Sergio Ledesma

Synthesis of fractional gaussian noise using linear approximation for generating self-similar network traffic

The present paper focuses on self-similar network traffic generation. Network traffic modeling studies the generation of synthetic sequences. The generated sequences must have similar features to the measured traffic. Exact methods for generating self-similar sequences are not appropriate for long traces. Our main objective in the present paper is to improve the efficiency of Paxsons method for synthesizing self-similar network traffic. Paxsons method uses a fast, approximate synthesis for the power spectrum of the FGN and uses the inverse Fourier transform to obtain the time-domain sequences. We demonstrate that a linear approximation can be used to determine the power spectrum of the FGN. This linear approximation reduces the complexity of the computation without compromising the accuracy in synthesizing the power spectrum of the FGN. Our results show that long traces can be generated in much less time. To compare our method with existing ones, we will measure the running time in generating long and short sample paths from the FGN. We will also conduct experiments to show that our method can generate self-similar traffic for specified Hurst parameters with high accuracy.

Practical Considerations for Simulated Annealing Implementation

a mathematical model, it can be used to solve a broad range of problems. Unfortunately, mapping a real problem to the domain of simulated annealing can be difficult and requires familiarity with the algorithm. More often than not, it is possible to encode the solution (solve the problem) using several approaches. In addition, there are other factors that determine the success of failure of this algorithm. This chapter reviews how to plan the encoding of the solution, and discusses how to decide which encoding is more appropriate for each application. Several practical considerations for the proper implementation of simulated annealing are reviewed and analyzed. These include how to perturb the solution, how to decide a proper cooling schedule, and most important, how to properly implement the algorithm. Several cooling schedules are covered, including exponential, linear and temperature cycling. Additionally, the impact of random number generators is examined; how they affect the speed and quality of the algorithm. Essentially, this chapter is focused for those who want to solve real problems using simulated annealing for artificial intelligence, engineering, or research. An illustrative example is solved using simulated annealing and implemented in a popular programming language using an object-orien ted approach. This chapter offers a great opportunity to understand the power of this algorithm as well as to appreciate its limitations. Finally, it is reviewed how is possible to combine simulated annealing with other optimization algorithms (including the deterministic ones) to solve complex optimization problems. In particular, it is discussed how to train artificial neural networks using simulated annealing with gradient based algorithms.

Temperature cycling on simulated annealing for neural network learning

Artificial neural networks are used to solve problems that are difficult for humans and computers. Unfortunately, artificial neural network training is time consuming and, because it is a random process, several cold starts are recommended. Neural network training is typically a two step process. First, the networks weights are initialized using a no greedy method to elude local minima. Second, an optimization method (i.e., conjugate gradient learning) is used to quickly find the nearest local minimum. In general, training must be performed to reduce the mean square error computed between the desired output and the actual network output. One common method for network initialization is simulated annealing; it is used to assign good starting values to the networks weights before performing the optimization. The performance of simulated annealing depends strongly on the cooling process. A cooling schedule based on temperature cycling is proposed to improve artificial neural network training. It is shown that temperature cycling reduces training time while decreasing the mean square error on autoassociative neural networks. Three auto-associative problems: The Trifolium, The Cardioid, and The Lemniscate of Bernoulli, are solved using exponential cooling, linear cooling and temperature cycling to verify our results.

Analysis of a variable speed vapor compression system using artificial neural networks

An artificial neural network (ANN) is a mathematical model that is inspired by the operation of biological neural networks. However, this is typically considered a computational model. An ANN can easily adapt to multiple situations and extract information that is apparently hidden in a system. An ANN can be used in three basic configurations: mapping, auto-association and classification. An ANN in a mapping configuration can be used to model a two port system with inputs and outputs. Therefore, a vapor compression system can be modeled using an ANN in a mapping configuration. That is, some parameters from the compression system can be used for input while other parameters can be used as output. The simulation experiments include the design, training and validation of a set of ANNs to find the best architecture while minimizing over-fitting. This paper presents a new method to model a variable speed vapor compression system. This method accurately estimates the number of neurons in the hidden layer of an ANN. The analysis and the experimental results provide new insights to understand the dependency between the input and output parameters in a vapor compression system, concluding that the model can predict the energetic performance of a variable speed vapor compression system. Additionally, the simulation results indicate that an ANN can extract, from the data sets, information that is implicit in the configuration of the vapor compression system.

