Dynamical approaches and multi-quadratic integer programming for seizure prediction

References

• Iasemidis , LD , Pardalos , P , Sackellares , JC and Shiau , D-S . 2001 . Quadratic binary programming and dynamical system approach to determine the predictability of epileptic seizures . Journal of Combinatorial Optimization , 5 : 9 – 26 .
   Google Scholar
• Iasemidis LD Shiau D-S Pardalos PM Sackellares JC 2002 Phase entrainment and predictability of epileptic seizures In: P.M. Pardalos and J. Principe (Eds) Biocomputing, Kluwer Academic Publishers
   Google Scholar
• Iasemidis , LD , Sackellares , JC , Zaveri , HP and Williams , WJ . 1990 . Phase space topography of the electrocorticogram and the Lyapunov exponent in partial seizures . Brain Topography , 2 : 187 – 201 .
   PubMedGoogle Scholar
• Iasemidis LD Sackellares JC 1991 The temporal evolution of the largest Lyapunov exponent on the human epileptic cortex In: D.W. Duck and W.S. Pritchard (Eds) Measuring Chaos in the Human Brain Singapore World Scientific
   Google Scholar
• Iasemidis LD Shiau D-S Sackellares JC Pardalos P 1999 Transition to epileptic seizures: optimization In: D.Z. Du, P.M. Pardalos and J. Wang (Eds) DIMACS series in Discrete Mathematics and Theoretical Computer Science 55 American Mathematical Society
   Google Scholar
• Martinerie , J , Adam , C , Le Van Quyen , M , Baulac , M , Clemenceu , S , Renault , B and Varela , FJ . 1998 . Epileptic seizures can be anticipated by non-linear analysis . Nature Medicine , 4 : 1173 – 1176 .
   PubMed Web of Science ®Google Scholar
• Elger , CE and Lehnertz , K . 1998 . Seizure prediction by non-linear time series analysis of brain electrical activity . European Journal of Neuroscience , 10 : 786 – 789 .
   PubMed Web of Science ®Google Scholar
• Lehnertz , K and Elger , CE . 1998 . Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity . Physics Review Letters , 80 : 5019 – 5022 .
   Web of Science ®Google Scholar
• LeVan Quyen , M , Martinerie , J , Baulac , M and Varela , F . 1999 . Anticipating epileptic seizures in real time by non-linear analysis of similarity between EEG recordings . NeuroReport , 10 : 2149 – 2155 .
   PubMedGoogle Scholar
• LeVan Quyen , M . 2001 . Anticipation of epileptic seizures from standard EEG recordings . Lancet , 357 : 183 – 188 .
   PubMedGoogle Scholar
• Wolf , A , Swift , JB , Swinney , HL and Vastano , JA . 1985 . Determining Lyapunov exponents from a time series . Physica D , 16 : 285 – 317 .
   Web of Science ®Google Scholar
• Iasemidis LD Principe JC Sackellares JC 2000 Measurement and quantification of spatiotemporal dynamics of human epileptic seizures In: M. Akay (Ed.) Nonlinear Biomedical Signal Processing II IEEE Press
   Google Scholar
• Mayer-Kress G (Ed.), 1986 Dimension and Entropies in Chaotic Systems Berlin Springer-Verlag
   Google Scholar
• Kostelich , EJ . 1992 . Problems in estimating dynamics from data . Physica D , 58 : 138 – 152 .
   Google Scholar
• Athanasiou , GG , Bachas , CP and Wolf , WF . 1987 . Invariant geometry of spin-glass states . Physical Review B , 35 : 1965 – 1968 .
   Google Scholar
• Barahona , F . 1982 . On the computational complexity of spin glass models . Journal of Physics A: Mathematical and General , 15 : 3241 – 3253 .
   Google Scholar
• Barahona , F . 1982 . On the exact ground states of three-dimensional Ising spin glasses . Journal of Physics A: Mathematical and General , 15 : L611 – L615 .
   Google Scholar
• Mezard M Parisi G Virasoro MA 1987 Spin Glass Theory and Beyond Singapore World Scientific
   Google Scholar
• Horst H Pardalos PM Thoai V 2000 Introduction to Global Optimization (2nd edn) Dordrecht Kluwer Academic Publishers
   Google Scholar
• Sackellares JC Iasemidis LD Gilmore RL Roper SN 1997 Epileptic seizures as neural resetting mechanisms Epilepsia 38 S3, 189
   PubMedGoogle Scholar
• Shiau DS Luo Q Gilmore RL Roper SN Pardalos P Sackellares JC Iasemidis LD 2000 Epileptic seizures resetting revisited Epilepsia 41 S7, 208 209
   Google Scholar