Search results for: singular value thresholding

Authors: Sakshi Bhalla

Abstract:

On the one hand, given their seemingly simplistic, near universal usage and understanding, emoji are discarded as a potential step back in the evolution of communication. On the other, their effectiveness, pervasiveness, and adaptability across and within contexts are undeniable. In this study, the responses of 40 people (categorized by age) were recorded based on a uniform two-part questionnaire where they were required to a) identify the meaning of 15 emoji when placed in isolation, and b) interpret the meaning of the same 15 emoji when placed in a context-defining posting on Twitter. Their responses were studied on the basis of deviation from their responses that identified the emoji in isolation, as well as the originally intended meaning ascribed to the emoji. Based on an analysis of these results, it was discovered that each of the five age categories uses, understands and perceives emoji differently, which could be attributed to the degree of exposure they have undergone. For example, in the case of the youngest category (aged < 20), it was observed that they were the least accurate at correctly identifying emoji in isolation (~55%). Further, their proclivity to change their response with respect to the context was also the least (~31%). However, an analysis of each of their individual responses showed that these first-borns of social media seem to have reached a point where emojis no longer inspire their most literal meanings to them. The meaning and implication of these emoji have evolved to imply their context-derived meanings, even when placed in isolation. These trends carry forward meaningfully for the other four groups as well. In the case of the oldest category (aged > 35), however, the trends indicated inaccuracy and therefore, a higher incidence of a proclivity to change their responses. When studied in a continuum, the responses indicate that slowly and steadily, emoji are evolving from pictograms to ideograms. That is to suggest that they do not just indicate a one-to-one relation between a singular form and singular meaning. In fact, they communicate increasingly complicated ideas. This is much like the evolution of ancient hieroglyphics on papyrus reed or cuneiform on Sumerian clay tablets, which evolved from simple pictograms to progressively more complex ideograms. This evolution within communication is parallel to and contingent on the simultaneous evolution of communication. What’s astounding is the capacity of humans to leverage different platforms to facilitate such changes. Twiterese, as it is now called, is one of the instances where language is adapting to the demands of the digital world. That it does not have a spoken component, an ostensible grammar, and lacks standardization of use and meaning, as some might suggest, may seem like impediments in qualifying it as the 'language' of the digital world. However, that kind of a declarative remains a function of time, and time alone.

Keywords: communication, emoji, language, Twitter

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Authors: E. V. Krishnan

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In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

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Authors: B. Kishore Kumar, Rakesh Pogula, T. Kishore Kumar

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The steepness of an audio signal which is produced by the musical instruments, specifically percussive instruments is the perception of how high tone or low tone which can be considered as a frequency closely related to the fundamental frequency. This paper presents a novel method for silence removal and segmentation of music signals produced by the percussive instruments and the performance of proposed method is studied with the help of MATLAB simulations. This method is based on two simple features, namely the signal energy and the spectral centroid. As long as the feature sequences are extracted, a simple thresholding criterion is applied in order to remove the silence areas in the sound signal. The simulations were carried on various instruments like drum, flute and guitar and results of the proposed method were analyzed.

Keywords: percussive instruments, spectral energy, spectral centroid, silence removal

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Authors: Lina Pan

Abstract:

In non-Gaussian clutter of a spherically invariant random vector, in the cases that a certain estimated covariance matrix could become singular, the adaptive target detection of high-range-resolution radar is addressed. Firstly, the restricted maximum likelihood (RML) estimates of unknown covariance matrix and scatterer amplitudes are derived for non-Gaussian clutter. And then the RML estimate of texture is obtained. Finally, a novel detector is devised. It is showed that, without secondary data, the proposed detector outperforms the existing Kelly binary integrator.

