Search results for: principle of stationary action

Authors: Elena Ezhova, Vadim Mottl, Olga Krasotkina

Abstract:

The problem of estimating time-varying regression is inevitably concerned with the necessity to choose the appropriate level of model volatility - ranging from the full stationarity of instant regression models to their absolute independence of each other. In the stationary case the number of regression coefficients to be estimated equals that of regressors, whereas the absence of any smoothness assumptions augments the dimension of the unknown vector by the factor of the time-series length. The Akaike Information Criterion is a commonly adopted means of adjusting a model to the given data set within a succession of nested parametric model classes, but its crucial restriction is that the classes are rigidly defined by the growing integer-valued dimension of the unknown vector. To make the Kullback information maximization principle underlying the classical AIC applicable to the problem of time-varying regression estimation, we extend it onto a wider class of data models in which the dimension of the parameter is fixed, but the freedom of its values is softly constrained by a family of continuously nested a priori probability distributions.

Keywords: Time varying regression, time-volatility of regression coefficients, Akaike Information Criterion (AIC), Kullback information maximization principle.

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Authors: Han Xiao, Xiaoyan Zhu

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Margin-Based Principle has been proposed for a long time, it has been proved that this principle could reduce the structural risk and improve the performance in both theoretical and practical aspects. Meanwhile, feed-forward neural network is a traditional classifier, which is very hot at present with a deeper architecture. However, the training algorithm of feed-forward neural network is developed and generated from Widrow-Hoff Principle that means to minimize the squared error. In this paper, we propose a new training algorithm for feed-forward neural networks based on Margin-Based Principle, which could effectively promote the accuracy and generalization ability of neural network classifiers with less labelled samples and flexible network. We have conducted experiments on four UCI open datasets and achieved good results as expected. In conclusion, our model could handle more sparse labelled and more high-dimension dataset in a high accuracy while modification from old ANN method to our method is easy and almost free of work.

Keywords: Max-Margin Principle, Feed-Forward Neural Network, Classifier.

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Authors: Hyun-Chool Shin

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In this paper we propose a simple adaptive algorithm iteratively solving the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates scalar normalization which is computationally much simpler. The analysis of stationary point is presented to show that the proposed algorithm indeed solves the constrained optimization problem. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.

Keywords: constrained optimization, unit-norm, LMS, principle component analysis.

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Authors: S. H. Sabzpoushan

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In this research we show that the dynamics of an action potential in a cell can be modeled with a linear combination of the dynamics of the gating state variables. It is shown that the modeling error is negligible. Our findings can be used for simplifying cell models and reduction of computational burden i.e. it is useful for simulating action potential propagation in large scale computations like tissue modeling. We have verified our finding with the use of several cell models.

Keywords: Linear model, Action potential, gating dynamics.

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Authors: S. Babaie-Kafaki, R. Ghanbari, S.H. Nasseri, E. Ardil

Abstract:

Bus networks design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. The genetic algorithm (GA) is a search and optimization technique which works based on evolutionary principle of natural chromosomes. Specifically, the evolution of chromosomes due to the action of crossover, mutation and natural selection of chromosomes based on Darwin's survival-of-the-fittest principle, are all artificially simulated to constitute a robust search and optimization procedure. In this paper, we first state the problem as a mixed integer programming (MIP) problem. Then we design a new crossover and mutation for bus terminal location problem (BTLP). We tested the different parameters of genetic algorithm (for a sample problem) and obtained the optimal parameters for solving BTLP with numerical try and error.

Keywords: Bus networks, Genetic algorithm (GA), Locationproblem, Mixed integer programming (MIP).

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Authors: Douangmala Kounsana, Xiang Wen, Toru Takahashi

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After a strong earthquake occurs, a secondary disaster due to strong aftershocks, flood, landslide or heavy snow can possible to occur and the secondary disaster due to resident-s action also can possible to happen. However, until now seldom researchers have paid attention at it. This paper focused on the Inhabitant-s action after the strong earthquake occurs when a terrible even becomes calm. An inappropriate behavior of people with disadvantaged climate after the worse earthquake can bring a tragedy to their life.

Keywords: Sichuan Earthquake, Secondary Disaster, Inhabitant's Action, inappropriate behavior.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

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This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: Nor Hafizah S., Salfarina A. G., Intan Hashimah H., Juliana A. W.

