Numerical implementation of the coarse step method with a varying differential group delay

The effect of having a fixed differential group delay term in the coarse step method results in a periodic pattern in the inserting a varying DGD term at each integration step, according to a Gaussian distribution. Simulation results are given to illustrate the phenomenon and provide some evidence about its statistical nature.

Numerical implementation of the coarse step method with a varying differential group delay

The effect of having a fixed differential-group delay term in the coarse-step method results in a periodic pattern in the autocorrelation function. We solve this problem by inserting a varying DGD term at each integration step, according to a Gaussian distribution. Simulation results are given to illustrate the phenomenon and provide some evidence, about its statistical nature.

Revealing statistical properties of quasi-CW fibre lasers in bandwidth-limited measurements

We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.

Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Power tapping function in near infra-red region based on 45° tilted fiber gratings

We report an efficient power tapping device working in near infra-red (800 nm) wavelength region based on UV-in- scribed 45° tilted fiber grating (45°-TFG) structure. Five 45°-TFGs were UV-inscribed in hydrogenated PS750 fiber using a custom-designed phase mask with different grating lengths of 3 mm, 5 mm, 9 mm, 12 mm and 15 mm, showing polarization dependent losses (PDLs) of 1 dB, 3 dB, 7 dB, 10 dB and 13 dB, respectively. The power side-tapping efficiency is clearly depending on the grating strength. It has been identified that the power tapping efficiency increases with the grating strength and deceases along the grating length. The side-tapped power profile has also been examined in azimuthal direction, showing a near-Gaussian distribution. These experimental results clearly demonstrated that 45°- TFGs may be used as in-fiber power tapping devices for applications requiring in-line signal monitoring.

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.

Generalizing of Neural Nets: Functional Nets of Special Type

Special generalizing for the artificial neural nets: so called RFT – FN – is under discussion in the report. Such refinement touch upon the constituent elements for the conception of artificial neural network, namely, the choice of main primary functional elements in the net, the way to connect them(topology) and the structure of the net as a whole. As to the last, the structure of the functional net proposed is determined dynamically just in the constructing the net by itself by the special recurrent procedure. The number of newly joining primary functional elements, the topology of its connecting and tuning of the primary elements is the content of the each recurrent step. The procedure is terminated under fulfilling “natural” criteria relating residuals for example. The functional proposed can be used in solving the approximation problem for the functions, represented by its observations, for classifying and clustering, pattern recognition, etc. Recurrent procedure provide for the versatile optimizing possibilities: as on the each step of the procedure and wholly: by the choice of the newly joining elements, topology, by the affine transformations if input and intermediate coordinate as well as by its nonlinear coordinate wise transformations. All considerations are essentially based, constructively and evidently represented by the means of the Generalized Inverse.

Dynamical Systems in Description of Nonlinear Recursive Regression Transformers

The task of approximation-forecasting for a function, represented by empirical data was investigated. Certain class of the functions as forecasting tools: so called RFT-transformers, – was proposed. Least Square Method and superposition are the principal composing means for the function generating. Besides, the special classes of beam dynamics with delay were introduced and investigated to get classical results regarding gradients. These results were applied to optimize the RFT-transformers. The effectiveness of the forecast was demonstrated on the empirical data from the Forex market.

Statistical properties of partially coherent CW fiber lasers

A detailed quantitative numerical analysis of partially coherent quasi-CW fiber laser is performed on the example of high-Q cavity Raman fiber laser. The key role of precise spectral performances of fiber Bragg gratings forming the laser cavity is clarified. It is shown that cross phase modulation between the pump and Stokes waves does not affect the generation. Amplitudes of different longitudinal modes strongly fluctuate obeying the Gaussian distribution. As intensity statistics is noticeably non-exponential, longitudinal modes should be correlated. © 2011 SPIE.

Message passing for distributed optimisation of power allocation with renewable resources

The increase in renewable energy generators introduced into the electricity grid is putting pressure on its stability and management as predictions of renewable energy sources cannot be accurate or fully controlled. This, with the additional pressure of fluctuations in demand, presents a problem more complex than the current methods of controlling electricity distribution were designed for. A global approximate and distributed optimisation method for power allocation that accommodates uncertainties and volatility is suggested and analysed. It is based on a probabilistic method known as message passing [1], which has deep links to statistical physics methodology. This principled method of optimisation is based on local calculations and inherently accommodates uncertainties; it is of modest computational complexity and provides good approximate solutions.We consider uncertainty and fluctuations drawn from a Gaussian distribution and incorporate them into the message-passing algorithm. We see the effect that increasing uncertainty has on the transmission cost and how the placement of volatile nodes within a grid, such as renewable generators or consumers, effects it.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Robust Stereo Visual Odometry through a Probabilistic Combination of Points and Line Segments

Most approaches to stereo visual odometry reconstruct the motion based on the tracking of point features along a sequence of images. However, in low-textured scenes it is often difficult to encounter a large set of point features, or it may happen that they are not well distributed over the image, so that the behavior of these algorithms deteriorates. This paper proposes a probabilistic approach to stereo visual odometry based on the combination of both point and line segment that works robustly in a wide variety of scenarios. The camera motion is recovered through non-linear minimization of the projection errors of both point and line segment features. In order to effectively combine both types of features, their associated errors are weighted according to their covariance matrices, computed from the propagation of Gaussian distribution errors in the sensor measurements. The method, of course, is computationally more expensive that using only one type of feature, but still can run in real-time on a standard computer and provides interesting advantages, including a straightforward integration into any probabilistic framework commonly employed in mobile robotics.

