Search results for: Inverse Gaussian distribution

Authors: E. S. Gower, M. O. J. Hawksford

Abstract:

An algorithm for learning an overcomplete dictionary using a Cauchy mixture model for sparse decomposition of an underdetermined mixing system is introduced. The mixture density function is derived from a ratio sample of the observed mixture signals where 1) there are at least two but not necessarily more mixture signals observed, 2) the source signals are statistically independent and 3) the sources are sparse. The basis vectors of the dictionary are learned via the optimization of the location parameters of the Cauchy mixture components, which is shown to be more accurate and robust than the conventional data mining methods usually employed for this task. Using a well known sparse decomposition algorithm, we extract three speech signals from two mixtures based on the estimated dictionary. Further tests with additive Gaussian noise are used to demonstrate the proposed algorithm-s robustness to outliers.

Keywords: expectation-maximization, Pitman estimator, sparsedecomposition

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Authors: Daniel Morariu, Lucian N. Vintan, Volker Tresp

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Text categorization is the problem of classifying text documents into a set of predefined classes. After a preprocessing step, the documents are typically represented as large sparse vectors. When training classifiers on large collections of documents, both the time and memory restrictions can be quite prohibitive. This justifies the application of feature selection methods to reduce the dimensionality of the document-representation vector. In this paper, three feature selection methods are evaluated: Random Selection, Information Gain (IG) and Support Vector Machine feature selection (called SVM_FS). We show that the best results were obtained with SVM_FS method for a relatively small dimension of the feature vector. Also we present a novel method to better correlate SVM kernel-s parameters (Polynomial or Gaussian kernel).

Keywords: Feature Selection, Learning with Kernels, SupportVector Machine, and Classification.

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Authors: Diako Azizi, Ahmad Gholami, Vahid Abbasi

Abstract:

Optimal selection of electrical insulations in electrical machinery insures reliability during operation. From the insulation studies of view for electrical machines, stator is the most important part. This fact reveals the requirement for inspection of the electrical machine insulation along with the electro-thermal stresses. In the first step of the study, a part of the whole structure of machine in which covers the general characteristics of the machine is chosen, then based on the electromagnetic analysis (finite element method), the machine operation is simulated. In the simulation results, the temperature distribution of the total structure is presented simultaneously by using electro-thermal analysis. The results of electro-thermal analysis can be used for designing an optimal cooling system. In order to design, review and comparing the cooling systems, four wiring structures in the slots of Stator are presented. The structures are compared to each other in terms of electrical, thermal distribution and remaining life of insulation by using Finite Element analysis. According to the steps of the study, an optimization algorithm has been presented for selection of appropriate structure.

Keywords: Electrical field, field distribution, insulation, winding, finite element method, electro thermal

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Authors: A. Jamekhorshid, G. Karimi, I. Noshadi, A. Jahangiri

Abstract:

Non-uniform current distribution in polymer electrolyte membrane fuel cells results in local over-heating, accelerated ageing, and lower power output than expected. This issue is very critical when fuel cell experiences water flooding. In this work, the performance of a PEM fuel cell is investigated under cathode flooding conditions. Two-dimensional partially flooded GDL models based on the conservation laws and electrochemical relations are proposed to study local current density distributions along flow fields over a wide range of cell operating conditions. The model results show a direct association between cathode inlet humidity increases and that of average current density but the system becomes more sensitive to flooding. The anode inlet relative humidity shows a similar effect. Operating the cell at higher temperatures would lead to higher average current densities and the chance of system being flooded is reduced. In addition, higher cathode stoichiometries prevent system flooding but the average current density remains almost constant. The higher anode stoichiometry leads to higher average current density and higher sensitivity to cathode flooding.

Keywords: Current distribution, Flooding, Hydrogen energysystem, PEM fuel cell.

