Search results for: dynamical localization

Authors: Ashish Payal, C. S. Rai, B. V. R. Reddy

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With the increasing use and application of Wireless Sensor Networks (WSN), need has arisen to explore them in more effective and efficient manner. An important area which can bring efficiency to WSNs is the localization process, which refers to the estimation of the position of wireless sensor nodes in an ad hoc network setting, in reference to a coordinate system that may be internal or external to the network. In this paper, we have done comparison and analysed Sigmoidal Feedforward Artificial Neural Networks (SFFANNs) and Radial Basis Function (RBF) networks for developing localization framework in WSNs. The presented work utilizes the Received Signal Strength Indicator (RSSI), measured by static node on 100 x 100 m² grid from three anchor nodes. The comprehensive evaluation of these approaches is done using MATLAB software. The simulation results effectively demonstrate that FFANNs based sensor motes will show better localization accuracy as compared to RBF.

Keywords: localization, wireless sensor networks, artificial neural network, radial basis function, multi-layer perceptron, backpropagation, RSSI, GPS

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Authors: Mohammad Reza Rahimi Khoygani, Reza Ghasemi

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In this paper, designing direct adaptive neural controller is applied for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) is used for the Neural network (NN). The adaptive neural controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are the merits of this paper. The promising performance of the proposed controllers investigates in simulation results.

Keywords: adaptive control, pendulum dynamical system, nonlinear control, adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

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Authors: Waqas Ahmad, Eisha Tahir, Shahper Aqeel, Imran Khalid Niazi, Amjad Iqbal

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Background: Breast conservation surgery applies a number of techniques for accurate localization of lesions. Wire localization remains the method of choice in non-palpable breast cancers post-neoadjuvant chemotherapy. Objective: The aim of our study was to determine the accuracy of wire localization procedures in our department and compare it with internationally set protocols as per the Royal College of Radiologists. Post wire mammography, as well as the margin status of the postoperative specimen, assessed the accuracy of the procedure. Methods: We retrospectively reviewed the data of 225 patients who presented to our department from May 2014 to June 2015 post neoadjuvant chemotherapy with non-palpable cancers. These patients are candidates for wire localized lumpectomies either under ultrasound or stereotactic guidance. Metallic marker was placed in all the patients at the time of biopsy. Post wire mammogram was performed in all the patients and the distance of the wire tip from the marker was calculated. The presence or absence of the metallic clip in the postoperative specimen, as well as the marginal status of the postoperative specimen, was noted. Results: 157 sonographic and 68 stereotactic wire localization procedures were performed. 95% of the wire tips were within 1 cm of the metallic marker. Marginal status was negative in 94% of the patients in histopathological specimen. Conclusion: Our audit report declares more than 95% accuracy of image guided wire localization in successful excision of non-palpable breast lesions.

Keywords: breast, cancer, non-palpable, wire localization

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Authors: Dennis L. Owuor, Okuthe P. Kogeda, Johnson I. Agbinya

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Mobile localization has attracted a great deal of attention recently due to the introduction of wireless networks. Although several localization algorithms and systems have been implemented and discussed in the literature, very few researchers have exploited the gap that exists between indoor localization, tracking, external storage of location information and outdoor localization for the purpose of digital forensics during and after a disaster. The contribution of this paper lies in the implementation of a robust system that is capable of locating, tracking mobile device users and store location information for both indoor and partially outdoor the cloud. The system can be used during disaster to track and locate mobile phone users. The developed system is a mobile application built based on Android, Hypertext Preprocessor (PHP), Cascading Style Sheets (CSS), JavaScript and MATLAB for the Android mobile users. Using Waterfall model of software development, we have implemented a three level system that is able to track, locate and store mobile device information in secure database (cloud) on almost a real time basis. The outcome of the study showed that the developed system is efficient with regard to the tracking and locating mobile devices. The system is also flexible, i.e. can be used in any building with fewer adjustments. Finally, the system is accurate for both indoor and outdoor in terms of locating and tracking mobile devices.