Abstract:

Collective action can be an effective means for local development as well as important strategy to enhance livelihoods especially among rural people. This article explores the level of collective action among members of Fishermen-s Wives Group (KUNITA) in Malaysia. KUNITA was established by the Malaysian Fishery Development Authority (LKIM) with an objective to increase the socio-economic status of fishermen-s families. The members who are mostly the wives and daughters of fishermen are strongly encouraged by LKIM to venture into entrepreneurship activities. The objective of this research was to see the level of collective action among members in KUNITA groups in the state of Selangor. The finding shows that high level of collective action among KUNITA members is strongly based on volunteerism. However, the level of cooperation among members in the group is relatively low. The findings present significant challenges for the group in maintaining the sustainability of KUNITA organization.

Keywords: Collective action, entrepreneurship, fishermen' swives group, LKIM.

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Authors: Mounira RouaÐùnia, Noureddine Doghmane

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In this paper we consider the problem of change detection and non stationary signals tracking. Using parametric estimation of signals based on least square lattice adaptive filters we consider for change detection statistical parametric methods using likelihood ratio and hypothesis tests. In order to track signals dynamics, we introduce a compensation procedure in the adaptive estimation. This will improve the adaptive estimation performances and fasten it-s convergence after changes detection.

Keywords: Change detection, Hypothesis test, likelihood ratioleast square lattice adaptive filters.

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Authors: Yingchun Jiang, Yan Tang

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In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces Hs(Rd) and H-s(Rd).

Keywords: Nonstationary, dual frames, dual Sobolev spaces, extension principle.

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Authors: Mahbod Seyednia, Shidvash Vakilipour, Mehran Masdari

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Computations for two-dimensional flow past a stationary and harmonically pitching wind turbine airfoil at a moderate value of Reynolds number (400000) are carried out by progressively increasing the angle of attack for stationary airfoil and at fixed pitching frequencies for rotary one. The incompressible Navier-Stokes equations in conjunction with Unsteady Reynolds Average Navier-Stokes (URANS) equations for turbulence modeling are solved by OpenFOAM package to investigate the aerodynamic phenomena occurred at stationary and pitching conditions on a NACA 6-series wind turbine airfoil. The aim of this study is to enhance the accuracy of numerical simulation in predicting the aerodynamic behavior of an oscillating airfoil in OpenFOAM. Hence, for turbulence modelling, k-ω-SST with low-Reynolds correction is employed to capture the unsteady phenomena occurred in stationary and oscillating motion of the airfoil. Using aerodynamic and pressure coefficients along with flow patterns, the unsteady aerodynamics at pre-, near-, and post-static stall regions are analyzed in harmonically pitching airfoil, and the results are validated with the corresponding experimental data possessed by the authors. The results indicate that implementing the mentioned turbulence model leads to accurate prediction of the angle of static stall for stationary airfoil and flow separation, dynamic stall phenomenon, and reattachment of the flow on the surface of airfoil for pitching one. Due to the geometry of the studied 6-series airfoil, the vortex on the upper surface of the airfoil during upstrokes is formed at the trailing edge. Therefore, the pattern flow obtained by our numerical simulations represents the formation and change of the trailing-edge vortex at near- and post-stall regions where this process determines the dynamic stall phenomenon.

Keywords: CFD, Moderate Reynolds number, OpenFOAM, pitching oscillation, unsteady aerodynamics, wind turbine.

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Authors: Ming-Hsiung Wu, Yu-Hsi Yuan

Abstract:

The aim of the research is to understand whether the accuracy of customer detection of employee emotional labor strategy would influence the overall service satisfaction. From path analysis, it was found that employee-s positive emotions positively influenced service quality. Service quality in turn influenced Customer detection of employee emotional deep action strategy and Customer detection of employee emotional surface action strategy. Lastly, Customer detection of employee emotional deep action strategy and Customer detection of employee emotional surface action strategy positively influenced service satisfaction. Based on the analysis results, suggestions are proposed to provide reference for human resource management and use in relative fields.

Keywords: Emotional labor, Emotional deep action strategy, Emotional surface action strategy, Service satisfaction

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Authors: Mohammed Benbrahim, Khalid Benjelloun, Aomar Ibenbrahim, Adil Daoudi

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The automatic classification of non stationary signals is an important practical goal in several domains. An essential classification task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, we present a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "Ben wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis.

Keywords: Seismic signals, Ben Wavelet, Dimensionality reduction, Artificial neural networks, Classification.