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Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

Abstract:

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: John N. Ellinas

Abstract:

In this paper, a robust watermarking algorithm using the wavelet transform and edge detection is presented. The efficiency of an image watermarking technique depends on the preservation of visually significant information. This is attained by embedding the watermark transparently with the maximum possible strength. The watermark embedding process is carried over the subband coefficients that lie on edges, where distortions are less noticeable, with a subband level dependent strength. Also, the watermark is embedded to selected coefficients around edges, using a different scale factor for watermark strength, that are captured by a morphological dilation operation. The experimental evaluation of the proposed method shows very good results in terms of robustness and transparency to various attacks such as median filtering, Gaussian noise, JPEG compression and geometrical transformations.

Keywords: Watermarking, wavelet transform, edge detection.

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Authors: Aylin Alin

Abstract:

In this paper, penalized power-divergence test statistics have been defined and their exact size properties to test a nested sequence of log-linear models have been compared with ordinary power-divergence test statistics for various penalization, λ and main effect values. Since the ordinary and penalized power-divergence test statistics have the same asymptotic distribution, comparisons have been only made for small and moderate samples. Three-way contingency tables distributed according to a multinomial distribution have been considered. Simulation results reveal that penalized power-divergence test statistics perform much better than their ordinary counterparts.

Keywords: Contingency table, Log-linear models, Penalization, Power-divergence measure, Penalized power-divergence measure.

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Authors: C. Iraklis, G. Evmiridis, A. Iraklis

Abstract:

Renewable energy sources and distributed power generation units already have an important role in electrical power generation. A mixture of different technologies penetrating the electrical grid, adds complexity in the management of distribution networks. High penetration of distributed power generation units creates node over-voltages, huge power losses, unreliable power management, reverse power flow and congestion. This paper presents an optimization algorithm capable of reducing congestion and power losses, both described as a function of weighted sum. Two factors that describe congestion are being proposed. An upgraded selective particle swarm optimization algorithm (SPSO) is used as a solution tool focusing on the technique of network reconfiguration. The upgraded SPSO algorithm is achieved with the addition of a heuristic algorithm specializing in reduction of power losses, with several scenarios being tested. Results show significant improvement in minimization of losses and congestion while achieving very small calculation times.

Keywords: Congestion, distribution networks, loss reduction, particle swarm optimization, smart grid.

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Authors: N. Norazlimi, R. Ramli

Abstract:

A study was conducted to determine the diversity and abundance of shorebird species habituating the mudflat area of Jeram Beach and Remis Beach, Selangor, Peninsular Malaysia. Direct observation technique (using binoculars and video camera) was applied to record the presence of bird species in the sampling sites from August 2013 until July 2014. A total of 32 species of shorebird were recorded during both migratory and non-migratory seasons. Of these, eleven species (48%) are migrants, six species (26%) have both migrant and resident populations, four species (17%) are vagrants and two species (9%) are residents. The compositions of the birds differed significantly in all months (χ2 = 84.35, p < 0.001). There is a significant difference in avian abundance between migratory and non-migratory seasons (Mann-Whitney, t = 2.39, p = 0.036). The avian abundance were differed significantly in Jeram and Remis Beaches during migratory periods (t = 4.39, p = 0.001) but not during non-migratory periods (t = 0.78, p = 0.456). Shorebird diversity was also affected by tidal cycle. There is a significance difference between high tide and low tide (Mann-Whitney, t = 78.0, p < 0.005). Frequency of disturbance also affected the shorebird distribution (Mann-Whitney, t = 57.0, p = 0.0134). Therefore, this study concluded that tides and disturbances are two factors that affecting temporal distribution of shorebird in mudflats area.

Keywords: Biodiversity, distribution, migratory birds, direct observation.

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Authors: Chang He, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

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In this study, the aim is to infer the slip limit (static friction limit) of contact interfaces in bolt friction joints by analyzing other bolt friction joints with the same contact surface but in a different shape. By using the Weibull distribution to deal with microelements on the contact surface statistically, the slip limit of a certain type of bolt joint was predicted from other types of bolt joint with the same contact surface. As a result, this research succeeded in predicting the slip limit of bolt joins with different numbers of contact surfaces and with different numbers of bolt rows.

Keywords: Bolt joints, slip coefficient, finite element method, Weibull distribution.