Keywords: non-Gaussian clutter, covariance matrix estimation, target detection, maximum likelihood

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Authors: Abdolvahab Ehsani Rad, Mohd Shafry Mohd Rahim, Alireza Norouzi

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Medical image analysis is one of the great effects of computer image processing. There are several processes to analysis the medical images which the segmentation process is one of the challenging and most important step. In this paper the segmentation method proposed in order to segment the dental radiograph images. Thresholding method has been applied to simplify the images and to morphologically open binary image technique performed to eliminate the unnecessary regions on images. Furthermore, horizontal and vertical integral projection techniques used to extract the each individual tooth from radiograph images. Segmentation process has been done by applying the level set method on each extracted images. Nevertheless, the experiments results by 90% accuracy demonstrate that proposed method achieves high accuracy and promising result.

Keywords: integral production, level set method, morphological operation, segmentation

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Authors: Abder-Rahman Ali, Adélaïde Albouy-Kissi, Manuel Grand-Brochier, Viviane Ladan-Marcus, Christine Hoeffl, Claude Marcus, Antoine Vacavant, Jean-Yves Boire

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In this paper, we present a new segmentation approach for focal liver lesions in contrast enhanced ultrasound imaging. This approach, based on a two-cluster Fuzzy C-Means methodology, considers type-II fuzzy sets to handle uncertainty due to the image modality (presence of speckle noise, low contrast, etc.), and to calculate the optimum inter-cluster threshold. Fine boundaries are detected by a local recursive merging of ambiguous pixels. The method has been tested on a representative database. Compared to both Otsu and type-I Fuzzy C-Means techniques, the proposed method significantly reduces the segmentation errors.

Keywords: defuzzification, fuzzy clustering, image segmentation, type-II fuzzy sets

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Y. Kourd, D. Lefebvre

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The monitoring of industrial processes is required to ensure operating conditions of industrial systems through automatic detection and isolation of faults. This paper proposes a method of fault diagnosis based on a neuro-fuzzy hybrid structure. This hybrid structure combines the selection of threshold and decision tree. The validation of this method is obtained with the DAMADICS benchmark. In the first phase of the method, a model will be constructed that represents the normal state of the system to fault detection. Signatures of the faults are obtained with residuals analysis and selection of appropriate thresholds. These signatures provide groups of non-separable faults. In the second phase, we build faulty models to see the flaws in the system that cannot be isolated in the first phase. In the latest phase we construct the tree that isolates these faults.

Keywords: decision tree, residuals analysis, ANFIS, fault diagnosis

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Authors: Manana Chumburidze

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We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Z. Aziz, S. Terkhi, Y. Sefir, R. Djelti, S. Bentata

Abstract:

The effect of a uniform electric field across multibarrier systems (InAs/InxGa1-xAs) is exhaustively explored by a computational model using exact airy function formalism and the transfer-matrix technique. In the case of biased DFHBSL structure a strong reduction in transmission properties was observed and the width of the miniband structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the miniband structure, which becomes increasingly important (Wannier-Stark Effect).

Keywords: dimer fibonacci height barrier superlattices, singular extended state, exact airy function, transfer matrix formalism

