Span design for reduced noise and nonlinear impairments in a dispersion-managed Raman amplified system

We study a periodic Raman amplified dispersion-managed system with backward-pumping configuration, considering noise and nonlinear impairments. A general optimization method based on nonlinearity management is applied in order to find the configuration that maximizes the system performance. The system is later tested using a full numerical implementation of the nonlinear Schrödinger equation and shown to effectively deliver its longest propagation distance in the same optimal region.

Shannon capacity of nonlinear communication channels

The exponentially increasing demand on operational data rate has been met with technological advances in telecommunication systems such as advanced multilevel and multidimensional modulation formats, fast signal processing, and research into new different media for signal transmission. Since the current communication channels are essentially nonlinear, estimation of the Shannon capacity for modern nonlinear communication channels is required. This PhD research project has targeted the study of the capacity limits of different nonlinear communication channels with a view to enable a significant enhancement in the data rate of the currently deployed fiber networks. In the current study, a theoretical framework for calculating the Shannon capacity of nonlinear regenerative channels has been developed and illustrated on the example of the proposed here regenerative Fourier transform (RFT). Moreover, the maximum gain in Shannon capacity due to regeneration (that is, the Shannon capacity of a system with ideal regenerators – the upper bound on capacity for all regenerative schemes) is calculated analytically. Thus, we derived a regenerative limit to which the capacity of any regenerative system can be compared, as analogue of the seminal linear Shannon limit. A general optimization scheme (regenerative mapping) has been introduced and demonstrated on systems with different regenerative elements: phase sensitive amplifiers and the proposed here multilevel regenerative schemes: the regenerative Fourier transform and the coupled nonlinear loop mirror.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.

Capacity-achieving techniques in nonlinear channels

Many of the current optical transmission techniques were developed for linear communication channels and are constrained by the fibre nonlinearity. This paper discusses the potential for radically different approaches to signal transmission and processing based on using inherently nonlinear techniques.

Nonlinear signal transformations:path to capacity above the linear AWGN Shannon limit

We present a methodology for simultaneous optimization of modulation format and regenerative transformations in nonlinear communication channels. We derived analytically the maximum regenerative Shannon capacity, towards which any regenerative channel tends at high SNR and large number of regenerators.

Optimization and characterization of femtosecond laser inscribed in-fiber microchannels for liquid sensing

In-fiber microchannels were fabricated directly in standard single mode fiber using the femtosecond laser inscribe and etch technique. This method of creating in-fiber microchannels offers great versatility, since it allows complex three-dimensional structures to be inscribed and then preferentially etched with hydrofluoric acid. In addition, inscription does not require a photosensitive fiber; the modification is induced through nonlinear processes triggered by an ultrashort laser pulse. Four in-fiber microchannel designs were experimentally investigated using this technique - microhole, microslot channel along the core, microslot channel perpendicular to the core and helical channel around the core. Each device design was evaluated through monitoring the optical spectral change while inserting a range of index matching oils into each microchannel; an R.I. sensitivity up to 1.55 dB/RIU was achieved in these initial tests. Furthermore, an all femtosecond laser inscribed Fabry-Pérot-based refractometer with an R.I. sensitivity of 2.75 nm/RIU was also demonstrated. The Fabry-Pérot refractometer was formed by positioning a microchannel between two femtosecond laser inscribed point-by-point fiber Bragg gratings.

Operation sequencing optimization for five-axis prismatic parts using a particle swarm optimization approach

Operation sequencing is one of the crucial tasks in process planning. However, it is an intractable process to identify an optimized operation sequence with minimal machining cost in a vast search space constrained by manufacturing conditions. Also, the information represented by current process plan models for three-axis machining is not sufficient for five-axis machining owing to the two extra degrees of freedom and the difficulty of set-up planning. In this paper, a representation of process plans for five-axis machining is proposed, and the complicated operation sequencing process is modelled as a combinatorial optimization problem. A modern evolutionary algorithm, i.e. the particle swarm optimization (PSO) algorithm, has been employed and modified to solve it effectively. Initial process plan solutions are formed and encoded into particles of the PSO algorithm. The particles 'fly' intelligently in the search space to achieve the best sequence according to the optimization strategies of the PSO algorithm. Meanwhile, to explore the search space comprehensively and to avoid being trapped into local optima, several new operators have been developed to improve the particle movements to form a modified PSO algorithm. A case study used to verify the performance of the modified PSO algorithm shows that the developed PSO can generate satisfactory results in optimizing the process planning problem. © IMechE 2009.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.

Stable optical vortices in nonlinear multicore fibers

The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF.

Mode-locking intracavity dynamics:modeling nonlinear power and energy fluctuations

Modern high-power, pulsed lasers are driven by strong intracavity fluctuations. Critical in driving the intracavity dynamics is the nontrivial phase profiles generated and their periodic modification from either nonlinear mode-coupling, spectral filtering or dispersion management. Understanding the theoretical origins of the intracavity fluctuations helps guide the design, optimization and construction of efficient, high-power and high-energy pulsed laser cavities. Three specific mode-locking component are presented for enhancing laser energy: waveguide arrays, spectral filtering and dispersion management. Each component drives a strong intracavity dynamics that is captured through various modeling and analytic techniques.

Optimization models for selecting bus stops for accessibility improvements for people with disabilities

Bus stops are key links in the journeys of transit patrons with disabilities. Inaccessible bus stops prevent people with disabilities from using fixed-route bus services, thus limiting their mobility. The Americans with Disabilities Act (ADA) of 1990 prescribes the minimum requirements for bus stop accessibility by riders with disabilities. Due to limited budgets, transit agencies can only select a limited number of bus stop locations for ADA improvements annually. These locations should preferably be selected such that they maximize the overall benefits to patrons with disabilities. In addition, transit agencies may also choose to implement the universal design paradigm, which involves higher design standards than current ADA requirements and can provide amenities that are useful for all riders, like shelters and lighting. Many factors can affect the decision to improve a bus stop, including rider-based aspects like the number of riders with disabilities, total ridership, customer complaints, accidents, deployment costs, as well as locational aspects like the location of employment centers, schools, shopping areas, and so on. These interlacing factors make it difficult to identify optimum improvement locations without the aid of an optimization model. This dissertation proposes two integer programming models to help identify a priority list of bus stops for accessibility improvements. The first is a binary integer programming model designed to identify bus stops that need improvements to meet the minimum ADA requirements. The second involves a multi-objective nonlinear mixed integer programming model that attempts to achieve an optimal compromise among the two accessibility design standards. Geographic Information System (GIS) techniques were used extensively to both prepare the model input and examine the model output. An analytic hierarchy process (AHP) was applied to combine all of the factors affecting the benefits to patrons with disabilities. An extensive sensitivity analysis was performed to assess the reasonableness of the model outputs in response to changes in model constraints. Based on a case study using data from Broward County Transit (BCT) in Florida, the models were found to produce a list of bus stops that upon close examination were determined to be highly logical. Compared to traditional approaches using staff experience, requests from elected officials, customer complaints, etc., these optimization models offer a more objective and efficient platform on which to make bus stop improvement suggestions.