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Authors: N. Hammouda, K. Belmokre

Abstract:

Paints are the most widely used methods of protection against atmospheric corrosion of metals. The aim of this work was to determine the protective performance of epoxy coating against sea water before and after damage. Investigations are conducted using stationary and non-stationary electrochemical tools such as electrochemical impedance spectroscopy has allowed us to characterize the protective qualities of these films. The application of the EIS on our damaged in-situ painting shows the existence of several capacitive loops which is an indicator of the failure of our tested paint. Microscopic analysis (micrograph) helped bring essential elements in understanding the degradation of our paint condition and immersion training corrosion products.

Keywords: Epoxy Paints, Electrochemical Impedance Spectroscopy, Corrosion Mechanisms, sea water.

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Authors: S. Maheswari, P. Arockia Jansi Rani

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Human action is recognized directly from the video sequences. The objective of this work is to recognize various human actions like run, jump, walk etc. Human action recognition requires some prior knowledge about actions namely, the motion estimation, foreground and background estimation. Region of interest (ROI) is extracted to identify the human in the frame. Then, optical flow technique is used to extract the motion vectors. Using the extracted features similarity measure based classification is done to recognize the action. From experimentations upon the Weizmann database, it is found that the proposed method offers a high accuracy.

Keywords: Background subtraction, human silhouette, optical flow, classification.

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Authors: Manouchehr Amiri

Abstract:

This article presents a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary Data Matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principle is investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Bekenstein, and mass-energy equivalence are derived.

Keywords: Physical theory of information, binary data matrix model, Shannon information theory, bit information principle.

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Authors: Pavlo Selyshchev

Abstract:

Irradiated material is a typical example of a complex system with nonlinear coupling between its elements. During irradiation the radiation damage is developed and this development has bifurcations and qualitatively different kinds of behavior. The accumulation of primary defects in irradiated crystals is considered in frame work of nonlinear evolution of complex system. The thermo-concentration nonlinear feedback is carried out as a mechanism of self-oscillation development. It is shown that there are two ways of the defect density evolution under stationary irradiation. The first is the accumulation of defects; defect density monotonically grows and tends to its stationary state for some system parameters. Another way that takes place for opportune parameters is the development of self-oscillations of the defect density. The stationary state, its stability and type are found. The bifurcation values of parameters (environment temperature, defect generation rate, etc.) are obtained. The frequency of the selfoscillation and the conditions of their development is found and rated. It is shown that defect density, heat fluxes and temperature during self-oscillations can reach much higher values than the expected steady-state values. It can lead to a change of typical operation and an accident, e.g. for nuclear equipment.

Keywords: Irradiation, Primary Defects, Solids, Self-oscillation.

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Authors: L. Rodriguez-Benitez, J. Moreno-Garcia, J.J. Castro-Schez, C. Solana, L. Jimenez

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In this paper the use of sequential machines for recognizing actions taken by the objects detected by a general tracking algorithm is proposed. The system may deal with the uncertainty inherent in medium-level vision data. For this purpose, fuzzification of input data is performed. Besides, this transformation allows to manage data independently of the tracking application selected and enables adding characteristics of the analyzed scenario. The representation of actions by means of an automaton and the generation of the input symbols for finite automaton depending on the object and action compared are described. The output of the comparison process between an object and an action is a numerical value that represents the membership of the object to the action. This value is computed depending on how similar the object and the action are. The work concludes with the application of the proposed technique to identify the behavior of vehicles in road traffic scenes.

Keywords: Approximate reasoning, finite state machines, video analysis.

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Authors: Tomáš Urbanec

Abstract:

Paper presents simple sixport principle and its frequency bandwidth. The novel multisixport approach is presented with its possibilities, typical parameters and frequency bandwidth. Practical implementation is shown with its measurement parameters and calibration. The bandwidth circa 1:100 is obtained.

Keywords: microwave measurement, sixport, VNA, wideband.

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Authors: F. Loffredo, M. Quarto, M. Pugliese, A. Mazzella, F. De Cicco, V. Roca

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The aim of this study is to evaluate the efficacy of radon remedial action in a school on the Ischia island, South Italy, affected by indoor radon concentration higher than the value of 500 Bq/m³. This value is the limit imposed by the Italian legislation, to above which corrective actions in schools are necessary. Before the application of remedial action, indoor radon concentrations were measured in 9 rooms of the school. The measurements were performed with LR-115 passive alpha detectors (SSNTDs) and E-Perm. The remedial action was conducted in one of the office affected by high radon concentration using a Radonstop paint applied after the construction of a concrete slab under the floor. The effect of remedial action was the reduction of the concentration of radon of 41% and moreover it has demonstrated to be durable over time. The chosen method is cheap and easy to apply and it could be designed for various types of building. This method can be applied to new and existing buildings that show high dose values.

