Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Neural Control of Chaos and Aplications

Signal processing is an important topic in technological research today. In the areas of nonlinear dynamics search, the endeavor to control or order chaos is an issue that has received increasing attention over the last few years. Increasing interest in neural networks composed of simple processing elements (neurons) has led to widespread use of such networks to control dynamic systems learning. This paper presents backpropagation-based neural network architecture that can be used as a controller to stabilize unsteady periodic orbits. It also presents a neural network-based method for transferring the dynamics among attractors, leading to more efficient system control. The procedure can be applied to every point of the basin, no matter how far away from the attractor they are. Finally, this paper shows how two mixed chaotic signals can be controlled using a backpropagation neural network as a filter to separate and control both signals at the same time. The neural network provides more effective control, overcoming the problems that arise with control feedback methods. Control is more effective because it can be applied to the system at any point, even if it is moving away from the target state, which prevents waiting times. Also control can be applied even if there is little information about the system and remains stable longer even in the presence of random dynamic noise.

Vector solitons in mode locked fibre lasers

We overview our recent results on polarisation dynamics of vector solitons in erbium doped fibre laser mode locked with carbon nanotubes. Our experimental and theoretical study revealed new families of vector solitons for fundamental and bound-state soliton operations. The observed scenario of the evolution of the states of polarisation (SOPs) on the Poincare sphere includes fast polarisation switching between two and three SOPs along with slow SOP evolution on a double scroll chaotic attractor. The underlying physics presents an interplay between effects of birefringence of the laser cavity and light induced anisotropy caused by polarisation hole burning. © 2014 IEEE.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Managua Relief

Bob del Toro, Dianne Haley and Others with Toys for Managuan Relief. On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum 887-3400. april 30, 1973. Cutlines: More than 350 dozens of various balls, skate boards and games were recently purchased by the Student Governance Committee of Florida International University for the young people of Managua, Nicaragua who not only do not have enough toys but are unable to attend schools which are closed. Left to right are, Bob del Toro, Dianne Haley, Chairman of the Student Governance Committee, Hialeah Councilman Jack Weaver of the Hialeah-Managua Sister City Committee, Barbara O'Nan and Margaret Klein.

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum From: City of Hialeah Publicity Bureu. 401 1/2 East 1st Ave. Hialeah, Fla. 887-3400. april 30, 1973. Cutlines: Florida International University students recently raised more than $ 1,000 for more than 300 dozens toys and balls for the youngsters of Managua, Nicaragua. With the balls above are shown student Committee members and oficials of the Hialeah-Managua Sister City Committee, left to rigth: Bob del Toro, Sister City Committe president Raymond R. Schultz, Student Governance Committee chairman Dianne Haley and Hialeah City councilman Jack Weaver.

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements by organizations were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum From: City of Hialeah Publicity Bureu. 401 1/2 East 1st Ave. Hialeah, Fla. 887-3400. april 30, 1973. Cutlines: Skate boards, paddle balls and flying saucers were among the big shipment of toys which was recently dispatched to Managua, Nicaragua by students of Florida International University through the Hialeah-Managua Sister Committee. Examining the toys above are, left to right: Margaret Klein, Hialeah councilman Jack Weaver and Barbara O'Nan.

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

The Miami News. Mon., March 19, 1973. Managuan Relief. Miami News Staff Photo by George Kochaniec. Raymond and Connie Schultz with toys. (Back) "Focuses on kids" article On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Survivability of Deterministic Dynamical Systems

Acknowledgements We acknowledge gratefully the support of BMBF, CoNDyNet, FK. 03SF0472A, of the EIT Climate-KIC project SWIPO and Nora Molkenthin for illustrating our illustration of the concept of survivability using penguins. We thank Martin Rohden for providing us with the UK high-voltage transmission grid topology and Yang Tang for very useful discussions. The publication of this article was funded by the Open Access Fund of the Leibniz Association.

Colectivos sociales y ciborgs: hacia una lectura feminista de los drones

Este artículo analiza el papel de los drones en la emergencia de nuevas formas de participación política e impugnación del poder por parte de colectivos sociales. El artículo plantea una lectura feminista de los drones como ciborgs (humanos-máquinas) para explorar las agencias distribuidas entre actores humanos y no humanos con el propósito de visibilizar las relaciones de poder y analizar la configuración de contra-realidades. Se presentan ocho casos de colectivos sociales que, con la ayuda de un dron, disputan el poder de gobiernos, empresas transnacionales además de desempeñar innovadoras intervenciones públicas.

Self-Organizing Map Neural Architectures Based on Limit Cycle Attractors

Recent efforts to develop large-scale neural architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason is that most conventional SOMs use a static encoding representation: Each input is typically represented by the fixed activation of a single node in the map layer. This not only carries information in an inefficient and unreliable way that impedes building robust multi-SOM neural architectures, but it is also inconsistent with rhythmic oscillations in biological neural networks. Here I develop and study an alternative encoding scheme that instead uses limit cycle attractors of multi-focal activity patterns to represent input patterns/sequences. Such a fundamental change in representation raises several questions: Can this be done effectively and reliably? If so, will map formation still occur? What properties would limit cycle SOMs exhibit? Could multiple such SOMs interact effectively? Could robust architectures based on such SOMs be built for practical applications? The principal results of examining these questions are as follows. First, conditions are established for limit cycle attractors to emerge in a SOM through self-organization when encoding both static and temporal sequence inputs. It is found that under appropriate conditions a set of learned limit cycles are stable, unique, and preserve input relationships. In spite of the continually changing activity in a limit cycle SOM, map formation continues to occur reliably. Next, associations between limit cycles in different SOMs are learned. It is shown that limit cycles in one SOM can be successfully retrieved by another SOM’s limit cycle activity. Control timings can be set quite arbitrarily during both training and activation. Importantly, the learned associations generalize to new inputs that have never been seen during training. Finally, a complete neural architecture based on multiple limit cycle SOMs is presented for robotic arm control. This architecture combines open-loop and closed-loop methods to achieve high accuracy and fast movements through smooth trajectories. The architecture is robust in that disrupting or damaging the system in a variety of ways does not completely destroy the system. I conclude that limit cycle SOMs have great potentials for use in constructing robust neural architectures.