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Authors: Lokesh Varshney, R. K. Saket

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This paper presents reliability indices evaluation of the rotor core magnetization of the induction motor operated as a self excited induction generator by using probability distribution approach and Monte Carlo simulation. Parallel capacitors with calculated minimum capacitive value across the terminals of the induction motor operated as a SEIG with unregulated shaft speed have been connected during the experimental study. A three phase, 4 poles, 50Hz, 5.5 hp, 12.3A, 230V induction motor coupled with DC Shunt Motor was tested in the electrical machine laboratory with variable reactive loads. Based on this experimental study, it is possible to choose a reliable induction machines operated as a SEIG for unregulated renewable energy application in remote area or where grid is not available. Failure density function, cumulative failure distribution function, survivor function, hazard model, probability of success and probability of failure for reliability evaluation of the three phase induction motor operating as a SEIG have been presented graphically in this paper.

Keywords: Residual magnetism, magnetization curve, induction motor, self excited induction generator, probability distribution, Monte Carlo simulation.

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Authors: P. Vaculík, P. Kaňovský

Abstract:

The following article presents Technology Centre of Ostrava (TCO) in the Czech Republic describing the structure and main research areas realized by the project ENET - Energy Units for Utilization of non Traditional Energy Sources. More details are presented from the research program dealing with transformation, accumulation and distribution of electric energy. Technology Centre has its own energy mix consisting of alternative sources of fuel sources that use of process gases from the storage part and also the energy from distribution network. The article will be focus on the properties and application possibilities SiC semiconductor devices for power semiconductor converter for photovoltaic systems.

Keywords: SiC, Si, Technology Centre of Ostrava, Photovoltaic Systems, DC/DC Converter, Simulation.

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Authors: Omid Gervei, Ahmad Ayatollahi, Navid Gervei

Abstract:

In this paper we present an approach for 3D face recognition based on extracting principal components of range images by utilizing modified PCA methods namely 2DPCA and bidirectional 2DPCA also known as (2D) 2 PCA.A preprocessing stage was implemented on the images to smooth them using median and Gaussian filtering. In the normalization stage we locate the nose tip to lay it at the center of images then crop each image to a standard size of 100*100. In the face recognition stage we extract the principal component of each image using both 2DPCA and (2D) 2 PCA. Finally, we use Euclidean distance to measure the minimum distance between a given test image to the training images in the database. We also compare the result of using both methods. The best result achieved by experiments on a public face database shows that 83.3 percent is the rate of face recognition for a random facial expression.

Keywords: 3D face recognition, 2DPCA, (2D) 2 PCA, Rangeimage

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Authors: Dongwon Lee, Eon Kyeong Joo

Abstract:

In this paper, the performance of three types of serial concatenated convolutional codes (SCCC) is compared and analyzed in additive white Gaussian noise (AWGN) channel. In Type I, only the parity bits of outer encoder are passed to inner encoder. In Type II and Type III, both the information bits and the parity bits of outer encoder are transferred to inner encoder. As results of simulation, Type I shows the best bit error rate (BER) performance at low signal-to-noise ratio (SNR). On the other hand, Type III shows the best BER performance at high SNR in AWGN channel. The simulation results are analyzed using the distance spectrum.

Keywords: Distance spectrum, MAP algorithm, SCCC.

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Authors: Akhil Kumar Arya, Jagdeep Singh Lather, Lillie Dewan

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In this paper is to evaluate audio and speech quality with the help of Digital Audio Watermarking Technique under the different types of attacks (signal impairments) like Gaussian Noise, Compression Error and Jittering Effect. Further attacks are considered as Hostile Environment. Audio and Speech Quality Evaluation is an important research topic. The traditional way for speech quality evaluation is using subjective tests. They are reliable, but very expensive, time consuming, and cannot be used in certain applications such as online monitoring. Objective models, based on human perception, were developed to predict the results of subjective tests. The existing objective methods require either the original speech or complicated computation model, which makes some applications of quality evaluation impossible.

Keywords: Digital Watermarking, DCT, Speech Quality, Attacks.