Two approximation methods to synthesize the power spectrum of fractional Gaussian noise

The simplest models with long-range dependence (LRD) are self-similar processes. Self-similar processes have been formally considered for modeling packet traffic in communication networks. The fractional Gaussian noise (FGN) is a proper example of exactly self-similar processes. Several numeric approximation methods are considered and reviewed, two methods are found that are able to provide a better accuracy and less running time than previous approximation methods for synthesizing the power spectrum of FGN. The first method is based on a second-order approximation. It is demonstrated that a parabolic curve can be indirectly used to approximate the power spectrum of FGN. The second method is based on cubic splines. Despite the fact that splines cannot be used directly to approximate the power spectrum of FGN, they can, however, considerably simplify the calculations while maintaining high accuracy. Both of the methods proposed can be used to estimate the Hurst parameter using Whittles estimator. Additionally, they can be used on synthesis of LRD sequences.

A fast method for generating self-similar network traffic

Recently, self-similar/fractal traffic models have been shown to be applicable to a variety of network traffic. This gives rise to new and challenging problems for statistical inference, stochastic modeling and synthetic traffic generation. The present paper focuses on self-similar traffic generation. Network traffic modeling studies the generation of synthetic sequences. The generated sequences must have similar features to the measured traffic. Exact methods for generating self-similar sequences from the fractional Gaussian noise (FGN) and the fractional autoregressive integrated moving average process models are not appropriate for long traces. Our main objective is to improve the efficiency of the method presented by Paxson (1997) for synthesizing self-similar sample paths. Paxsons method uses a fast, approximate synthesis for the power spectrum of the FGN and uses the inverse Fourier transform to obtain the time-domain sequences. We demonstrate that a linear approximation can be used to determine the power spectrum of the FGN. This linear approximation reduces the complexity of the computation without compromising the accuracy in synthesizing the power spectrum of the FGN. Our results show that long traces can be generated in much less time. To compare our method with existing ones, we measure the running time in generating long and short sample paths from the FGN. We also conduct experiments to show that our method can generate self-similar traffic for specified Hurst parameters with high accuracy.

Tunable apodizers and tunable focalizers using helical pairs

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

Feature Selection Using Artificial Neural Networks

Machine learning is useful for building robust learning models, and it is based on a set of features that identify a state of an object. Unfortunately, some data sets may contain a large number of features making, in some cases, the learning process time consuming and the generalization capability of machine learning poor. To make a data set easy to learn and understand, it is typically recommended to remove the most irrelevant features from the set. However, choosing what data should be kept or eliminated may be performed by complex selection algorithms, and optimal feature selection may require an exhaustive search of all possible subsets of features which is computationally expensive. This paper proposes a simple method to perform feature selection using artificial neural networks. It is shown experimentally that genetic algorithms in combination with artificial neural networks can easily be used to extract those features that are required to produce a desired result. Experimental results show that very few hidden neurons are required for feature selection as artificial neural networks are only used to assess the quality of an individual, which is a chosen subset of features.

Tunable focalizers: axicons, lenses, and axilenses

We propose the use of a pair of phase masks, which have both radial and angular variations, for implementing several varifocal devices. One mask of the proposed pair has a complex amplitude transmittance that is the complex conjugate of the other member of the pair. We show that the overall complex amplitude transmittance has only a radial variation after introducing an in-plane rotation, say by an angle β, between the members of the pair. However, we note that the optical power is proportional to the rotation angle β. As examples of the proposed method, we show that the refractive pair is useful for implementing varifocal lenses, tunable axicons, controllable axilenses, as well as annularly distributed focalizers.

Hyper Gaussian windows with fractional wavefronts

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP