# Kevin K Lin

**Review articles, extended abstracts, etc.**

Nonequilibrium steady-states

Monte Carlo, data assimilation, and related methods

Shear-induced chaos

Scaling laws and chaotic dynamics

Theses

### Research papers

- G Lajoie, K K Lin, J-P Thivierge, and E Shea-Brown, "Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination",
*submitted*(2016)

- F Lu, K K Lin, and A Chorin, "Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation",
*submitted*(2015)[ preprint ] - J Goodman, K K Lin, and M Morzfeld, "Small-noise analysis and symmetrization of implicit Monte Carlo samplers",
*to appear in**Commun. Pure Appl. Math.*(2015)[ published version ] [ preprint ] - G Hooker, K K Lin, and B Rogers, "Control theory and experimental design in diffusion processes",
*SIAM JUQ***3**(2015)*pp. 234--264*[ preprint ] [ published version ] - K K Lin and J Mattingly, "Efficient sensitivity analysis for stochastic differential equations",
*in preparation*(2014) - K C A Wedgwood, K K Lin, R Thul, and S Coombes, "Phase-amplitude descriptions of neural oscillator models",
*J. Math. Neurosci.***3**(2013)[ published version ] [ preprint ] - D Lyttle, B Gereke, K K Lin, and J-M Fellous, "Spatial scale and place field stability in a grid-to-place cell model of the dorsoventral axis of the hippocampus",
*Hippocampus***23**(2013)*pp. 729--744*

- K K Lin, K C A Wedgwood, S Coombes, and L-S Young, "Limitations of perturbative techniques in the analysis of rhythms and oscillations",
*J. Math. Biol.***66**(2013)*pp. 139--161*[ published version ] [ preprint ] - G Lajoie, K K Lin, and E Shea-Brown, "Chaos and reliability in balanced spiking networks with temporal drive",
*Phys. Rev. E***87**(2013)[ published version ] [ preprint ] - A Barrat, B Fernandez, K K Lin, and L-S Young, "Modeling temporal networks using random itineraries",
*Phys. Rev. Lett.***110**(2013)*(article no 158702)*[ published version ] [ preprint ] - K K Lin and L-S Young, "Dynamics of periodically-kicked oscillators",
*Journal of Fixed Point Theory and Applications***7**(2010)*pp. 291--312*[ published version ] [ preprint ] - K K Lin and L-S Young, "Nonequilibrium steady states for certain Hamiltonian models",
*J. Stat. Phys.***139**(2010)*pp. 630--657*[ published version ] [ preprint ] - P Balint, K K Lin, and L-S Young, "Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains",
*Commun. Math. Phys.***294**(2010)*pp. 199--228*[ published version ] [ preprint ] - K K Lin, E Shea-Brown, and L-S Young, "Reliability of layered neural oscillator networks",
*Commun. Math. Sci.***7**(2009)*pp. 239--247*[ preprint ] [ published version ] - K K Lin, E Shea-Brown, and L-S Young, "Reliability of coupled oscillators",
*J. Nonlin. Sci.***19**(2009)*pp. 497--545*

- K K Lin, E Shea-Brown, and L-S Young, "Spike-time reliability of layered neural oscillator networks",
*J. Computat. Neurosci.***27**(2009)*pp. 135--160*[ published version ] [ preprint ] - K K Lin and J Goodman, "Coupling control variates in dynamic Monte Carlo",
*J. Computat. Phys.***228**(2009)*pp. 7127--7136*[ published version ] [ preprint ] - K K Lin and L-S Young, "Shear-induced chaos",
*Nonlinearity***21**(2008)*pp. 899--922**This was one of Nonlinearity's "high profile articles of 2008"*[ published version ] [ preprint ] - K K Lin and L-S Young, "Correlations in nonequilibrium steady-states of random-halves models",
*J. Stat. Phys.***128**(2007)*pp. 607--639*[ published version ] [ preprint ] - K K Lin, "Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator",
*SIAM J. Applied Dyn. Sys.***5**(2006)*pp. 179--204*[ published version ] [ preprint ] - F Hoppensteadt and K K Lin, "Propagating coalitions in networks of nonlinear oscillators",
*Sci. Math. Jap.***64**(2006)*pp. 779--784* - K K Lin, "Convergence of invariant densities in the small-noise limit",
*Nonlinearity***18**(2005)*pp. 659--683*[ published version ] [ preprint ] - L Guillopé, K K Lin, and M Zworski, "The Selberg zeta function for convex co-compact Schottky groups",
*Commun. Math. Phys.***245**(2004)*pp. 149--176*[ published version ] [ preprint ] - K K Lin, "Numerical study of quantum resonances in chaotic scattering",
*J. Computat. Phys.***176**(2002)*pp. 295--329*[ published version ] [ preprint ] - K K Lin and M Zworski, "Quantum resonances in chaotic scattering",
*Chem. Phys. Lett.***355**(2002)*pp. 201--205*[ published version ] [ preprint ]

