Addresses: Dept of Mathematics &
VOICE: (315)-268-2399, FAX: (315)-268-2395
My dissertation research focused on application of algorithms for numerical exploration of unstable invariant sets to low dimensional systems. In particular, the effort was focused on transient chaos within finite dimensional Galerkin models of planar Couette flow, with a goal of increasing the understanding of the onset of turbulence within these systems. Currently, we our tackling a number of research items over a diversity of subjects, with a general concentration in nonlinear dynamics and stochastic processes. A short list of current research topics includes (but is not limited to):
Study of complex and evolving networks. Generally, we have looked specifically at issues of synchronization of networks of chaotic systems, though we primarily view synchronization as a probe into the behavior of dynamics on networks. Some of this work has included an examination of the implication of delay to the synchronization process (research led by Ryan Huddy (MS, 2008).
Epidemiology on networks. Using tools and models developed above, we explore disease transmission models on networks, where the contact network is driven by the motion of agents in space. This ongoing work has a strong undergraduate research component, with students Andrew Davis and Taoufik Youbi contribution to that program. Initial results were presented at conference in April 2008.
Mostly Conjugate. This foundational research in dynamical systems is supported through NSF grant. A fundamental tenet of dynamical systems is that two systems can be viewed as equivalent if there is a homeomorphism that relates the two systems - a conjugacy. But if model a system, we are creating a simplified version, which will not be conjugate. Then how do we express the degree to which the dynamics of the system are described by the model. How can we choose optimal models, and what do we mean by optimal in this setting.
Control Entropy. We apply entropy methods to time series data in a unique way, computing entropy on moving windows of the data set (similar to finite time lyapunov exponents). The resultant time series provides a complexity measure on the original data, where that complexity is varying in time. We apply these techniques to physiological data and find that the technique provides insight into how the body shifts control strategies as it fatigues.
Postural Sway. We are working closely with biomedical researchers in the Clarkson's Center for Rehabilitation Engineering & Science Technology (CREST) to study postural control behavior across a range of subjects. Postural control describes the system of how people are able to stand up without falling over. The research goal is to improve the understanding of how that system responds to very small movements. Understanding the behavior of this system near detection threshold will lead to improved techniques to assist elderly and diabetic patients to minimize their risk of falling.
Uncertainty. This work attempts to understand the propagation of uncertainty in models of complex systems, with a hope of improving the ability to model these systems in a way that yields supportable conclusions. This research includes entropy methods, polynomial chaos approaches, evidence theory, and certain techniques taken from the field of datamining. This focus ties in with the study of complex and evolving networks by considering how such systems may be analyzed if the network topology is not observable.
Geospatial Datamining. Recent research has focused on application of datamining tools to complex data sets, to include datamining within the context of geospatially related information. Geospatial data provides a unique challenges because the cross-correlations in the data are extremely heterogeneous. When a geography is overlayed with a network topology, issues of "closeness" and "adjacency" will very not only from place to place (and varying with time), but will vary with respect to the particular systems under consideration. I serve as the Clarkson University POC for the New York Geospatial Information System (GIS) Clearinghouse.
WHY DO MATH? - Check out this SIAM website where I have material posted about the Cochlear Implant.
Erik M. Bollt, Joseph D. Skufca, Stephen J McGregor, "Control Entropy: A Complexity Measure for Nonstationary Signals," to appear Mathematical Biosciences and Engineering, (2008). (pdf)
Joseph D. Skufca, Erik M. Bollt, "A Concept of Homeomorphic Defect for Defining Mostly Conjugate Dynamical Systems," Chaos: An Interdisciplinary Journal of Nonlinear Science, 18 013118 (2008). (pdf)
Joseph D Relaxing Conjugacy To Fit Modelling in Dynamical Systems , Erik M Bollt, "," Virtual J. of Biological Physics, 14 5 (2007). link
R. J. Schilling, E. M. Bollt, G. D. Fulk, J. D. Skufca, A. F. Al-Ajlouni, R. Robinson, and C. J. Robinson, "A Quiet Standing Index for Testing the Postural Sway of Healthy and Diabetic Adults Across a Range of Ages," to appear IEEE Trans. on BME. (pdf)
Joseph D Skufca, Erik M Bollt, "Relaxing Conjugacy To Fit
Modelling in Dynamical Systems," Physical Review E, 76 026220 (2007). (pdf)
James P. Bagrow, Erik M. Bollt, Joseph D. Skufca, and Daniel ben-Avraham, "Portraits of Complex Networks," Euro Physics Letters, EPL 81 68004 (2007). (pdf)
Maurizio M. Porfiri, Daniel J. Stilwell, Erik M. Bollt, Joseph D. Skufca, "Stochastic synchronization over a moving neighborhood network," Proceedings of the IEEE 2007 American Control Conference, July (2007). (pdf)
Maurizio Porfiri, Dan Stilwell, Erik M. Bollt, Joseph D. Skufca, "Random Talk: Random Walk and Synchronizability in a Moving Neighborhood Network," Physica D: Nonlinear Phenomena, vol:224;1-2, p102-113 (2006). (pdf)
K. R. Gue, R. M. Meller, J. D. Skufca, "The Effects of In-the-Aisle Congestion on Picking Policies for an Order Fulfillment Center," IIE Transactions, vol 38; 10 (2006) (pdf) .