Keywords: indoor localization, digital forensics, fingerprinting, tracking and cloud

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Authors: Minas Balyan

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In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: Adedayo Oke Adelakun

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The chaotic dynamics of periodically forced oscillators with smooth potential has been extensively investigated via theoretical, numerical and experimental simulations. With the advent of the study of chaotic dynamics by means of method of multiple time scale analysis, Melnikov theory, bifurcation diagram, Poincare's map, bifurcation diagrams and Lyapunov exponents, it has become necessary to seek for a better understanding of nonlinear oscillator with noisy term. In this paper, we examine the influence of noise on complex dynamical behaviour of periodically forced F6 - Duffing oscillator for specific choice of noisy parameters. The inclusion of noisy term improves the dynamical behaviour of the oscillator which may have wider application in secure communication than smooth potential.

Keywords: hierarchical structure, periodically forced oscillator, noisy parameters, dynamical behaviour, F6 - duffing oscillator

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Authors: Trupti Chavan, Ramachandra Guda, Kameshwar Rao

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The lack of data is a pain problem in medical image analysis using a convolutional neural network (CNN). This work uses various spatial transformation techniques to address the medical image augmentation issue for knee detection and localization using an enhanced single shot detector (SSD) network. The spatial transforms like a negative, histogram equalization, power law, sharpening, averaging, gaussian blurring, etc. help to generate more samples, serve as pre-processing methods, and highlight the features of interest. The experimentation is done on the OpenKnee dataset which is a collection of knee images from the openly available online sources. The CNN called enhanced single shot detector (SSD) is utilized for the detection and localization of the knee joint from a given X-ray image. It is an enhanced version of the famous SSD network and is modified in such a way that it will reduce the number of prediction boxes at the output side. It consists of a classification network (VGGNET) and an auxiliary detection network. The performance is measured in mean average precision (mAP), and 99.96% mAP is achieved using the proposed enhanced SSD with spatial transformations. It is also seen that the localization boundary is comparatively more refined and closer to the ground truth in spatial augmentation and gives better detection and localization of knee joints.

Keywords: data augmentation, enhanced SSD, knee detection and localization, medical image analysis, openKnee, Spatial transformations

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Authors: Beier Zhu, Rui Zhang, Qi Song

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Text contained within fixed-layout documents can be of great semantic value and so requires a high localization accuracy, such as ID cards, invoices, cheques, and passports. Recently, algorithms based on deep convolutional networks achieve high performance on text detection tasks. However, for text localization in fixed-layout documents, such algorithms detect word bounding boxes individually, which ignores the layout information. This paper presents a novel architecture built on convolutional neural networks (CNNs). A global text localization network and a regional bounding-box regression network are introduced to tackle the problem in a coarse-to-fine manner. The text localization network simultaneously locates word bounding points, which takes the layout information into account. The bounding-box regression network inputs the features pooled from arbitrarily sized RoIs and refine the localizations. These two networks share their convolutional features and are trained jointly. A typical type of fixed-layout documents: ID cards, is selected to evaluate the effectiveness of the proposed system. These networks are trained on data cropped from nature scene images, and synthetic data produced by a synthetic text generation engine. Experiments show that our approach locates high accuracy word bounding boxes and achieves state-of-the-art performance.

Keywords: bounding box regression, convolutional networks, fixed-layout documents, text localization

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Authors: Meiling Yang, Shuguo Xie, Yilong Zhu

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Nowadays, due to diverse electric products and complex electromagnetic environment, the localization and troubleshooting of the electromagnetic radiation source is urgent and necessary especially on the condition of far field. However, based on the existing DOA positioning method, the system or devices are complex, bulky and expensive. To address this issue, this paper proposes a single antenna radiation source localization method. A single antenna moves to form a virtual antenna array combined with DOA and MUSIC algorithm to position accurately, meanwhile reducing the cost and simplify the equipment. As shown in the results of simulations and experiments, the virtual antenna array DOA estimation modeling is correct and its positioning is credible.

Keywords: virtual antenna array, DOA, localization, far field

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Authors: Nana Weng

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Firstly, based on two diamond models and Value-Rarity-Inimitability-Organization framework, this paper analyzes the Country Specific factors of and firm specific factors which influence subsidiaries’ sustainable competitive advantage. Then, according to the main content of Strategic Human Resource Management (SHRM) research that HRM strategy should fit into corporate strategy, we explained what the SHRM practices should be in the context of localization strategies within Multinational Enterprise (MNE) companies. Then we choose two Japanese MNE subsidiaries in the same industry and tested the hypothesis that localization SHRM practices positively impact on subsidiary’s sustainable competitive advantage, further positively affect firm integrated performance (both financial performance and organizational and organizational performance) lever through High Performance Work Practices (HPWPs) of local employees.