### Review articles, extended abstracts, etc.

- K K Lin, "Spike-time reliability of layered neural oscillator networks",
*Proceedings of the 12th Granada Seminar*(2013)*Extended abstract from the 12th Granada Seminar on Computational and Statistical Physics: Physics, Computation, and the Mind - Advances and Challenges at Interfaces* - K K Lin, "Stimulus-response reliability of biological networks",
*Nonautonomous and Random Dynamical Systems in Life Sciences*(2012)*Invited review article in collection edited by P Kloeden and C Poetzsche.*

- K K Lin, "Reliable and unreliable behavior in oscillator networks",
*Oberwolfach Reports***8**(2011)*pp. 2293--2295**(This is an extended abstract from a mini-workshop in August 2011.)*

## Dynamics of neurons and neuronal networks

- G Lajoie, K K Lin, J-P Thivierge, and E Shea-Brown, "Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination",
*submitted*(2016)

- K K Lin, "Spike-time reliability of layered neural oscillator networks",
*Proceedings of the 12th Granada Seminar*(2013)*Extended abstract from the 12th Granada Seminar on Computational and Statistical Physics: Physics, Computation, and the Mind - Advances and Challenges at Interfaces* - K C A Wedgwood, K K Lin, R Thul, and S Coombes, "Phase-amplitude descriptions of neural oscillator models",
*J. Math. Neurosci.***3**(2013)[ published version ] [ preprint ] - D Lyttle, B Gereke, K K Lin, and J-M Fellous, "Spatial scale and place field stability in a grid-to-place cell model of the dorsoventral axis of the hippocampus",
*Hippocampus***23**(2013)*pp. 729--744*

- K K Lin, K C A Wedgwood, S Coombes, and L-S Young, "Limitations of perturbative techniques in the analysis of rhythms and oscillations",
*J. Math. Biol.***66**(2013)*pp. 139--161*[ published version ] [ preprint ] - G Lajoie, K K Lin, and E Shea-Brown, "Chaos and reliability in balanced spiking networks with temporal drive",
*Phys. Rev. E***87**(2013)[ published version ] [ preprint ] - K K Lin, "Stimulus-response reliability of biological networks",
*Nonautonomous and Random Dynamical Systems in Life Sciences*(2012)*Invited review article in collection edited by P Kloeden and C Poetzsche.*[ preprint ] - K K Lin, "Reliable and unreliable behavior in oscillator networks",
*Oberwolfach Reports***8**(2011)*pp. 2293--2295**(This is an extended abstract from a mini-workshop in August 2011.)*

- K K Lin, E Shea-Brown, and L-S Young, "Reliability of layered neural oscillator networks",
*Commun. Math. Sci.***7**(2009)*pp. 239--247*[ preprint ] [ published version ] - K K Lin, E Shea-Brown, and L-S Young, "Reliability of coupled oscillators",
*J. Nonlin. Sci.***19**(2009)*pp. 497--545*

- K K Lin, E Shea-Brown, and L-S Young, "Spike-time reliability of layered neural oscillator networks",
*J. Computat. Neurosci.***27**(2009)*pp. 135--160*[ published version ] [ preprint ] - K K Lin, "Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator",
*SIAM J. Applied Dyn. Sys.***5**(2006)*pp. 179--204*[ published version ] [ preprint ]

## Nonequilibrium steady-states

- K K Lin and L-S Young, "Nonequilibrium steady states for certain Hamiltonian models",
*J. Stat. Phys.***139**(2010)*pp. 630--657*