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Authors: Anatoli Torokhti, Stanley Miklavcic

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Suppose KY and KX are large sets of observed and reference signals, respectively, each containing N signals. Is it possible to construct a filter F : KY → KX that requires a priori information only on few signals, p  N, from KX but performs better than the known filters based on a priori information on every reference signal from KX? It is shown that the positive answer is achievable under quite unrestrictive assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.

Keywords: Wiener filter, filtering of stochastic signals.

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Authors: Valentina Koliskina, Inta Volodko

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Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotive force per unit length of the double conductor line is calculated in the form of an improper integral.

Keywords: Transient eddy currents, Laplace transform, double conductor line.

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Authors: R. Kamalakannan, N. Ravi Kumar

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Feeder protection is important in transmission and distribution side because if any fault occurs in any feeder or transformer, man power is needed to identify the problem and it will take more time. In the existing system, directional overcurrent elements with load further secured by a load encroachment function can be used to provide necessary security and sensitivity for faults on remote points in a circuit. It is validated only in renewable plant collector circuit protection applications over a wide range of operating conditions. In this method, the directional overcurrent feeder protection is developed by using monitoring of feeder section through internet. In this web based monitoring, the fault and power theft are identified by using Toro dial sensor and its information is received by SCADA (Supervisory Control and Data Acquisition) and controlled by ARM microcontroller. This web based monitoring is also used to monitor the feeder management, directional current detection, demand side management, overload fault. This monitoring system is capable of monitoring the distribution feeder over a large area depending upon the cost. It is also used to reduce the power theft, time and man power. The simulation is done by MATLAB software.

Keywords: Current sensor, distribution feeder protection, directional overcurrent, power theft, protective relay.

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Authors: Yuyun Wabula, B. J. Dewancker

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In the past decade, the social networking app has been growing very rapidly. Geolocation data is one of the important features of social media that can attach the user's location coordinate in the real world. This paper proposes the use of geolocation data from the Twitter social media application to gain knowledge about urban dynamics, especially on human mobility behavior. This paper aims to explore the relation between geolocation Twitter with the existence of people in the urban area. Firstly, the study will analyze the spread of people in the particular area, within the city using Twitter social media data. Secondly, we then match and categorize the existing place based on the same individuals visiting. Then, we combine the Twitter data from the tracking result and the questionnaire data to catch the Twitter user profile. To do that, we used the distribution frequency analysis to learn the visitors’ percentage. To validate the hypothesis, we compare it with the local population statistic data and land use mapping released by the city planning department of Makassar local government. The results show that there is the correlation between Twitter geolocation and questionnaire data. Thus, integration the Twitter data and survey data can reveal the profile of the social media users.

Keywords: Geolocation, Twitter, distribution analysis, human mobility.

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Authors: Mohamed Idris S. Abozaed, Suliman Mohamed Elrajoubi

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Researches and concerns in power quality gained significant momentum in the field of power electronics systems over the last two decades globally. This sudden increase in the number of concerns over power quality problems is a result of the huge increase in the use of non-linear loads. In this paper, power quality evaluation of some distribution networks at Misurata - Libya has been done using a power quality and energy analyzer (Fluke 437 Series II). The results of this evaluation are used to minimize the problems of power quality. The analysis shows the main power quality problems that exist and the level of awareness of power quality issues with the aim of generating a start point which can be used as guidelines for researchers and end users in the field of power systems.

Keywords: Power Quality Disturbances, Power Quality Evaluation, Statistical Analysis.

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Authors: Juan Blas, Alfonso Bahillo, Santiago Mazuelas, David Bullido, Patricia Fernandez, Ruben M. Lorenzo, Evaristo J. Abril

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This paper presents a low cost automatic system for sampling the electric field in a limited area. The scanning area is a flat surface parallel to the ground at a selected height. We discuss in detail the hardware, software and all the arrangements involved in the system operation. In order to show the system performance we include a campaign of narrow band measurements with 6017 sample points in the surroundings of a cellular base station. A commercial isotropic antenna with three orthogonal axes was used as sampling device. The results are analyzed in terms of its space average, standard deviation and statistical distribution.

Keywords: measurement device, propagation, spatial sampling.

