There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

In this paper, we proposed a novel spam detection method that focused on reducing the false positive error of mislabeling nonspam as spam. First, we used the wrapper-based feature selection method to extract crucial features. Second, the decision tree was chosen as the classifier model with C4.5 as the training algorithm. Third, the cost matrix was introduced to give different weights to two error types, i.e., the false positive and the false negative errors. We define the weight parameter as a to adjust the relative importance of the two error types. Fourth, K-fold cross validation was employed to reduce out-of-sample error. Finally, the binary PSO with mutation operator (MBPSO) was used as the subset search strategy. Our experimental dataset contains 6000 emails, which were collected during the year of 2012. We conducted a Kolmogorov–Smirnov hypothesis test on the capital-run-length related features and found that all the p values were less than 0.001. Afterwards, we found a = 7 was the most appropriate in our model. Among seven meta-heuristic algorithms, we demonstrated the MBPSO is superior to GA, RSA, PSO, and BPSO in terms of classification performance. The sensitivity, specificity, and accuracy of the decision tree with feature selection by MBPSO were 91.02%, 97.51%, and 94.27%, respectively. We also compared the MBPSO with conventional feature selection methods such as SFS and SBS. The results showed that the MBPSO performs better than SFS and SBS. We also demonstrated that wrappers are more effective than filters with regard to classification performance indexes. It was clearly shown that the proposed method is effective, and it can reduce the false positive error without compromising the sensitivity and accuracy values.

Binary PSO with mutation operator for feature selection using decision tree applied to spam detection

This paper presents an approach to implement vibration, pressure, and current signals for fault diagnosis of the valves in reciprocating compressors. Due to the complexity of structure and motion of such compressor, the acquired vibration signal normally involves transient impacts and noise. This causes the useful information to be corrupted and difficulty in accurately diagnosing the faults with traditional methods. To reveal the fault patterns contained in this signal, the Teager-Kaiser energy operation (TKEO) is proposed to estimate the amplitude envelopes. In case of pressure and current, the random noise is removed by using a denoising method based on wavelet transform. Subsequently, statistical measures are extracted from all signals to represent the characteristics of the valve conditions. In order to classify the faults of compressor valves, a new type of learning architecture for deep generative model called deep belief networks (DBNs) is applied. DBN employs a hierarchical structure with multiple stacked restricted Boltzmann machines (RBMs) and works through a greedy layer-by-layer learning algorithm. In pattern recognition research areas, DBN has proved to be very effective and provided with high performance for binary values. However, for implementing DBN to fault diagnosis where most of signals are real-valued, RBM with Bernoulli hidden units and Gaussian visible units is considered in this study. The proposed approach is validated with the signals from a two-stage reciprocating air compressor under different valve conditions. To confirm the superiority of DBN in fault classification, its performance is compared with that of relevant vector machine and back propagation neuron networks. The achieved accuracy indicates that the proposed approach is highly reliable and applicable in fault diagnosis of industrial reciprocating machinery.

An approach to fault diagnosis of reciprocating compressor valves using Teager-Kaiser energy operator and deep belief networks

An Algebraic Solution of the GPS Equations

Cryptanalysis of a dynamic identity-based remote user authentication schemewithverifiable password update

The present paper has the goal of studying close approaches between a planet and a group of particles. The mathematical model includes the presence of the atmosphere of the planet. This cloud is assumed to be created by the passage of the spacecraft in the atmosphere of the planet, which can cause the explosion of the spacecraft. The system is assumed to be formed by the Sun, the planet, and the spacecraft that explodes and becomes a cloud of particles. The Sun and the planet are assumed to be in circular orbits and the motion is planar. The equations of motion are the ones given by the circular planar restricted three-body problem combined with the forces given by the atmospheric drag. In the numerical simulations, the planet Jupiter is the celestial body used for the close approaches. The initial positions and velocities of the spacecraft and the particles are specified at the periapsis, because it is assumed that this is the point where the explosion occurs.