Keywords: E-Perm, LR 115 detectors, radon remediation, school.

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Authors: Mohammad Javad Dehghani

Abstract:

In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying amplitudes. The techniques include the Discrete Wavelet Transform (DWT), and the S-Transform. Several power quality problems are analyzed using both the discrete wavelet transform and S–transform, showing clearly the advantage of the S– transform in detecting, localizing, and classifying the power quality problems.

Keywords: Power quality, S-Transform, Short Time FourierTransform , Wavelet Transform, instantaneous sag, swell.

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

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This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: Online data updates, covariance matrix, online principle component analysis (OPCA), matrix perturbation.

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Authors: R. I. Khrapko

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As is known, the role of the energy-momentum pseudotensors of the gravitational field is to extend the conservation law to the gravitational interaction by taking into account the energy and momentum of the gravitational field. We calculated the contribution of the Einstein pseudotensor to the total mass of a stationary material body and its gravitational field. It turned out that this contribution is positive, despite the fact that the mass-energy of a stationary gravitational field is negative. We concluded that the pseudotensor incorrectly describes the energy of the gravitational field. Nevertheless, this pseudotensor has been used in a large number of scientific works for 100 years. We explain this by the fact that the covariant component of the pseudotensor was regarded as the mass-energy. Besides, we prove the advantage of the covariant energy-momentum conservation law for matter in the Minkowski space-time.

Keywords: Conservation law, covariant integration, gravitation field, isolated system.

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Authors: Olfa.Ben Ahmed, Mahmoud. Mejdoub, Chokri. Ben Amar

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Recognizing human action from videos is an active field of research in computer vision and pattern recognition. Human activity recognition has many potential applications such as video surveillance, human machine interaction, sport videos retrieval and robot navigation. Actually, local descriptors and bag of visuals words models achieve state-of-the-art performance for human action recognition. The main challenge in features description is how to represent efficiently the local motion information. Most of the previous works focus on the extension of 2D local descriptors on 3D ones to describe local information around every interest point. In this paper, we propose a new spatio-temporal descriptor based on a spacetime description of moving points. Our description is focused on an Accordion representation of video which is well-suited to recognize human action from 2D local descriptors without the need to 3D extensions. We use the bag of words approach to represent videos. We quantify 2D local descriptor describing both temporal and spatial features with a good compromise between computational complexity and action recognition rates. We have reached impressive results on publicly available action data set

Keywords: Accordion, Bag of Features, Human action, Motion, Moving point, Space-Time Descriptor, SIFT, Video.

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Authors: B. Sudhakar, K. A. Ponnusamy

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In India cotton was the major commercial crop and cultivating all the states. In recent years, area of cotton declined due to pest and disease attack, drought, lower price for the produces etc. The first reason as pest and disease attack will be the challenges and it is of utmost importance that in future the insect problems would have to be tackled through Integrated Pest Management (IPM). The present study deals with principle knowledge of IPM adopting cotton cultivators in irrigated and rainfed conditions. Under irrigated conditions, among cultural practices, all respondents had principle knowledge about growing high yielding and pest resistant hybrids, sowing quality and certified seeds and avoiding cotton ratoon cropping. Regarding mechanical practices all respondents had principle knowledge about collecting and destroying egg, larvae and pupae of pests and removing and destroying pest and disease infected cotton squares, flowers and other shed materials. With regard to biological practices, 93% of them had principle knowledge about spraying neem oil, followed by 82% about tying Trichogramma eggcard. Among chemical practices, more than 90% of the respondents had principle knowledge about of spraying herbicide (96%), identifying ETL (Economic Threshold Level) for cotton pests (94%), and applying safe insecticides (90%). Under rainfed condition, among cultural practices, all respondents had principle knowledge about sowing quality and certified seeds and growing high yielding and pest resistant hybrids seeds. Regarding mechanical practices hundred percentage of the respondents had principle knowledge on the mechanical practices viz., collecting and destroying egg, larvae and pupae of pests and removing and destroying pest and disease infected cotton squares, flowers and other shed materials. With regard to biological practices, 96% of the respondents had correct in principle knowledge about spraying neem oil, followed by 89% about tying Trichogramma eggcard. With regard to chemical practices, more than 90% of the respondents had principle knowledge of applying safe insecticides (95%), avoiding repeated use of the same insecticides (95%), identifying ETL for cotton pests (94%) and applying granular insecticides (90%).

