William Erik Sherwood
William Erik Sherwood
Ph. D. Candidate
Center for Applied Mathematics
657 Rhodes Hall
Cornell University
Ithaca, NY 14853
Phone: +1.607.255.4195
Fax: +1.607.255.9860
Email: sherwood@cam.cornell.edu
Advisor: John Guckenheimer
Like every writer, he measured other men's virtues by what they had accomplished, yet asked
that other men measure him by what he planned someday to do. —
“The Secret Miracle”, Jorge Luis Borges
We're working harder so we can go home earlier. — Dr. Bunsen Honeydew
Research
My main research area is dynamical systems, with specific application to computational neuroscience.
My dissertation research has focused on the development and analysis of biophysically realistic
models of a mammalian locomotor central pattern generator. This central pattern generator is an
autonomous neuronal network in the neonatal mouse spinal cord which is responsible for generating the
basic rhythmic patterns of walking, such as left-right hindlimb alternation. My work concentrates on
elucidating the mechanisms by which phase relationships in networks of bursting neurons are
established and maintained, and distinguishing the role of intrinsic neuronal properties versus
network architecture in shaping the phasing patterns of locomotor output.
Our collaborators in the
Harris-Warrick lab group
at Cornell are doing extensive experimental work
to measure the intrinsic membrane properties of the various neuron classes that comprise the central
pattern generator and the output neurons, and they are also studying the behavior of the network under
various kinds of neuromodulation. Our modeling approach is to represent the biological network
as a coupled-cell network of
ordinary differential equations, with parameterizations and topology taken from experimental data.
We use simulation, bifurcation analysis, and multiple time scale decomposition to study the properties
of individual neurons and collections of neurons representing functional subnetworks of the full model.
To understand the phasing properties of the network,
we have extended standard phase response curve (PRC) techniques to realistic burst PRCs.
Insights from burst PRCs have been incorporated into the development of coupled map techniques
that reduce the dynamics of interacting bursting neurons to discrete maps of spike trains.
These coupled maps can be used to study both the asymptotic and transient dynamics of complex networks
of biophysically realistic neurons, and this analysis of the model behavior adds to our understanding of the results from
biological experiments. The creation of new
software tools for dynamical systems modeling has also been a substantial component of the research effort.
Scientific Interests
- Dynamical systems, bifurcation theory, numerical methods
- Mathematical biology, particularly computational neuroscience and systems biology
- Scientific computing and software development (Python, C/C++, Java)
- Additional interests:
- Structure and dynamics of complex networks
- Stochastic dynamical systems and stochastic resonance
Software Development
PyDSTool is a flexible, open source toolkit for data-driven, integrated dynamical systems modeling and analysis, written in Python and C. It includes tools for creating complex, hierarchical models of many types, including ordinary differential equations, differential-algebraic equations, discrete maps, hybrid dynamical systems, and coupled-cell systems, with automatic code generation, compilation, and dynamic linking. The entire system is object-oriented, scriptable, and user-extensible. It features fast, low-level integrators for stiff and non-stiff ODE and DAE vector fields; multiple user-defined events and support for event-driven simulations; and direct input of data traces into vector fields during integration. Tools for numerical bifurcation analysis and continuation are incorporated via direct invocation of AUTO routines, and there are modules for parameter estimation, optimization, and dimension reduction. Modules for building models of neural systems, biochemical reaction networks, and biomechanical systems are also included.
Developers: Rob Clewley, Drew Lamar, Erik Sherwood
ODETools is an open source, object-oriented Matlab package for dynamical systems modeling and analysis, supporting ordinary differential equation and hybrid vector fields. It is scriptable and user-extensible via the Matlab language and environment, and it provides fast, low-level integration of stiff and non-stiff vector fields via the MEX interface. ODETools supports multiple user defined events for event driven simulation and high-accuracy Taylor series integration of ODE, DAE, and hybrid vector fields using automatic differentiation via the ADMC++ package. Bifurcation analysis and continuation routines for ODE vector fields are also implemented.
NOTE: ODETools is no longer under active development and there is no support for it. It has been superseded by PyDSTool.
Developers: Ricardo Oliva, Eric Phipps, Erik Sherwood
DsTool
DsTool is a program for simulation, visualization, and phase plane analysis of dynamical systems. It can handle ordinary differential equation vector fields and discrete maps. The program was written for UNIX computers running XWindow, and the current version requires tcl.
NOTE: DsTool is no longer under active development by anyone at the Center for Applied Mathematics..
Publications/Talks/Works in Progress
Talks:
Posters:
Publications:
- forsan et haec olim meminisse iuvabit
Teaching/Outreach
Courses taught:
Research Experiences for Undergraduates:
Outreach and related activities:
Curriculum Vitæ