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Authors: Ayami Umemura

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Without exception, all the bodies dissected in the gross anatomical practices are bodies that have lived irreplaceable lives, laughing and talking with family and friends. While medical education aims to cultivate medical knowledge that is universally applicable to all human bodies, it relies on a unique, irreplaceable, and singular entity. In this presentation, we will explore the ``irreplaceable relationship'' that is cultivated between medical students and anonymous cadavers during gross anatomical practices, drawing on Emmanuel Levinas's ``ethics of the face'' and Martin Buber's discussion of “I-Thou.'' Through this, we aim to present ``a different ethic'' that emerges only in the context of face-to-face relationships, which differs from the generalized, institutionalized, mass-produced ethics like seen in so-called ``ethics codes.'' Since the 1990s, there has been a movement around the world to use gross anatomical practices as an "educational tool" for medical professionalism and medical ethics, and some educational institutions have started disclosing the actual names, occupations, and places of birth of corpses to medical students. These efforts have also been criticized because they lack medical calmness. In any case, the issue here is that this information is all about the past that medical students never know directly. The critical fact that medical students are building relationships from scratch and spending precious time together without any information about the corpses before death is overlooked. Amid gross anatomical practices, a medical student is exposed to anonymous cadavers with faces and touching and feeling them. In this presentation, we will examine a collection of essays written by medical students on gross anatomical practices collected by the Japanese Association for Volunteer Body Donation from medical students across the country since 1978. There, we see the students calling out to the corpse, being called out to, being encouraged, superimposing the carcasses on their own immediate family, regretting parting, and shedding tears. Then, medical students can be seen addressing the dead body in the second person singular, “you.” These behaviors reveal an irreplaceable relationship between the anonymous cadavers and the medical students. The moment they become involved in an irreplaceable relationship between “I and you,” an accidental and anonymous encounter becomes inevitable. When medical students notice being the inevitable takers of voluntary and addressless gifts, they pledge to become “Good Doctors” owing the anonymous persons. This presentation aims to present “a different ethic” based on uniqueness and irreplaceability that comes from the faces of the others embedded in each context, which is different from “routine” and “institutionalized” ethics. That can only be realized ``because of anonymity''.

Keywords: anonymity, irreplaceability, uniqueness, singularlity, emanuel levinas, martin buber, alain badiou, medical education

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Authors: Daniel A. Walzer

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As the options for course delivery and development expand, plenty of misconceptions still exist concerning e-learning and online course delivery. Classroom instructors often discuss pedagogy, methodologies, and best practices regarding teaching from a singular, traditional in-class perspective. As more professors integrate online, blended, and hybrid courses into their dossier, a clearly defined rubric for gauging online course delivery is essential. The transition from a traditional learning structure towards an updated distance-based format requires careful planning, evaluation, and revision. This paper examines how new media stimulates reflective practice and guided inquiry to improve pedagogy, engage interdisciplinary collaboration, and supply rich qualitative data for future research projects in media arts disciplines.

Keywords: action research, inquiry, new media, reflection

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Authors: A. Biran, P. Sobhe Bidari, A. Almazroe, V. Lakshminarayanan, K. Raahemifar

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Diabetic Retinopathy (DR) is a severe retinal disease which is caused by diabetes mellitus. It leads to blindness when it progress to proliferative level. Early indications of DR are the appearance of microaneurysms, hemorrhages and hard exudates. In this paper, an automatic algorithm for detection of DR has been proposed. The algorithm is based on combination of several image processing techniques including Circular Hough Transform (CHT), Contrast Limited Adaptive Histogram Equalization (CLAHE), Gabor filter and thresholding. Also, Support Vector Machine (SVM) Classifier is used to classify retinal images to normal or abnormal cases including non-proliferative or proliferative DR. The proposed method has been tested on images selected from Structured Analysis of the Retinal (STARE) database using MATLAB code. The method is perfectly able to detect DR. The sensitivity specificity and accuracy of this approach are 90%, 87.5%, and 91.4% respectively.

Keywords: diabetic retinopathy, fundus images, STARE, Gabor filter, support vector machine

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Authors: Samba Raju, Chiluveru, Manoj Tripathy

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Intelligibility is an essential characteristic of a speech signal, which is used to help in the understanding of information in speech signal. Background noise in the environment can deteriorate the intelligibility of a recorded speech. In this paper, we presented a simple variance subtracted - variable level discrete wavelet transform, which improve the intelligibility of speech. The proposed algorithm does not require an explicit estimation of noise, i.e., prior knowledge of the noise; hence, it is easy to implement, and it reduces the computational burden. The proposed algorithm decides a separate decomposition level for each frame based on signal dominant and dominant noise criteria. The performance of the proposed algorithm is evaluated with speech intelligibility measure (STOI), and results obtained are compared with Universal Discrete Wavelet Transform (DWT) thresholding and Minimum Mean Square Error (MMSE) methods. The experimental results revealed that the proposed scheme outperformed competing methods

