Adaptive back-propagation in on-line learning of multilayer networks

An adaptive back-propagation algorithm is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, both numerical studies and a rigorous analysis show that the adaptive back-propagation method results in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

Polarization multiplexed 16QAM transmission employing modified digital back-propagation

We experimentally demonstrate performance enhancements enabled by weighted digital back propagation method for 28 Gbaud PM-16QAM transmission systems, over a 250 km ultra-large area fibre, using only one back-propagation step for the entire link, enabling up to 3 dB improvement in power tolerance with respect to linear compensation only. We observe that this is roughly the same improvement that can be obtained with the conventional, computationally heavy, non-weighted digital back propagation compensation with one step per span. As a further benchmark, we analyze performance improvement as a function of number of steps, and show that the performance improvement saturates at approximately 20 steps per span, at which a 5 dB improvement in power tolerance is obtained with respect to linear compensation only. Furthermore, we show that coarse-step self-phase modulation compensation is inefficient in wavelength division multiplexed transmission.

Polarization multiplexed 16QAM transmission employing modified digital back-propagation

We experimentally demonstrate performance enhancements enabled by weighted digital back propagation method for 28 Gbaud PM-16QAM transmission systems, over a 250 km ultra-large area fibre, using only one back-propagation step for the entire link, enabling up to 3 dB improvement in power tolerance with respect to linear compensation only. We observe that this is roughly the same improvement that can be obtained with the conventional, computationally heavy, non-weighted digital back propagation compensation with one step per span. As a further benchmark, we analyze performance improvement as a function of number of steps, and show that the performance improvement saturates at approximately 20 steps per span, at which a 5 dB improvement in power tolerance is obtained with respect to linear compensation only. Furthermore, we show that coarse-step self-phase modulation compensation is inefficient in wavelength division multiplexed transmission.

Characterizing femtosecond laser inscribed Bragg grating spectra

We present numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Method that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics. (C) 2010 Optical Society of America

Numerical modelling of complex femtosecond laser inscribed fiber gratings - comparison wih experiment

We present experimental studies and numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Modeling that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics.

Femtosecond laser inscribed superstructure fibre gratings

We demonstrate the development of femtosecond laser inscribed superstructure fiber gratings (fsSFG) in silica optical fibre. We utilise a single step process, to inscribe low loss and polarisation independent, sampled gratings in optical fibres using the point by point femtosecond laser inscription method. Our approach results in a controlled modulated index change with complete suppression of any overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. We also solve Maxwell's equations and calculate the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis and the estimation of inscription parameters such as ac index modulation, wavelength and the relative peak strength. We also explore how changes in the grating's period influence the reflection spectrum.

Superstructure fiber gratings via single step femtosecond laser inscription

We present the development of superstructure fiber gratings (SFG) in Ge-doped, silica optical fiber using femtosecond laser inscription. We apply a simple but extremely effective single step process to inscribe low loss, sampled gratings with minor polarization dependence. The method results in a controlled modulated index change with complete suppression of mode coupling associated with the overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. The devices are characterized and compared with numerical modeling by solving Maxwell's equations and calculating the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis, allowing for the estimation of inscription parameters such as the ac index modulation change, and the wavelength, position and relative strength of each significant resonance peak. We also present results on temperature and refractive index measurements showing potential for sensing applications.

Superstructure fiber gratings via single step femtosecond laser inscription

We present the development of superstructure fiber gratings (SFG) in Ge-doped, silica optical fiber using femtosecond laser inscription. We apply a simple but extremely effective single step process to inscribe low loss, sampled gratings with minor polarization dependence. The method results in a controlled modulated index change with complete suppression of mode coupling associated with the overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. The devices are characterized and compared with numerical modeling by solving Maxwell's equations and calculating the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis, allowing for the estimation of inscription parameters such as the ac index modulation change, and the wavelength, position and relative strength of each significant resonance peak. We also present results on temperature and refractive index measurements showing potential for sensing applications.

