmic pattern generator. The Journal of Neuroscience,
Leiser, Randolph, & Rotstein, Horacio (2017). Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity. Physical Review E,
Rotstein, Horacio (2017). Resonance modulation, annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics. Journal of Computational Neuroscience,
Fox, David, & Tseng, Hua-an, & Smolinsky, Tomasz, & Rotstein, Horacio, & Nadim, Farzan (2017). Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents. PLoS Comp Biology,
Rotstein, Horacio (2017). The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales. Journal of Computational Neuroscience,
Zhou, Julia , & Vo, Theodore, & Rotstein, Horacio, & McCarthy, Michelle , & Kopell, Nancy (2016). M-current expands the range of gamma frequency inputs to which the neuronal target entrains. Journal of Mathematical Neuroscience, 8, 13.
Rotstein, Horacio, & Olarinre, Motolani, & Golowasch, Jorge (2016). Dynamic compensation mechanism give rise to period and duty cycle level sets in oscillatory neuronal models. Journal of Neurophysiology, Online First,
Chen, Yinbo, & Li, Xinping, & Rotstein, Horacio, & Nadim, Farzan (2016). Membrane potential resonance frequency directly influences network frequency through gap junctions. Journal of Neurophysiology, 116, 1554-1563.
Espanol, Malena, & Rotstein, Horacio (2015). Complex mixed-mode oscillatory patterns in a periodically forced excitable Oregonator. Chaos, 25, 064601 (18 pages).
Schindewolf, Craig, & Kim, Donwgook, & Bel, Andrea, & Rotstein, Horacio (2015). Complex patterns in networks hyperexcitable neurons with multiple time scales. Theoretical Computer Science C - Natural Computing, focus issue on "Brain and Neural Networks Computing,
Rotstein, Horacio (2015). Cluster-size dynamics: A phenomenological model for the interaction between coagulation and fragmentation. Journal of Chemical Physics, 142, 224101 (11 pages).
Rotstein, Horacio (2015). Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents . Journal of Computational Neuroscience, 38, 325 - 354.
Rotstein, Horacio (2015). Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents. J Comp Neurosci, Online First,
Rotstein, Horacio, & Nadim, Farzan (2014). Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. Journal of Computational Neuroscience, 37, 9-28.
Rotstein, Horacio (2014). Frequency preference response to oscillatory inputs in two-dimensional neural models: a geometric approach to subthreshold amplitude and phase resonance. Journal of Mathematical Neuroscience, 4, 1 - 41 (article number 4).
Kaper, Tasso, & Kramer, Mark, & Rotstein, Horacio (2013). Introduction to the focus issue: Rhythms and Dynamic Transitions in Neurological Disease: Modeling, Computation, and Experiment . Chaos , 23, 046001.
Rotstein, Horacio (2013). Preferred frequency responses to oscillatory inputs in an electrochemical cell model: Linear amplitude and phase resonance . Physical Review E, 88, 062913 .
Rotstein, Horacio, & Nadim, Farzan (2013). Neurons and neural networks: Computational models. Encyclopedia of Life Sciences (ohn Wiley \& Sons, Ltd: Chicheste), DOI: 10.1002/9780470015902.a0000089.pub2.
Rotstein, Horacio (2013). Abrupt and gradual transitions between low and hyperexcited firing frequencies in neuronal models with fast synaptic excitation: A comparative study. Chaos,
Stark, Eran, & Eichler, Ronny, & Roux, Lisa , & Fujisawa, Shigeyoshi, & Rotstein, Horacio, & Buzsaki, Gyorgy (2013). Inhibition induced theta resonance in cortical circuits. Neuron, 80, 1263 - 1276.
Rotstein, Horacio, & Nadim, Farzan (2013). Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. Journal of Computational Neuroscience, Online First, 1 - 20.
Rotstein, Horacio, & Wu, Hui (2012). Swing, release, and escape mechanisms contribute to the generation of phase-locked patterns in a globablly coupled FitzHugh-Nagumo model. Physical Review E, 35.
Rotstein, Horacio, & Wu, Hui (2012). Dynamic mechanisms of generation of oscillatory cluster patterns in a globally coupled chemical system. The Journal of Chemical Physics, 137, 104908 (1-20).
Rotstein, Horacio, & Coombes, Stephen, & Gheorghe, Ana (2012). Canard-like explosion of limit cycles in two-dimensional piecewise-linear models of FitzHugh-Nagumo type. SIAM Journal on Applied Dynamical Systems (SIADS), 11, 135 - 180.
Kispersky, Tilman , & White, John , & Rotstein, Horacio (2010). The Mechanism of abrupt transition from normal to hyperexcitable (epileptic) spiking activity in medial entorhinal cortex layer II stellate cells. PLoS One, 5, e13697 (1-21).