Keywords: discrete wavelet transform, speech intelligibility, STOI, standard deviation

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Abraham Terán Salcedo, Didier Samayoa Ochoa

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This work presents a numerical implementation of a method for estimating the box-counting dimension of self-avoiding curves on a planar space, fractal objects captured on digital images; this method is named fractioning estimator. Classical methods of digital image processing, such as noise filtering, contrast manipulation, and thresholding, among others, are used in order to obtain binary images that are suitable for performing the necessary computations of the fractioning estimator. A user interface is developed for performing the image processing operations and testing the fractioning estimator on different captured images of real-life fractal objects. To analyze the results, the estimations obtained through the fractioning estimator are compared to the results obtained through other methods that are already implemented on different available software for computing and estimating the box-counting dimension.

Keywords: box-counting, digital image processing, fractal dimension, numerical method

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Authors: Z. Aziz, S. Terkhi, Y. Sefir, R. Djelti, S. Bentata

Abstract:

The effect of a uniform electric field across multi-barrier systems (InAs/InxGa1-xAs) is exhaustively explored by a computational model using exact Airy function formalism and the transfer-matrix technique. In the case of biased DFHBSL structure a strong reduction in transmission properties was observed and the width of the mini-band structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the mini-band structure, which becomes increasingly important (Wannier-Stark Effect).

Keywords: dimer fibonacci height barrier superlattices, singular extended state, exact Airy function and transfer matrix formalism, bioinformatics

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Authors: Aziz Zoubir, Sefir Yamina, Djelti Redouan, Bentata Samir

Abstract:

The effect of a uniform electric field across multibarrier systems (GaAs/AlxGa1-xAs) is exhaustively explored by a computational model using exact Airy function formalism and the transfer-matrix technique. In the case of biased Dimer Fibonacci Height Barrier superlattices (DFHBSL) structure a strong reduction in transmission properties was observed and the width of the miniband structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the miniband structure, which becomes increasingly important (Wannier-Stark effect).

Keywords: Dimer Fibonacci Height Barrier superlattices, singular extended states, exact Airy function, transfer matrix formalism

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Authors: Vahid Anari, Mina Bakhshi

Abstract:

Visual search and identification of immunohistochemically stained tissue of meningioma was performed manually in pathologic laboratories to detect and diagnose the cancers type of meningioma. This task is very tedious and time-consuming. Moreover, because of cell's complex nature, it still remains a challenging task to segment cells from its background and analyze them automatically. In this paper, we develop and test a computerized scheme that can automatically identify cells in microscopic images of meningioma and classify them into positive (proliferative) and negative (normal) cells. Dataset including 150 images are used to test the scheme. The scheme uses Fuzzy C-means algorithm as a color clustering method based on perceptually uniform hue, saturation, value (HSV) color space. Since the cells are distinguishable by the human eye, the accuracy and stability of the algorithm are quantitatively compared through application to a wide variety of real images.

Keywords: positive cell, color segmentation, HSV color space, immunohistochemistry, meningioma, thresholding, fuzzy c-means

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Authors: A. Biran, P. Sobhe Bidari, K. Raahemifar

Abstract:

Diabetic Retinopathy (DR) is an eye disease that leads to blindness. The earliest signs of DR are the appearance of red and yellow lesions on the retina called hemorrhages and exudates. Early diagnosis of DR prevents from blindness; hence, many automated algorithms have been proposed to extract hemorrhages and exudates. In this paper, an automated algorithm is presented to extract hemorrhages and exudates separately from retinal fundus images using different image processing techniques including Circular Hough Transform (CHT), Contrast Limited Adaptive Histogram Equalization (CLAHE), Gabor filter and thresholding. Since Optic Disc is the same color as the exudates, it is first localized and detected. The presented method has been tested on fundus images from Structured Analysis of the Retina (STARE) and Digital Retinal Images for Vessel Extraction (DRIVE) databases by using MATLAB codes. The results show that this method is perfectly capable of detecting hard exudates and the highly probable soft exudates. It is also capable of detecting the hemorrhages and distinguishing them from blood vessels.