Femtosecond laser inscribed superstructure fibre gratings

We demonstrate the development of femtosecond laser inscribed superstructure fiber gratings (fsSFG) in silica optical fibre. We utilise a single step process, to inscribe low loss and polarisation independent, sampled gratings in optical fibres using the point by point femtosecond laser inscription method. Our approach results in a controlled modulated index change with complete suppression of any overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. We also solve Maxwell's equations and calculate the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis and the estimation of inscription parameters such as ac index modulation, wavelength and the relative peak strength. We also explore how changes in the grating's period influence the reflection spectrum.

Numerical modelling of complex femtosecond laser inscribed fiber gratings - comparison wih experiment

We present experimental studies and numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Modeling that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics.

Belief propagation vs. TAP for decoding corrupted messages

We employ two different methods, based on belief propagation and TAP,for decoding corrupted messages encoded by employing Sourlas's method, where the code word comprises products of K bits selected randomly from the original message. We show that the equations obtained by the two approaches are similar and provide the same solution as the one obtained by the replica approach in some cases K=2. However, we also show that for K>=3 and unbiased messages the iterative solution is sensitive to the initial conditions and is likely to provide erroneous solutions; and that it is generally beneficial to use Nishimori's temperature, especially in the case of biased messages.

Soliton propagation through a disordered system:statistics of the transmission delay

We have studied the soliton propagation through a segment containing random pointlike scatterers. In the limit of small concentration of scatterers when the mean distance between the scatterers is larger than the soliton width, a method has been developed for obtaining the statistical characteristics of the soliton transmission through the segment. The method is applicable for any classical particle traversing through a disordered segment with the given velocity transformation after each act of scattering. In the case of weak scattering and relatively short disordered segment the transmission time delay of a fast soliton is mostly determined by the shifts of the soliton center after each act of scattering. For sufficiently long segments the main contribution to the delay is due to the shifts of the amplitude and velocity of a fast soliton after each scatterer. Corresponding crossover lengths for both cases of light and heavy solitons have been obtained. We have also calculated the exact probability density function of the soliton transmission time delay for a sufficiently long segment. In the case of weak identical scatterers the latter is a universal function which depends on a sole parameter—the mean number of scatterers in a segment.

Palette-colouring: a belief propagation approach

We consider a variation of the prototype combinatorial optimization problem known as graph colouring. Our optimization goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximize the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call palette-colouring, has been recently addressed as a basic example of a problem arising in the context of distributed data storage. Even though it has not been proved to be NP-complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach at the cost of increased computational effort. We also investigate the emergence of a satisfiable-to-unsatisfiable 'phase transition' as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ('thermodynamic') limit.

Decentralised supply chain formation:a belief propagation-based approach

Decentralised supply chain formation involves determining the set of producers within a network able to supply goods to one or more consumers at the lowest cost. This problem is frequently tackled using auctions and negotiations. In this paper we show how it can be cast as an optimisation of a pairwise cost function. Optimising this class of functions is NP-hard but good approximations to the global minimum can be obtained using Loopy Belief Propagation (LBP). Here we detail a LBP-based approach to the supply chain formation problem, involving decentralised message-passing between potential participants. Our approach is evaluated against a well-known double-auction method and an optimal centralised technique, showing several improvements: it obtains better solutions for most networks that admit a competitive equilibrium Competitive equilibrium as defined in [3] is used as a means of classifying results on certain networks to allow for minor inefficiencies in their auction protocol and agent bidding strategies. while also solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions.

Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm

We investigate a digital back-propagation simplification method to enable computationally-efficient digital nonlinearity compensation for a coherently-detected 112 Gb/s polarization multiplexed quadrature phase shifted keying transmission over a 1,600 km link (20x80km) with no inline compensation. Through numerical simulation, we report up to 80% reduction in required back-propagation steps to perform nonlinear compensation, in comparison to the standard back-propagation algorithm. This method takes into account the correlation between adjacent symbols at a given instant using a weighted-average approach, and optimization of the position of nonlinear compensator stage to enable practical digital back-propagation.