- P Balint, K K Lin, and L-S Young, "Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains",
*Commun. Math. Phys.***294**(2010)*pp. 199--228*[ published version ] [ preprint ] - K K Lin and J Goodman, "Coupling control variates in dynamic Monte Carlo",
*J. Computat. Phys.***228**(2009)*pp. 7127--7136*[ published version ] [ preprint ] - K K Lin and L-S Young, "Correlations in nonequilibrium steady-states of random-halves models",
*J. Stat. Phys.***128**(2007)*pp. 607--639*[ published version ] [ preprint ]

## Monte Carlo, data assimilation, and related methods

- F Lu, K K Lin, and A Chorin, "Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation",
*submitted*(2015)

- J Goodman, K K Lin, and M Morzfeld, "Small-noise analysis and symmetrization of implicit Monte Carlo samplers",
*to appear in**Commun. Pure Appl. Math.*(2015)[ published version ] [ preprint ] - G Hooker, K K Lin, and B Rogers, "Control theory and experimental design in diffusion processes",
*SIAM JUQ***3**(2015)*pp. 234--264*[ preprint ] [ published version ] - K K Lin and J Mattingly, "Efficient sensitivity analysis for stochastic differential equations",
*in preparation*(2014) - K K Lin and J Goodman, "Coupling control variates in dynamic Monte Carlo",
*J. Computat. Phys.***228**(2009)*pp. 7127--7136*[ published version ] [ preprint ] - K K Lin, "Random perturbations of SRB measures and numerical studies of chaotic dynamics",
*LBNL Technical Report***53522**(2003)*(PhD thesis in Mathematics)*[ Abstract ]

## Shear-induced chaos

- K C A Wedgwood, K K Lin, R Thul, and S Coombes, "Phase-amplitude descriptions of neural oscillator models",
*J. Math. Neurosci.***3**(2013)

- K K Lin, K C A Wedgwood, S Coombes, and L-S Young, "Limitations of perturbative techniques in the analysis of rhythms and oscillations",
*J. Math. Biol.***66**(2013)*pp. 139--161*[ published version ] [ preprint ] - K K Lin and L-S Young, "Dynamics of periodically-kicked oscillators",
*Journal of Fixed Point Theory and Applications***7**(2010)*pp. 291--312*[ published version ] [ preprint ] - K K Lin and L-S Young, "Shear-induced chaos",
*Nonlinearity***21**(2008)*pp. 899--922**This was one of Nonlinearity's "high profile articles of 2008"*[ published version ] [ preprint ] - K K Lin, "Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator",
*SIAM J. Applied Dyn. Sys.***5**(2006)*pp. 179--204*[ published version ] [ preprint ]

## Scaling laws and chaotic dynamics

- K K Lin, "Convergence of invariant densities in the small-noise limit",
*Nonlinearity***18**(2005)*pp. 659--683*

- L Guillopé, K K Lin, and M Zworski, "The Selberg zeta function for convex co-compact Schottky groups",
*Commun. Math. Phys.***245**(2004)*pp. 149--176*[ published version ] [ preprint ] - K K Lin, "Numerical study of quantum resonances in chaotic scattering",
*J. Computat. Phys.***176**(2002)*pp. 295--329*[ published version ] [ preprint ] - K K Lin and M Zworski, "Quantum resonances in chaotic scattering",
*Chem. Phys. Lett.***355**(2002)*pp. 201--205*[ published version ] [ preprint ]

## Theses

- K K Lin, "Random perturbations of SRB measures and numerical studies of chaotic dynamics",
*LBNL Technical Report***53522**(2003)*(PhD thesis in Mathematics)*

- K K Lin, "Coordinate-independent computations on differential equations",
*MIT AI Tech Memo***1631**(1997)*(MEng thesis in Computer Science and Engineering)*[ Abstract ]

The work described above have been supported by the National Science Foundation, the Fannie and John Hertz Foundation, the LBL Math Department and NERSC, and Project MAC.

**Collaborators:**
Peter
Balint,
Alain Barrat,
Alexandre Chorin,
Steve
Coombes,
Jean-Marc
Fellous,
Bastien
Fernandez,
Jonathan
Goodman,
Laurent
Guilllopé,
Giles Hooker,
Frank Hoppensteadt,
Guillaume
Lajoie,
Fei Lu,
David
Lyttle,
Jonathan
Mattingly,
Matthias
Morzfeld,
Bruce
Rogers,
Eric
Shea-Brown,
Rüdiger
Thul,
JP Thivierge,
Kyle Wedgwood,
Lai-Sang
Young,
and Maciej
Zworski.