Advanced Mission Synthesis Algorithms for Vibration-based Accelerated Life-testing

In the field of vibration qualification testing, with the popular Random Control mode of shakers, the specimen is excited by random vibrations typically set in the form of a Power Spectral Density (PSD). The corresponding signals are stationary and Gaussian, i.e. featuring a normal distribution. Conversely, real-life excitations are frequently non-Gaussian, exhibiting high peaks and/or burst signals and/or deterministic harmonic components. The so-called kurtosis is a parameter often used to statistically describe the occurrence and significance of high peak values in a random process. Since the similarity between test input profiles and real-life excitations is fundamental for qualification test reliability, some methods of kurtosis-control can be implemented to synthesize realistic (non-Gaussian) input signals. Durability tests are performed to check the resistance of a component to vibration-based fatigue damage. A procedure to synthesize test excitations which starts from measured data and preserves both the damage potential and the characteristics of the reference signals is desirable. The Fatigue Damage Spectrum (FDS) is generally used to quantify the fatigue damage potential associated with the excitation. The signal synthesized for accelerated durability tests (i.e. with a limited duration) must feature the same FDS as the reference vibration computed for the component’s expected lifetime. Current standard procedures are efficient in synthesizing signals in the form of a PSD, but prove inaccurate if reference data are non-Gaussian. This work presents novel algorithms for the synthesis of accelerated durability test profiles with prescribed FDS and a non-Gaussian distribution. An experimental campaign is conducted to validate the algorithms, by testing their accuracy, robustness, and practical effectiveness. Moreover, an original procedure is proposed for the estimation of the fatigue damage potential, aiming to minimize the computational time. The research is thus supposed to improve both the effectiveness and the efficiency of excitation profile synthesis for accelerated durability tests.

Automatic classification of stellar orbits in axisymmetric potentials

Within the classification of orbits in axisymmetric stellar systems, we present a new algorithm able to automatically classify the orbits according to their nature. The algorithm involves the application of the correlation integral method to the surface of section of the orbit; fitting the cumulative distribution function built with the consequents in the surface of section of the orbit, we can obtain the value of its logarithmic slope m which is directly related to the orbit’s nature: for slopes m ≈ 1 we expect the orbit to be regular, for slopes m ≈ 2 we expect it to be chaotic. With this method we have a fast and reliable way to classify orbits and, furthermore, we provide an analytical expression of the probability that an orbit is regular or chaotic given the logarithmic slope m of its correlation integral. Although this method works statistically well, the underlying algorithm can fail in some cases, misclassifying individual orbits under some peculiar circumstances. The performance of the algorithm benefits from a rich sampling of the traces of the SoS, which can be obtained with long numerical integration of orbits. Finally we note that the algorithm does not differentiate between the subtypes of regular orbits: resonantly trapped and untrapped orbits. Such distinction would be a useful feature, which we leave for future work. Since the result of the analysis is a probability linked to a Gaussian distribution, for the very definition of distribution, some orbits even if they have a certain nature are classified as belonging to the opposite class and create the probabilistic tails of the distribution. So while the method produces fair statistical results, it lacks in absolute classification precision.

A comparison of different choices for the regularization parameter in inverse electrocardiography models

Calculating the potentials on the heart’s epicardial surface from the body surface potentials constitutes one form of inverse problems in electrocardiography (ECG). Since these problems are ill-posed, one approach is to use zero-order Tikhonov regularization, where the squared norms of both the residual and the solution are minimized, with a relative weight determined by the regularization parameter. In this paper, we used three different methods to choose the regularization parameter in the inverse solutions of ECG. The three methods include the L-curve, the generalized cross validation (GCV) and the discrepancy principle (DP). Among them, the GCV method has received less attention in solutions to ECG inverse problems than the other methods. Since the DP approach needs knowledge of norm of noises, we used a model function to estimate the noise. The performance of various methods was compared using a concentric sphere model and a real geometry heart-torso model with a distribution of current dipoles placed inside the heart model as the source. Gaussian measurement noises were added to the body surface potentials. The results show that the three methods all produce good inverse solutions with little noise; but, as the noise increases, the DP approach produces better results than the L-curve and GCV methods, particularly in the real geometry model. Both the GCV and L-curve methods perform well in low to medium noise situations.