Boubendir, Yassine, & Mendez, Vicenc, & Rotstein, Horacio (2010). Dynamics of one- and two-dimensional fronts in a bistable equation with delayed global coupling: localization and control.. Physical Review E, 82(1539-3755 (Print) - 1550-2376 (Online) ), 036601 (1-20).
Rotstein, Horacio, & Jalics, Jozsi, & Krupa, Martin (2010). Mixed-mode oscillations in a three time scale system of ODEs motivated by a neural model. Dynamical Systems: An International Journal, iFirst, 1-38.
Rotstein, Horacio, & Wechselberger, Martin , & Kopell, Nancy (2008). Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model. SIAM Journal on Applied Dynamical Systems (SIADS), 7, 1582 - 1611.
Tran, Trinh, & Unal, Cagri, & Zaborszky, Laszlo, & Kirkwood, Alfredo, & Rotstein, Horacio, & Golowasch, Jorge (2019). Ionic current correlations are ubiquitous across phyla. Scientific Reports, 9, 1687.
Rotstein, Horacio (2018). Subthreshold amplitude and phase resonance in single neurons: 2D models. Encyclopedia of Computational Neuroscience,
Rotstein, Horacio (2018). Subthreshold antiresonance and antiphasonance in single neurons: 3D models . Encyclopedia of Computational Neuroscience,
Turnquist, Axel, & Rotstein, Horacio (2018). Quadratization: From conductance-based models to caricature models with parabolic nonlinearities. Encyclopedia of Computational Neuroscience,
Kass, Robert, & Amari, Shun-ichi, & Arai, Kensuke, & Brown, Emery, & Diekman, Casey, & Diesmann, Markus, & Doiron, Brent, & Eden, Uri, & Fairhall, Adrienne, & Fiddyment, Grant, & Fukai, Tomoki, & Grun, Sonja, & Harrison, Matthew, & Helias, Moritz, & Nakahara, Hiroyuki, & Teramae, Jun-nosuke, & Thomas, Peter, & Reimers, Mark, & Rodu, Jordan, & Rotstein, Horacio, & Shea-Brown, Eric, & Shimazaki, Hideaki, & Shinomoto, Shigeru, & Yu, Byron, & Kramer, Mark (2018). Computational neuroscience: mathematical and statistical perspectives. Annual Review of Statistics and its Applications, 5(1), 183-214.
Burke, Dennis, & Rotstein, Horacio, & Álvarez, Verónica (2017). Striatal local circuitry: a new framework for lateral inhibition . Neuron,
Rotstein, Horacio (2017). Spiking resonances in models with the same slow resonant and fast amplifying ionic currents but different subthreshold dynamic properties. Journal of Computational Neuroscience,
Rotstein, Horacio, & Schneider, Elisa , & Szczupak, Lidia (2017). Feedback signal from motoneurons influences a rhythmic pattern generator. The Journal of Neuroscience,
Leiser, Randolph, & Rotstein, Horacio (2017). Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity. Physical Review E,
Rotstein, Horacio (2017). Resonance modulation, annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics. Journal of Computational Neuroscience,
Fox, David, & Tseng, Hua-an, & Smolinsky, Tomasz, & Rotstein, Horacio, & Nadim, Farzan (2017). Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents. PLoS Comp Biology,
Rotstein, Horacio (2017). The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales. Journal of Computational Neuroscience,
Zhou, Julia , & Vo, Theodore, & Rotstein, Horacio, & McCarthy, Michelle , & Kopell, Nancy (2016). M-current expands the range of gamma frequency inputs to which the neuronal target entrains. Journal of Mathematical Neuroscience, 8, 13.
Rotstein, Horacio, & Olarinre, Motolani, & Golowasch, Jorge (2016). Dynamic compensation mechanism give rise to period and duty cycle level sets in oscillatory neuronal models. Journal of Neurophysiology, Online First,
Chen, Yinbo, & Li, Xinping, & Rotstein, Horacio, & Nadim, Farzan (2016). Membrane potential resonance frequency directly influences network frequency through gap junctions. Journal of Neurophysiology, 116, 1554-1563.
Espanol, Malena, & Rotstein, Horacio (2015). Complex mixed-mode oscillatory patterns in a periodically forced excitable Oregonator. Chaos, 25, 064601 (18 pages).
Schindewolf, Craig, & Kim, Donwgook, & Bel, Andrea, & Rotstein, Horacio (2015). Complex patterns in networks hyperexcitable neurons with multiple time scales. Theoretical Computer Science C - Natural Computing, focus issue on "Brain and Neural Networks Computing,
Rotstein, Horacio (2015). Cluster-size dynamics: A phenomenological model for the interaction between coagulation and fragmentation. Journal of Chemical Physics, 142, 224101 (11 pages).