Keywords: localization SHRM, firm integrated performance, Japanese MNE subsidiaries, Vietnam

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Authors: Rukshana Pervin

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We report a detailed study on the transport properties of a 40 nm thick granular aluminum film. As measured by temperature-dependent resistance R(T), a resistance peak is observed before the transition to superconductivity, which indicates that the diffusion channel is subjected to weak localization and electron-electron interaction, and the superconductor channel is subjected to SC fluctuations (SCFs). The zero-magnetic field transport measurement demonstrated that Electron-Electron Interaction (EEI), weak localization, and SCFs are closely related in this granular aluminum film. The characteristic temperature at which SCFs emerge on the sample is determined by measuring the R(T) during cooling. The SCF of the film is studied in terms of the direct contribution of the Aslamazov-Larkin's fluctuation Cooper pair density and the indirect contribution of the Maki-Thomson's quasiparticle pair density. In this sample, the rise in R(T) above the SCF characteristic temperature indicates the WL and/or EEI. Comparative analyses are conducted on how the EEI and WL contribute to the upturn in R(T).

Keywords: fluctuation superconductivity, weak localization, thermal deposition, electron-electron interaction

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Authors: Anju Kumari, R. P. Sharma

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The localization of Kinetic Alfvén Wave (KAW) caused by finite amplitude background density fluctuations has been studied in intermediate beta plasma. KAW breaks up into localized large amplitude structures when perturbed by MHD fluctuations of the medium which are in the form of magnetosonic waves. Numerical simulation has been performed to analyse the localized structures and resulting turbulent spectrum of KAW applicable to magnetopause. Simulation results reveal that power spectrum deviates from Kolmogorov scaling at the transverse size of KAW, equal to ion gyroradius. Steepening of power spectrum at shorter wavelengths may be accountable for heating and acceleration of the plasma particles. The obtained results are compared with observations collected from the THEMIS spacecraft in magnetopause.

Keywords: Kinetic Alfvén Wave (KAW), localization, turbulence, turbulent spectrum

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Authors: Iftikhar Ahmad, A. Benallegue, A. El Hadri

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In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method.

Keywords: non-linear systems, sliding mode observer, disturbance rejection, nonlinear control

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Authors: Mariana P. Medeiros, Amanda P. Carvallo, Augusta Isaac, Milos Janecek, Peter Minarik, Mayerling Martinez Celis, Roberto. R. Figueiredo

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The effect of high pressure torsion processing on mechanical properties and corrosion behavior of pure magnesium and Mg-Zn, Mg-Zn-Ca, Mg-Li-Y, and Mg-Y-RE alloys is investigated. Micro-tomography and SEM characterization are used to estimate corrosion rate and evaluate non-uniform corrosion features. The results show the severe plastic deformation processing improves the strength of all magnesium alloys, but deformation localization can take place in the Mg-Zn-Ca and Mg-Y-RE alloys. The occurrence of deformation localization is associated with low strain rate sensitivity in these alloys and with severe corrosion localization. Pure magnesium and Mg-Zn and Mg-Li-Y alloys display good corrosion resistance with low corrosion rate and maintained integrity after 28 days of immersion in Hank`s solution.

Keywords: magnesium alloys, severe plastic deformation, corrosion, biodegradable alloys

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Authors: Andrey V. Timofeev

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The practical efficient approach is suggested to estimate the high-speed objects instant bounds in C-OTDR monitoring systems. In case of super-dynamic objects (trains, cars) is difficult to obtain the adequate estimate of the instantaneous object localization because of estimation lag. In other words, reliable estimation coordinates of monitored object requires taking some time for data observation collection by means of C-OTDR system, and only if the required sample volume will be collected the final decision could be issued. But it is contrary to requirements of many real applications. For example, in rail traffic management systems we need to get data off the dynamic objects localization in real time. The way to solve this problem is to use the set of statistical independent parameters of C-OTDR signals for obtaining the most reliable solution in real time. The parameters of this type we can call as 'signaling parameters' (SP). There are several the SP’s which carry information about dynamic objects instant localization for each of C-OTDR channels. The problem is that some of these parameters are very sensitive to dynamics of seismoacoustic emission sources but are non-stable. On the other hand, in case the SP is very stable it becomes insensitive as a rule. This report contains describing the method for SP’s co-processing which is designed to get the most effective dynamic objects localization estimates in the C-OTDR monitoring system framework.