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Authors: Funda Erdem Şahnali, Ş. Özgür Atayılmaz, Tolga N. Aynur

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Almost all of the domestic refrigerators operate on the principle of the vapor compression refrigeration cycle and removal of heat from the refrigerator cabinets is done via one of the two methods: natural convection or forced convection. In this study, airflow and temperature distributions inside a 375L no-frost type larder cabinet, in which cooling is provided by forced convection, are evaluated both experimentally and numerically. Airflow rate, compressor capacity and temperature distribution in the cooling chamber are known to be some of the most important factors that affect the cooling performance and energy consumption of a refrigerator. The objective of this study is to evaluate the original temperature distribution in the larder cabinet, and investigate for better temperature distribution solutions throughout the refrigerator domain via system optimizations that could provide uniform temperature distribution. The flow visualization and airflow velocity measurements inside the original refrigerator are performed via Stereoscopic Particle Image Velocimetry (SPIV). In addition, airflow and temperature distributions are investigated numerically with Ansys Fluent. In order to study the heat transfer inside the aforementioned refrigerator, forced convection theories covering the following cases are applied: closed rectangular cavity representing heat transfer inside the refrigerating compartment. The cavity volume has been represented with finite volume elements and is solved computationally with appropriate momentum and energy equations (Navier-Stokes equations). The 3D model is analyzed as transient, with k-ε turbulence model and SIMPLE pressure-velocity coupling for turbulent flow situation. The results obtained with the 3D numerical simulations are in quite good agreement with the experimental airflow measurements using the SPIV technique. After Computational Fluid Dynamics (CFD) analysis of the baseline case, the effects of three parameters: compressor capacity, fan rotational speed and type of shelf (glass or wire) are studied on the energy consumption; pull down time, temperature distributions in the cabinet. For each case, energy consumption based on experimental results is calculated. After the analysis, the main effective parameters for temperature distribution inside a cabin and energy consumption based on CFD simulation are determined and simulation results are supplied for Design of Experiments (DOE) as input data for optimization. The best configuration with minimum energy consumption that provides minimum temperature difference between the shelves inside the cabinet is determined.

Keywords: Air distribution, CFD, DOE, energy consumption, larder cabinet, refrigeration, uniform temperature.

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Authors: H. Kaatuzian, M. Sedghi, S. Khatami

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In this paper, by exploiting a single semiconductor optical amplifier-Mach Zehnder Interferometer (SOA-MZI), an integratable all-optical flip-flop (AOFF) is proposed. It is composed of a SOA-MZI with a bidirectional coupler at the output. Output signals of both bar and crossbar of the SOA-MZI is fed back to SOAs located in the arms of the Mach-Zehnder Interferometer (MZI). The injected photon-rates to the SOAs are modulated by feedback signals in order to form optical flip-flop. According to numerical analysis, Gaussian optical pulses with the energy of 15.2 fJ and 20 ps duration with the full width at half-maximum criterion, can switch the states of the SR-AOFF. Also simulation results show that the SR-AOFF has the contrast ratio of 8.5 dB between two states with the transition time of nearly 20 ps.

Keywords: All Optical, Flip-Flop, Mach-Zehnder Interferometer (MZI), Semiconductor Optical Amplifier (SOA).

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Authors: N. Rezaee, M Nayeripour, A. Roosta, T. Niknam

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With the prevalence of computer and development of information technology, Geographic Information Systems (GIS) have long used for a variety of applications in electrical engineering. GIS are designed to support the analysis, management, manipulation and mapping of spatial data. This paper presents several usages of GIS in power utilities such as automated route selection for the construction of new power lines which uses a dynamic programming model for route optimization, load forecasting and optimizing planning of substation-s location and capacity with comprehensive algorithm which involves an accurate small-area electric load forecasting procedure and simulates the different cost functions of substations.

Keywords: Geographic information systems (GIS), optimallocation and capacity, power distribution planning, route selection, spatial load forecasting.