Keywords: diabetic retinopathy, fundus, CHT, exudates, hemorrhages

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Authors: Ahmed Elrewainy

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Mixing in the hyperspectral imaging occurs due to the low spatial resolutions of the used cameras. The existing pure materials “endmembers” in the scene share the spectra pixels with different amounts called “abundances”. Unmixing of the data cube is an important task to know the present endmembers in the cube for the analysis of these images. Unsupervised unmixing is done with no information about the given data cube. Sparsity is one of the recent approaches used in the source recovery or unmixing techniques. The l₁-norm optimization problem “basis pursuit” could be used as a sparsity-based approach to solve this unmixing problem where the endmembers is assumed to be sparse in an appropriate domain known as dictionary. This optimization problem is solved using proximal method “iterative thresholding”. The l₁-norm basis pursuit optimization problem as a sparsity-based unmixing technique was used to unmix real and synthetic hyperspectral data cubes.

Keywords: basis pursuit, blind source separation, hyperspectral imaging, spectral unmixing, wavelets

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Authors: Saif Bareq, Vivek Mirgane

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The present paper seeks to explicate the pronunciation of the ‘-s’ and ‘-ed’ suffixes when applied in their relative places in word endings. It attempts to investigate the problems faced by Yemenis in the pronunciation of these suffixes in all occurrences and realizations. It discusses the realization of ‘s’ in the four areas of plural, 3rd person singular and genitive markers, and contraction of ‘has’ and ‘is’ as in he’s, it’s ..,etc. and shows how they are differently represented by three different sounds /s/, /z/ and /z/ based on the phonological structure of the words in which they occur. Similarly, it explains the realization of the ‘-ed’ suffix of the past and past participle marker and how it is realized differently by three sounds governed by the phonological structure of these words. Besides, it tries to shed some light on the English morphophonemic and phonological rules that govern the pronunciation of such troublesome endings. It is hypothesized that the absence of such phenomenon in the mother tongue pronunciation of these suffixes.

Keywords: Suffixes' Pronunciation, Phonological Structure, Phonological Rules, Morpho-Phonemics, Yemeni English

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Authors: H. Nouri, A. Tabbel, N. Douib, H. Aitsaid, Y. Zebboudj

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This study and the field test comparisons were carried out on the Algerian Derguna-Setif transmission systems. The transmission line of normal voltage 225 kV is 65 km long, transported and uses twin bundle conductors protected with two shield wires of transposed galvanized steel. An iterative finite-element method is used to solve Poisons equation. Two algorithms are proposed for satisfying the current continuity condition and updating the space-charge density. A new approach to the problem of corona discharge in transmission system has been described in this paper. The effect of varying the configurations and wires number is also investigated. The analysis of this steady is important in the design of HVDC transmission lines. The potential and electric field have been calculating in locations singular points of the system.

Keywords: corona discharge, finite element method, electric field, HVDC

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Authors: R.T.O. Lacerda, L. Ensslin., S.R. Ensslin, L. Knoff

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This research paper aims to discover research opportunities in business process management and performance measurement from a constructivist view. The nature of this research is exploratory and descriptive and the research method was performed in a qualitative way. The process narrowed down 2142 articles, gathered after a search in scientific databases, and identified 16 articles that were relevant to the research and highly cited. The analysis found that most of the articles uses realistic approach and there is a need to analyze the decision making process in a singular manner. The measurement criteria are identified from scientific literature searching, in most cases, using ordinal scale without any integration process to present the results to the decision maker. Regarding management aspects, most of the articles do not have a structured process to measure the current situation and generate improvements opportunities.

