Stochastic perturbations in open chaotic systems: random versus noisy maps

We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate $\kappa$ and dimensions $D$ of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of $\kappa$ and $D$, and show that the improvement of the precision of the estimations with the number of trajectories $N$ is extremely slow ($\propto 1/\ln N$). We also argue that the finite-size $D$ estimators are typically biased. General theoretical results are combined with analytical calculations and numerical simulations in area-preserving baker maps.Comment: 12 pages, 3 figures, 1 table, manuscript submitted to Physical Review

After 9/11

After 9/11 presents 17 interviews with America´s leading political thinkers. Renowned experts such as Zbigniew Brzezinski, Francis Fukuyama, and Noam Chomsky discuss the nation’s foreign policy in the post-9/11 world. Yet, they also comment on their own role in US society – and the mounting challenges they face today. The conversations illustrate the hopes and expectations, the anger and frustration, the shattered beliefs and unshakable convictions of the nation´s preeminent minds – at a time when America made its epic transition from George W. Bush to Barack Obama. Renowned experts engage in a vibrant debate about their nation´s position on the global stage: What is America´s foreign policy in the post-9/11 world? What should it be? What led to the catastrophe of September 11? How best to prevent another one, and how to restore America´s damaged reputation? What to expect of Obama? While struggling to define their nation´s role in a world that has changed since the terror attacks, the intellectuals discuss their own role in 21st-century society – a society that thrives on public discourse. The book is written for students, graduates, and lecturers in political science, sociology, culture studies, philosophy, and history. However, anyone interested not only in the political positions of America´s most prominent thinkers but also in how these thinkers feel about what they do and how they do it will enjoy this book. Interview partners: Benjamin Barber John Bolton Zbigniew Brzezinski Noam Chomsky Francis Fukuyama Jean Bethke Elshtain Robert O. Keohane James M. Lindsay Michael Novak Joseph Nye Clyde Prestowitz Anne-Marie Slaughter Nancy Soderberg Strobe Talbott Michael Walzer Cornel West Howard Zinn (†

After 9/11

After 9/11 presents 17 interviews with America’s leading political thinkers. Renowned experts such as Zbigniew Brzezinski, Francis Fukuyama, and Noam Chomsky discuss the nation’s foreign policy in the post-9/11 world. Yet, they also comment on their own role in US society – and the mounting challenges they face today

Outcome after surgery for isthmic spondylolisthesis and degenerative disc disease

Individuals with isthmic spondylolisthesis and lumbar degenerative disc disease may have low back and leg pain. Those with persistent symptoms non-responsive to conservative treatment are sometimes treated surgically. Various surgical methods have been introduced, but long-term outcome comparisons are scarce. The Swedish Spine register (Swespine) was used to study long term outcome after fusion surgery for isthmic spondylolisthesis and lumbar degenerative disc disease. In addition, we determined the effect of loss to follow-up on patient reported outcome interpretation, as well as the diagnostic accuracy of surgical information in Swespine. Another cohort was used to determine the long-term risk of radiologically verified adjacent segment degeneration after interbody fusion and posterolateral fusion. We found that the Swedish Spine register gives fairly reliable information about the surgical event. Loss to follow-up is of minor importance in the outcome interpretation after lumbar spine surgery. At long term, patient reported outcome was similar when comparing interbody fusion and posterolateral fusion in isthmic spondylolisthesis and degenerative disc disease. The long-term risk of radiologically verified adjacent segment degeneration was similar after interbody fusion and posterolateral fusion. The risk of additional lumbar spine surgery for any reason was significantly higher in those individuals that had undergone interbody fusion compared to those that had undergone posterolateral fusion. Even though patient reported outcome was improved after surgery for isthmic spondylolisthesis, the quality of life did not reach the levels of the normative population

Investigating Variability in Teaching Performance...Seeking Pathways to Excellence

Teacher learning is critical to student learning (Darling-Hammond, 2002, 2010). The work documented here is driven by an investigation of a long-standing and complex problem of educational practice: the inequitable learning opportunities for students that result from variability in the selection, learning and placement of practicing and aspiring teachers. A multidisciplinary perspective is used to situate the problem of practice theoretically, within a body of empirical research, and within a context of educational practice. Among the perspectives used to examine the problem of practice are theoretical frameworks that support the claim that the problem is a matter of social justice. The investigation also argues that inequitable learning opportunities for students are impacted by a fusion of two critical factors including the avenues by which people are recruited for and granted access to teacher preparation programs and the structure and quality of professional development provided to practicing teachers. The argument acknowledges the concept of variability within systems and practices, but contends that variability within excellence is the environment that will afford quality teachers for all students. Efforts to understand and address the problem are addressed to reveal what has been learned in the investigation to date and how what needs to be learned will form a leadership agenda that engages a diversity of stakeholders collaborating on an effort to improve an educational system in which the problem of practice exists. The implications of the effort are discussed for individuals, for the system, and with regard to leadership issues that bear on the problem of practice. The work concludes with a summary of what has been learned through the investigation and the implications of that learning for the professional leadership agenda that will be pursued in order to establish collaboratively engaged improvement efforts as a norm of practice at the level of schools and school districts

Editorial : Q & A John A. Endler

John A. Endler is a Professor of Sensory Ecology and Evolution at Deakin University and an Adjunct professor of Zoology at James Cook University, both in Australia. He regards himself as a 19th century natural historian who uses 21st century techniques to answer questions generated originally from field observations. His research is in the area of overlap among Evolutionary Biology, Sensory Ecology, Behavioural Ecology, Animal Behaviour, Neuroethology and Biophysics. He enjoys combining field work, field experiments, lab work, and theoretical methods as well as constructing electromechanical-optical equipment and software for himself and students

Noise-enhanced trapping in chaotic scattering

We show that noise enhances the trapping of trajectories in scattering systems. In fully chaotic systems, the decay rate can decrease with increasing noise due to a generic mismatch between the noiseless escape rate and the value predicted by the Liouville measure of the exit set. In Hamiltonian systems with mixed phase space we show that noise leads to a slower algebraic decay due to trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands. We argue that these noise-enhanced trapping mechanisms exist in most scattering systems and are likely to be dominant for small noise intensities, which is confirmed through a detailed investigation in the Henon map. Our results can be tested in fluid experiments, affect the fractal Weyl's law of quantum systems, and modify the estimations of chemical reaction rates based on phase-space transition state theory.Comment: 5 pages, 5 figure