Dynamic moment invariants for nonlinear Hamiltonian systems

Distributions of particles being transported through a nonlinear Hamiltonian system are studied. Using normal form techniques, a procedure to obtain invariant functions of moments of the distribution is given. These functions are invariant for the given Hamiltonian system and are called dynamic moment invariants. These techniques are used to obtain dynamic moment invariants for the nonlinear pendulum Hamiltonian system

Computation of the Lyapunov spectrum for continuous-time dynamical systems and discrete maps

In this paper, we describe in detail a method of computing Lyapunov exponents for a continuous-time dynamical system and extend the method to discrete maps. Using this method, a partial Lyapunov spectrum can be computed using fewer equations as compared to the computation of the full spectrum, there is no difficulty in evaluating degenerate Lyapunov spectra, the equations are straightforward to generalize to higher dimensions, and the minimal set of dynamical variables is used. Explicit proofs and other details not given in previous work are included here. [S1063-651X(99)07212-8]

Emerging treatment for ALK-positive lung cancer

Introduction: Lung cancer is associated with poor prognosis and limited benefit from chemotherapy. The treatment of non-small cell lung cancer (NSCLC) has been revolutionized by the discovery of targetable genetic alterations, including the ALK fusion oncogene. Areas covered: Three drugs have been approved for clinical use in ALK-positive patients - crizotinib, ceritinib and alectinib. Unfortunately, treatment resistance inevitably develops. Several mechanisms of acquired resistance are reported. In this review, we will discuss emerging treatment options in ALK-positive advanced NSCLC and strategies to overcome resistance mechanisms, including newer generation of ALK inhibitors, Hsp90 inhibitors and immunotherapy. Expert opinion: Tremendous advances have been made in the treatment of ALK-positive lung cancers, but management hurdles still exist, including universal development of resistance to ALK inhibitors and limited CNS activity. Given that specific treatment strategies target distinct patterns of resistance, re-biopsy at the time of progression appears necessary to optimize management. However, there remain many issues in routine clinical application including the burden placed on the patients by serial biopsies and the risks of repeat invasive procedures. Future studies are needed to validate the usage of non-or minimally invasive tests and to determine the optimal orders of utilizing different ALK inhibitors