Keywords: Biological practices, chemical practices, cultural practices, mechanical practices, integrated pest management.

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Authors: Jie Cai, David C. Levy

Abstract:

Electronic nose (array of chemical sensors) are widely used in food industry and pollution control. Also it could be used to locate or detect the direction of the source of emission odors. Usually this task is performed by electronic nose (ENose) cooperated with mobile vehicles, but when a source is instantaneous or surrounding is hard for vehicles to reach, problem occurs. Thus a method for stationary ENose to detect the direction of the source and locate the source will be required. A novel method which uses the ratio between the responses of different sensors as a discriminant to determine the direction of source in natural wind surroundings is presented in this paper. The result shows that the method is accurate and easily to be implemented. This method could be also used in movably, as an optimized algorithm for robot tracking source location.

Keywords: Electronic nose, Nature wind situation, Source direction detection.

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Authors: P. G. Siddheshwar, B. R. Revathi

Abstract:

The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.

Keywords: Dielectric liquid, Nusselt number, amplitude equation.

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Authors: A. Ouanane, A. Serir

Abstract:

In this paper, a novel algorithm based on Ridgelet Transform and support vector machine is proposed for human action recognition. The Ridgelet transform is a directional multi-resolution transform and it is more suitable for describing the human action by performing its directional information to form spatial features vectors. The dynamic transition between the spatial features is carried out using both the Principal Component Analysis and clustering algorithm K-means. First, the Principal Component Analysis is used to reduce the dimensionality of the obtained vectors. Then, the kmeans algorithm is then used to perform the obtained vectors to form the spatio-temporal pattern, called set-of-labels, according to given periodicity of human action. Finally, a Support Machine classifier is used to discriminate between the different human actions. Different tests are conducted on popular Datasets, such as Weizmann and KTH. The obtained results show that the proposed method provides more significant accuracy rate and it drives more robustness in very challenging situations such as lighting changes, scaling and dynamic environment

Keywords: Human action, Ridgelet Transform, PCA, K-means, SVM.

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Authors: Mouse, cardiac myocytes, computer simulation, action potential.

Abstract:

Heterogeneous repolarization causes dispersion of the T-wave and has been linked to arrhythmogenesis. Such heterogeneities appear due to differential expression of ionic currents in different regions of the heart, both in healthy and diseased animals and humans. Mice are important animals for the study of heart diseases because of the ability to create transgenic animals. We used our previously reported model of mouse ventricular myocytes to develop 2D mouse ventricular tissue model consisting of 14,000 cells (apical or septal ventricular myocytes) and to study the stability of action potential propagation and Ca2+ dynamics. The 2D tissue model was implemented as a FORTRAN program code for highperformance multiprocessor computers that runs on 36 processors. Our tissue model is able to simulate heterogeneities not only in action potential repolarization, but also heterogeneities in intracellular Ca2+ transients. The multicellular model reproduced experimentally observed velocities of action potential propagation and demonstrated the importance of incorporation of realistic Ca2+ dynamics for action potential propagation. The simulations show that relatively sharp gradients of repolarization are predicted to exist in 2D mouse tissue models, and they are primarily determined by the cellular properties of ventricular myocytes. Abrupt local gradients of channel expression can cause alternans at longer pacing basic cycle lengths than gradual changes, and development of alternans depends on the site of stimulation.

Keywords: Mouse, cardiac myocytes, computer simulation, action potential

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Authors: Rado Flajs

Abstract:

In the present paper the extreme shear stresses with the corresponding planes are established using the freely available computer tools like the Gnuplot, Sage, R, Python and Octave. In order to support these freely available computer tools, their strong symbolical and graphical abilities are illustrated. The nature of the stationary points obtained by the Method of Lagrangian Multipliers can be determined using freely available computer symbolical tools like Sage. The characters of the stationary points can be explained in the easiest way using freely available computer graphical tools like Gnuplot, Sage, R, Python and Octave. The presented figures improve the understanding of the problem and the obtained solutions for the majority of students of civil or mechanical engineering.

Keywords: engineering, continuum mechanics, extreme shear stresses, Gnuplot, Sage, R, Python, Octave

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