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Authors: Abd Elrahman Elgamala, N. Darwish, I. Bondouk, Sh. Hamada

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Available experimental angular distributions for ⁶Li elastically scattered from ¹⁶O nucleus in the energy range 13.0–50.0 MeV are investigated and reanalyzed using optical model of the conventional phenomenological potential and also using double folding optical model of different interaction models: DDM3Y1, CDM3Y1, CDM3Y2, and CDM3Y3. All the involved models of interaction are of M3Y Paris except DDM3Y1 which is of M3Y Reid and the main difference between them lies in the different values for the parameters of the incorporated density distribution function F(ρ). We have extracted the renormalization factor N_R for ⁶Li+¹⁶O nuclear system in the energy range 13.0–50.0 MeV using the aforementioned interaction models.

Keywords: Elastic scattering, optical model, folding potential, density distribution.

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Authors: S. Anna Durai, E. Anna Saro

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Image Compression using Artificial Neural Networks is a topic where research is being carried out in various directions towards achieving a generalized and economical network. Feedforward Networks using Back propagation Algorithm adopting the method of steepest descent for error minimization is popular and widely adopted and is directly applied to image compression. Various research works are directed towards achieving quick convergence of the network without loss of quality of the restored image. In general the images used for compression are of different types like dark image, high intensity image etc. When these images are compressed using Back-propagation Network, it takes longer time to converge. The reason for this is, the given image may contain a number of distinct gray levels with narrow difference with their neighborhood pixels. If the gray levels of the pixels in an image and their neighbors are mapped in such a way that the difference in the gray levels of the neighbors with the pixel is minimum, then compression ratio as well as the convergence of the network can be improved. To achieve this, a Cumulative distribution function is estimated for the image and it is used to map the image pixels. When the mapped image pixels are used, the Back-propagation Neural Network yields high compression ratio as well as it converges quickly.

Keywords: Back-propagation Neural Network, Cumulative Distribution Function, Correlation, Convergence.

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Authors: Nam Lethanh, Bryan T. Adey

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In this paper, the potential use of an exponential hidden Markov model to model a hidden pavement deterioration process, i.e. one that is not directly measurable, is investigated. It is assumed that the evolution of the physical condition, which is the hidden process, and the evolution of the values of pavement distress indicators, can be adequately described using discrete condition states and modeled as a Markov processes. It is also assumed that condition data can be collected by visual inspections over time and represented continuously using an exponential distribution. The advantage of using such a model in decision making process is illustrated through an empirical study using real world data.

Keywords: Deterioration modeling, Exponential distribution, Hidden Markov model, Pavement management

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Authors: Gaurav Shinde, Sai Charan Gongiguntla, Prajwal Shirur, Ahmed Hambaba

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Health issues are significantly increasing, putting a substantial strain on healthcare services. This has accelerated the integration of machine learning in healthcare, particularly following the COVID-19 pandemic. The utilization of machine learning in healthcare has grown significantly. We introduce DeClEx, a pipeline which ensures that data mirrors real-world settings by incorporating gaussian noise and blur and employing autoencoders to learn intermediate feature representations. Subsequently, our convolutional neural network, paired with spatial attention, provides comparable accuracy to state-of-the-art pre-trained models while achieving a threefold improvement in training speed. Furthermore, we provide interpretable results using explainable AI techniques. We integrate denoising and deblurring, classification and explainability in a single pipeline called DeClEx.

Keywords: Machine learning, healthcare, classification, explainability.

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Authors: Samir Brahim Belhaouari

Abstract:

By taking advantage of both k-NN which is highly accurate and K-means cluster which is able to reduce the time of classification, we can introduce Cluster-k-Nearest Neighbor as "variable k"-NN dealing with the centroid or mean point of all subclasses generated by clustering algorithm. In general the algorithm of K-means cluster is not stable, in term of accuracy, for that reason we develop another algorithm for clustering our space which gives a higher accuracy than K-means cluster, less subclass number, stability and bounded time of classification with respect to the variable data size. We find between 96% and 99.7 % of accuracy in the lassification of 6 different types of Time series by using K-means cluster algorithm and we find 99.7% by using the new clustering algorithm.

Keywords: Pattern recognition, Time series, k-Nearest Neighbor, k-means cluster, Gaussian Mixture Model, Classification

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Authors: Thomas Kampke

Abstract:

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.

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