/pdf/studying-close-approaches-for-a-cloud-of-particles-2wcn68dkv7.pdf

Studying Close Approaches for a Cloud of Particles Considering Atmospheric Drag

1 INPE-DMC, Avenida dos Astronautas 1758, 12227-010 Sao Jose dos Campos, SP, Brazil 2 IEEC and Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain 3 Universidade Estadual Paulista, UNESP, CEP 12516-410, Campus de Guaratingueta, Guaratingueta, SP, Brazil 4Universidade Estadual Paulista, UNESP, Caixa Postal 178, CEP 13500-970, Campus de Rio Claro, Rio Claro, SP, Brazil

/pdf/mathematical-methods-applied-to-the-celestial-mechanics-of-4w69zbecro.pdf

Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites

In this paper we perform a study of the effects of a close approach in the three-dimensional space between a planet and a cloud of particles, with the goal of understanding the dispersion of this cloud in terms of the variations of velocity, energy, angular momentum and inclination. It is assumed that the cloud is formed at the periapsis and the particles differ only by the magnitude of the velocity at this point. In this research we use the three-dimensional circular restricted three-body problem as the basic model for this close approach. A numerical algorithm is developed and implemented to study this problem and then it is applied to a cloud of particles, based in an analytical description of the close approach maneuver in the three-dimensional space. Analytical equations based in the patched conics approximation are used to calculate the variation in velocity, angular momentum, energy and inclination of the spacecraft that performs this maneuver.

/pdf/a-study-of-the-impact-of-the-initial-energy-in-a-close-4tmaewxqnh.pdf

A study of the impact of the initial energy in a close approach of a cloud of particles

The idea of the present paper is to study the swing-by maneuver between one of the planets of the Solar System and a cloud of particles. This is what happens when a fragmented comet crosses the orbit of a planet like Jupiter, Saturn, etc. We used the dynamical system that is formed by two main bodies (the Sun and one of the planets of the Solar System) and we assumed that they are in circular orbits around their center of mass and a cloud of particles is moving under the gravitational attraction of these two primaries. The motion is assumed to be planar for all the particles and the dynamics given by the "patched-conic" approximation is used, which means that a series of two-body problems are used to generate analytical equations that describe the problem. The main obejctive is to understand the change of the orbit of this cloud of particles after the close approach with the planet. It is assumed that all the particles that belong to the cloud have semi-major axis a ± da and eccentricity e ± de before the close approach with the planet. It is desired to known those values after the close approach. In particular, we will study the effects of the periapsis distance in this maneuver.

/pdf/swing-by-maneuvers-for-a-cloud-of-particles-with-planets-of-3invu9x5a8.pdf

Swing-By Maneuvers for a Cloud of Particles with Planets of the Solar System

This paper considers the problem of out of plane orbital maneuvers for station keeping of satellites. The main idea is to consider that a satellite is in an orbit around the Earth and that it has its orbit is disturbed by one or more forces. Then, it is necessary to perform a small amplitude orbital correction to return the satellite to its original orbit, to keep it performing its mission. A low thrust propulsion is used to complete this task. It is important to search for solutions that minimize the fuel consumption to increase the lifetime of the satellite. To solve this problem a hybrid optimal control approach is used. The accuracy of the satisfaction of the constraints is considered, in order to try to decrease the fuel expenditure by taking advantage of this freedom. This type of problem presents numerical difficulties and it is necessary to adjust parameters, as well as details of the algorithm, to get convergence. In this versions of the algorithm that works well for planar maneuvers are usually not adequate for the out of plane orbital corrections. In order to illustrate the method, some numerical results are presented.

/pdf/low-thrust-out-of-plane-orbital-station-keeping-maneuvers-1jkdaijnxg.pdf

Vivian Martins Gomes

Papers

Studying Close Approaches for a Cloud of Particles Considering Atmospheric Drag

Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites

A study of the impact of the initial energy in a close approach of a cloud of particles

Swing-By Maneuvers for a Cloud of Particles with Planets of the Solar System

Low-Thrust Out-of-Plane Orbital Station-Keeping Maneuvers for Satellites