J. D. Skufca, James A. Yorke, B. Eckhardt, "Edge of Chaos in a Parallel Shear Flow," Physical Review Letters, vol 96;17 (2006) (pdf).
J. D. Skufca, "k-workers in a Circular Warehouse A random walk on a circle, without passing," SIAM Review, vol 47;2 (2005) (pdf).
J. D. Skufca, "Analysis Still Matters: A Surprising Failure of Runge-Kutta-Felberg ODE Solvers," SIAM Review, vol 46; 4 (2004) (pdf).
J. D. Skufca, E. M. Bollt, "Communication and Synchronization in Disconnected Networks with Dynamic Topology Moving Neighborhood Networks," Mathematical Biosciences and Engineering, vol 1; 2 (2004) (pdf).
J. D. Skufca, E. M. Bollt, "Feedback control with finite accuracy: more knowledge and better control for free," Physica D, vol 179, (2003) (pdf).
"Markov Partitions" (coauthored with E. M. Bollt) in Encyclopedia of Nonlinear Science (in press), Paul Sutcliffe, Routledge, 2004(pdf).
What Can You Chant at Lane Stadium - Synchronization on Networks with Delay, Presented at International Conference on Mathematical Theory of Networks and Systems (MTNS08), Blacksburg, Va, July 2008. (Awarded prize for best title in session.)
Epidemics on adaptive networks, Presented by Andrew Davis at Undergraduate Biomathematics Day, National Conference, Apr 2008.
Tony Soprano and Singular Functions, Presented to Clarkson SIAM student chapter, Dec 2007.
Applications of Lebesgue Singular Functions to Dynamical Systems, Presented to SUNY Potsdam/Clarkson REU, July 2007.
Symbol Dynamics of close dynamical systems, Presented at SIAM DS07, International Conference on Dynamical Systems, May 2007.
The Edge of Chaos in a parallel shear flow, Presented at University of Missouri, Fall 2006.
Mostly Conjugate, Presented at University of Missouri, Fall 2006.
Boundary to Transient
Turbulence in Plane Couette Flow Presented at Math Department seminar and
Mechanical Engineering Seminar (
The Edge of Chaos Presented at
The Edge of Chaos Presented at
Analysis of the chaotic saddle in a 9-dimensional model
of plane Couette flow Presented at The United States Naval Academy,
January 2005, and
Chaos in Two Fluids, (joint talk with Dr. J. Yorke
and John Harlin). Presented at the
Inaugural Burgers Symposium,
Random Walk on a Circle Without Passing and Application to Order Fulfilment Centers. Presented at Clarkson University, April 2004.
A Review of the 1965 Lorenz paper on the 28-variable Model of the Atmosphere Presented at University of Maryland, February, 2002, and at USNA in April, 2002.
Feedback Control with
Finite Accuracy Measurements Better control and Greater Knowledge, for free. Presented at
Applicability of Undergraduate Mathematics within the Navy Nuclear Propulsion Program. Presented at USNA Mathematics Colloquium, Spring 2001.
Professor, Mathematics Department,
1985-2005, Submarine Warfare Officer in the United States Navy
2003-2005 All-Source Analyst, Defense Intelligence Agency. Provided technical direction to establish a Modeling and Simulation capability to address analysis of complex interconnected networks, to include both behavioral modeling and data-mining tools.
1996-1998, Requirements Officer, Office of Chief of Naval Operations. Responsible for a scientific research and development program to enhance the understanding of the fundamental physics issues affecting submarine detection.
1990-1992, Company Officer and Instructor,
1986-1987, Instructor, Nuclear Propulsion Training Unit,
PhD in Applied Mathematics, University of Maryland, College Park, 2005.
MS in Applied Mathematics, University of Maryland, College Park, 2002.
BS in English, United States Naval Academy, 1985 (with distinction).
Hailing from central