Keywords: C-OTDR-system, co-processing of signaling parameters, high-speed objects localization, multichannel monitoring systems

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Authors: Kathia Melbouci, Sylvie Naudet Collette, Vincent Gay-Bellile, Omar Ait-Aider, Michel Dhome

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In this paper, we handle the problem of real time localization and mapping in indoor environment assisted by a partial prior 3D model, using an RGBD sensor. The proposed solution relies on a feature-based RGBD SLAM algorithm to localize the camera and update the 3D map of the scene. To improve the accuracy and the robustness of the localization, we propose to combine in a local bundle adjustment process, geometric information provided by a prior coarse 3D model of the scene (e.g. generated from the 2D floor plan of the building) along with RGBD data from a Kinect camera. The proposed approach is evaluated on a public benchmark dataset as well as on real scene acquired by a Kinect sensor.

Keywords: SLAM, global localization, 3D sensor, bundle adjustment, 3D model

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Authors: Marcell Serra de Almeida Martins, Benedito de Souza Ribeiro Neto, Gerson Lima Serejo, Carlos Gustavo Resque Dos Santos

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Indoor positioning systems use sensors such as Bluetooth, ZigBee, and Wi-Fi, as well as cameras for image capture, which can be fixed or mobile. These computer vision-based positioning approaches are low-cost to implement, mainly when it uses a mobile camera. The present study aims to create a design of a fiducial marker for a low-cost indoor localization system. The marker is tape-shaped to perform a continuous reading employing two detection algorithms, one for greater distances and another for smaller distances. Therefore, the location service is always operational, even with variations in capture distance. A minimal localization and reading algorithm were implemented for the proposed marker design, aiming to validate it. The accuracy tests consider readings varying the capture distance between [0.5, 10] meters, comparing the proposed marker with others. The tests showed that the proposed marker has a broader capture range than the ArUco and QRCode, maintaining the same size. Therefore, reducing the visual pollution and maximizing the tracking since the ambient can be covered entirely.

Keywords: multiscale recognition, indoor localization, tape-shaped marker, fiducial marker

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Authors: M. P. Nanda Kumar, K. Dheeraj

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The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: inverse optimal control, radial basis function, neural network, controller design

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: R. Ghasemi, M. R. Rahimi Khoygani

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This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Muhammad Fiaz

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The article in hand is the study of complex features like Zero Hopf Bifurcation, Chaos and Synchronization of integer and fractional order version of a new 3D finance system. Trusted tools of averaging theory and active control method are utilized for investigation of Zero Hopf bifurcation and synchronization for both versions respectively. Inventiveness of the paper is to find the answer of a question that is it possible to find a chaotic system which can be synchronized with any other of the same dimension? Based on different examples we categorically develop a theory that if a couple of master and slave chaotic dynamical system is synchronized by selecting a suitable gain matrix with special conditions then the master system is synchronized with any chaotic dynamical system of the same dimension. With the help of this study we developed generalized theorems for synchronization of n-dimension dynamical systems for integer as well as fractional versions. it proposed that this investigation will contribute a lot to control dynamical systems and only a suitable gain matrix with special conditions is enough to synchronize the system under consideration with any other chaotic system of the same dimension. Chaotic properties of fractional version of the new finance system are also analyzed at fractional order q=0.87. Simulations results, where required, also provided for authenticity of analytical study.