Keywords: performance measurement, BPM, decision, research opportunities

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Authors: Amit Kumar, Himanshu Singal, Arnav Bhavsar

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In this modern era of automation, most of the academic exams and competitive exams are Multiple Choice Questions (MCQ). The responses of these MCQ based exams are recorded in the Optical Mark Reader (OMR) sheet. Evaluation of the OMR sheet requires separate specialized machines for scanning and marking. The sheets used by these machines are special and costs more than a normal sheet. Available process is non-economical and dependent on paper thickness, scanning quality, paper orientation, special hardware and customized software. This study tries to tackle the problem of evaluating the OMR sheet without any special hardware and making the whole process economical. We propose an image processing based algorithm which can be used to read and evaluate the scanned OMR sheets with no special hardware required. It will eliminate the use of special OMR sheet. Responses recorded in normal sheet is enough for evaluation. The proposed system takes care of color, brightness, rotation, little imperfections in the OMR sheet images.

Keywords: OMR, image processing, hough circle trans-form, interpolation, detection, binary thresholding

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Authors: Angely Sim Jia Wun, Sasa Arsovski

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Numerous studies have been conducted on the segmentation of medical images. Segmenting the lungs is one of the common research topics in those studies. Our research stemmed from the lack of solutions for automatic bone, airway, and vessel segmentation, despite the existence of multiple lung segmentation techniques. Consequently, currently, available software tools used for medical image segmentation do not provide automatic lung, bone, airway, and vessel segmentation. This paper presents segmentation techniques along with an interactive software tool architecture for segmenting bone, lung, airway, and vessel tissues. Additionally, we propose a method for creating binary masks from automatically generated segments. The key contribution of our approach is the technique for automatic image thresholding using adjustable Hounsfield values and binary mask extraction. Generated binary masks can be successfully used as a training dataset for deep-learning solutions in medical image segmentation. In this paper, we also examine the current software tools used for medical image segmentation, discuss our approach, and identify its advantages.

Keywords: lung segmentation, binary masks, U-Net, medical software tools

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Authors: Saumya Srivastava, Rina Maiti

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In order to achieve a better performance of vehicle detection in a complex environment, we present an efficient approach for a multi-vehicle detection system using an adaptive sliding window technique. For a given frame, image segmentation is carried out to establish the region of interest. Gradient computation followed by thresholding, denoising, and morphological operations is performed to extract the binary search image. Near-region field and far-region field are defined to generate hypotheses using the adaptive sliding window technique on the resultant binary search image. For each vehicle candidate, features are extracted using a histogram of oriented gradients, and a pre-trained support vector machine is applied for hypothesis verification. Later, the Kalman filter is used for tracking the vanishing point. The experimental results show that the method is robust and effective on various roads and driving scenarios. The algorithm was tested on highways and urban roads in India.

Keywords: gradient, vehicle detection, histograms of oriented gradients, support vector machine

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Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Amir Hadi Ziaie, Mostafa Hashemi, Shahram Jalalzadeh

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It is now known that the end state of the collapse process of a dense star under its own gravity is the formation of a spacetime singularity. This is the spacetime event where the energy density and spacetime curvature diverge, and the classical general relativity breaks down. As we know, a realistic star is composed of fermions so that their spin effects could alter the final fate of the collapse scenario. The underlying theory within which the inclusion of spin effects can be worked out is the Einstein-Cartan theory. In this theory, the spacetime torsion which is defined as a geometrical quantity, is related to an intrinsic angular momentum of fermions (spin). In this work, we study the collapse process of a homogeneous spin fluid in such a framework and show that taking into account the spin effects of the collapsing cloud could prevent the formation of spacetime singularity.

Keywords: gravitational collapse, einstein-cartan theory, spacetime singularity, black hole physics

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