Rotstein, Horacio (2015). Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents . Journal of Computational Neuroscience, 38, 325 - 354.
Rotstein, Horacio (2015). Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents. J Comp Neurosci, Online First,
Rotstein, Horacio, & Nadim, Farzan (2014). Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. Journal of Computational Neuroscience, 37, 9-28.
Rotstein, Horacio (2014). Frequency preference response to oscillatory inputs in two-dimensional neural models: a geometric approach to subthreshold amplitude and phase resonance. Journal of Mathematical Neuroscience, 4, 1 - 41 (article number 4).
Kaper, Tasso, & Kramer, Mark, & Rotstein, Horacio (2013). Introduction to the focus issue: Rhythms and Dynamic Transitions in Neurological Disease: Modeling, Computation, and Experiment . Chaos , 23, 046001.
Rotstein, Horacio (2013). Preferred frequency responses to oscillatory inputs in an electrochemical cell model: Linear amplitude and phase resonance . Physical Review E, 88, 062913 .
Rotstein, Horacio, & Nadim, Farzan (2013). Neurons and neural networks: Computational models. Encyclopedia of Life Sciences (ohn Wiley \& Sons, Ltd: Chicheste), DOI: 10.1002/9780470015902.a0000089.pub2.
Rotstein, Horacio (2013). Abrupt and gradual transitions between low and hyperexcited firing frequencies in neuronal models with fast synaptic excitation: A comparative study. Chaos,
Stark, Eran, & Eichler, Ronny, & Roux, Lisa , & Fujisawa, Shigeyoshi, & Rotstein, Horacio, & Buzsaki, Gyorgy (2013). Inhibition induced theta resonance in cortical circuits. Neuron, 80, 1263 - 1276.
Rotstein, Horacio, & Nadim, Farzan (2013). Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. Journal of Computational Neuroscience, Online First, 1 - 20.
Rotstein, Horacio, & Wu, Hui (2012). Swing, release, and escape mechanisms contribute to the generation of phase-locked patterns in a globablly coupled FitzHugh-Nagumo model. Physical Review E, 35.
Rotstein, Horacio, & Wu, Hui (2012). Dynamic mechanisms of generation of oscillatory cluster patterns in a globally coupled chemical system. The Journal of Chemical Physics, 137, 104908 (1-20).
Rotstein, Horacio, & Coombes, Stephen, & Gheorghe, Ana (2012). Canard-like explosion of limit cycles in two-dimensional piecewise-linear models of FitzHugh-Nagumo type. SIAM Journal on Applied Dynamical Systems (SIADS), 11, 135 - 180.
Kispersky, Tilman , & White, John , & Rotstein, Horacio (2010). The Mechanism of abrupt transition from normal to hyperexcitable (epileptic) spiking activity in medial entorhinal cortex layer II stellate cells. PLoS One, 5, e13697 (1-21).
Boubendir, Yassine, & Mendez, Vicenc, & Rotstein, Horacio (2010). Dynamics of one- and two-dimensional fronts in a bistable equation with delayed global coupling: localization and control.. Physical Review E, 82(1539-3755 (Print) - 1550-2376 (Online) ), 036601 (1-20).
Rotstein, Horacio, & Jalics, Jozsi, & Krupa, Martin (2010). Mixed-mode oscillations in a three time scale system of ODEs motivated by a neural model. Dynamical Systems: An International Journal, iFirst, 1-38.
Rotstein, Horacio, & Wechselberger, Martin , & Kopell, Nancy (2008). Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model. SIAM Journal on Applied Dynamical Systems (SIADS), 7, 1582 - 1611.
COLLAPSE
Chapter
Fox, David, & Rotstein, Horacio, & Nadim, Farzan (2014). Bursting in Neurons and Small Networks, Jaeger, Dieter; Jung, Ranu (Eds.), Springer. (pp. 1-17). New York: Springer
Rotstein, Horacio (2014). Subthreshold amplitude and phase resonance in single cells, Jaeger, Dieter; Jung, Ranu (Eds.), Springer. (pp. 1 - 12). New York: Springer
Rotstein, Horacio (2014). Mixed-mode oscillations in single neurons, Jaeger, Dieter; Jung, Ranu (Eds.), Springer. (pp. 1 - 13). New York: Springer
Rotstein, Horacio (2014). Subthreshold amplitude and phase resonance in single cells, Jaeger, Dieter; Jung, Ranu (Eds.), Springer. (pp. 1 - 12). New York: Springer
Rotstein, Horacio (2014). Mixed-mode oscillations in single neurons, Jaeger, Dieter; Jung, Ranu (Eds.), Springer. (pp. 1 - 13). New York: Springer