Keywords: complex analysis, chaos, generalized synchronization, control dynamics, fractional order analysis

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Authors: Nurgül Şenol, Melda Azman

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In this study, gastrointestinal immunohistochemistry in the Vimba vimba and the localization of CCK/gastrin were determined. Although there are a number of studies which relate to the gastrointestinal histochemistry and the localization of the peptides, a literature research in this field revealed that no histochemical or immunohistochemical study covering also the species had been found in our country. In this research, species will be provided from Vimba vimba located in Eğirdir lake. Stomach samples and intestinal samples of these fish will be exposed to routine histological tissue process, embedded in paraffin blocks, and 5-6 μ -thick sections will be taken. Using the PAP (Peroxidase anti-peroxidase) method, localization of the peptides CCK/gastrin was to be found. The densities of peptides of this species were compared, and then the findings obtained were to be evaluated through the statistical analysis methods (SPSS). Endocrine cells reactive to gastrin/CCK antiserum were demonstrated in the stomach and intestinal mucosa. There is a significant difference between gastrin and CCK when compared to regions.

Keywords: CCK, gastrin, immunoreactivity, vimba vimba

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Authors: Naser Safdarian, Nader Jafarnia Dabanloo

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In this paper we used four features i.e. Q-wave integral, QRS complex integral, T-wave integral and total integral as extracted feature from normal and patient ECG signals to detection and localization of myocardial infarction (MI) in left ventricle of heart. In our research we focused on detection and localization of MI in standard ECG. We use the Q-wave integral and T-wave integral because this feature is important impression in detection of MI. We used some pattern recognition method such as Artificial Neural Network (ANN) to detect and localize the MI. Because these methods have good accuracy for classification of normal and abnormal signals. We used one type of Radial Basis Function (RBF) that called Probabilistic Neural Network (PNN) because of its nonlinearity property, and used other classifier such as k-Nearest Neighbors (KNN), Multilayer Perceptron (MLP) and Naive Bayes Classification. We used PhysioNet database as our training and test data. We reached over 80% for accuracy in test data for localization and over 95% for detection of MI. Main advantages of our method are simplicity and its good accuracy. Also we can improve accuracy of classification by adding more features in this method. A simple method based on using only four features which extracted from standard ECG is presented which has good accuracy in MI localization.

Keywords: ECG signal processing, myocardial infarction, features extraction, pattern recognition

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Authors: Bououden Soraya

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This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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Authors: T. K. Dutta, K. K. Das, N. Dutta

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The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research.

Keywords: Feigenbaum universality, chaos, Lyapunov exponent, fractal dimensions

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Authors: N. V. Kazmiruk, Y. R. Nartsissov

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Phosphate activated glutaminase (GA, E.C. 3.5.1.2) plays a key role in glutamine/glutamate homeostasis in mammalian brain, catalyzing the hydrolytic deamidation of glutamine to glutamate and ammonium ions. GA is mainly localized in mitochondria, where it has the catalytically active form on the inner mitochondrial membrane (IMM) and the other soluble form, which is supposed to be dormant. At present time, the exact localization of the membrane glutaminase active site remains a controversial and an unresolved issue. The first hypothesis called c-side localization suggests that the catalytic site of GA faces the inter-membrane space and products of the deamidation reaction have immediate access to cytosolic metabolism. According to the alternative m-side localization hypothesis, GA orients to the matrix, making glutamate and ammonium available for the tricarboxylic acid cycle metabolism in mitochondria directly. In our study, we used a multi-compartment kinetic approach to simulate metabolism of glutamate and glutamine in the astrocytic cytosol and mitochondria. We used physiologically important ratio between the concentrations of glutamine inside the matrix of mitochondria [Glnₘᵢₜ] and glutamine in the cytosol [Glncyt] as a marker for precise functioning of the system. Since this ratio directly depends on the mitochondrial glutamine carrier (MGC) flow parameters, key observation was to investigate the dependence of the [Glnmit]/[Glncyt] ratio on the maximal velocity of MGC at different initial concentrations of mitochondrial glutamate. Another important task was to observe the similar dependence at different inhibition constants of the soluble GA. The simulation results confirmed the experimental c-side localization hypothesis, in which the glutaminase active site faces the outer surface of the IMM. Moreover, in the case of such localization of the enzyme, a 3-fold decrease in ammonium production was predicted.

Keywords: glutamate metabolism, glutaminase, kinetic approach, mitochondrial membrane, multi-compartment modeling

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Authors: Lana Horvat Dmitrović

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The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems.

Keywords: bifurcation, box dimension, invariant manifold, orbit near fixed point

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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