Search results for: Problem Based Learning

Authors: Santosh Kumar Singh, Krishna Chandra Roy, Vibhakar Pathak

Abstract:

Spectrum is a scarce commodity, and considering the spectrum scarcity faced by the wireless-based service providers led to high congestion levels. Technical inefficiencies from pooled, since all networks share a common pool of channels, exhausting the available channels will force networks to block the services. Researchers found that cognitive radio (CR) technology may resolve the spectrum scarcity. A CR is a self-configuring entity in a wireless networking that senses its environment, tracks changes, and frequently exchanges information with their networks. However, CRN facing challenges and condition become worst while tracks changes i.e. reallocation of another under-utilized channels while primary network user arrives. In this paper, channels or resource reallocation technique based on DNA-inspired computing algorithm for CRN has been proposed.

Keywords: Ad hoc networks, channels reallocation, cognitive radio, DNA local sequence alignment.

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Authors: Ellips Masehian, Davoud Sedighizadeh

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This paper reviews the major contributions to the Motion Planning (MP) field throughout a 35-year period, from classic approaches to heuristic algorithms. Due to the NP-Hardness of the MP problem, heuristic methods have outperformed the classic approaches and have gained wide popularity. After surveying around 1400 papers in the field, the amount of existing works for each method is identified and classified. Especially, the history and applications of numerous heuristic methods in MP is investigated. The paper concludes with comparative tables and graphs demonstrating the frequency of each MP method's application, and so can be used as a guideline for MP researchers.

Keywords: Robot motion planning, Heuristic algorithms.

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Authors: Rawan I. Zaghloul, Enas F. Al-Rawashdeh

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In this paper a simple watermarking method for color images is proposed. The proposed method is based on watermark embedding for the histograms of the HSV planes using visual cryptography watermarking. The method has been proved to be robust for various image processing operations such as filtering, compression, additive noise, and various geometrical attacks such as rotation, scaling, cropping, flipping, and shearing.

Keywords: Histogram, HSV image, Visual Cryptography, Watermark.

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Authors: S. Ali, R. Yunus, A. Arif, Y. Ayaz, M. Baber Sial, R. Asif, N. Naseer, M. Jawad Khan

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In this study, we have proposed a gesture to emotion recognition method using flex sensors mounted on metacarpophalangeal joints. The flex sensors are fixed in a wearable glove. The data from the glove are sent to PC using Wi-Fi. Four gestures: finger pointing, thumbs up, fist open and fist close are performed by five subjects. Each gesture is categorized into sad, happy, and excited class based on the velocity and acceleration of the hand gesture. Seventeen inspectors observed the emotions and hand gestures of the five subjects. The emotional state based on the investigators assessment and acquired movement speed data is compared. Overall, we achieved 77% accurate results. Therefore, the proposed design can be used for emotional state detection applications.

Keywords: Emotion identification, emotion models, gesture recognition, user perception.

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Authors: Minky Son, Chanin Park, Ayoung Baek, Shalini John, Keun Woo Lee

Abstract:

3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGR) catalyzes the conversion of HMG-CoA to mevalonate using NADPH and the enzyme is involved in rate-controlling step of mevalonate. Inhibition of HMGR is considered as effective way to lower cholesterol levels so it is drug target to treat hypercholesterolemia, major risk factor of cardiovascular disease. To discover novel HMGR inhibitor, we performed structure-based pharmacophore modeling combined with molecular dynamics (MD) simulation. Four HMGR inhibitors were used for MD simulation and representative structure of each simulation were selected by clustering analysis. Four structure-based pharmacophore models were generated using the representative structure. The generated models were validated used in virtual screening to find novel scaffolds for inhibiting HMGR. The screened compounds were filtered by applying drug-like properties and used in molecular docking. Finally, four hit compounds were obtained and these complexes were refined using energy minimization. These compounds might be potential leads to design novel HMGR inhibitor.

Keywords: Anti-hypercholesterolemia drug, HMGR inhibitor, Molecular dynamics simulation, Structure-based pharmacophore modeling.

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Authors: K. Massila, R. D. Stein, S. M. Suhaizan, A. A. Azlianor

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A number of mass spectrometry applications are already available as web-based and windows-based systems to calculate isotope pattern and to display the mass spectrum based on the specific molecular formula besides providing necessary information. These applications were evaluated and compared with our new alternative application called Theoretical Isotope Generator (TIG) in terms of its functionality and features provided to prove this new application is working better and performing well. TIG provides extra features than others, complete with several functionality such as drawing, normalizing and zooming the generated graph that convey with the molecular information in a number of formats by providing the details of the calculation and molecules. Thus, any chemist, students, lecturers and researchers from anywhere could use TIG to gain related information on molecules and their relative intensity.

Keywords: Isotope pattern calculator, mass number, massspectrum, relative intensity.

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Authors: Sobir T. Navruzov

Abstract:

The problem of complex use of water resources in Central Asia by taking into consideration the sovereignty of the states and increasing demand on use of water for economic aspects are considered. Complex program with appropriate mathematical software intended for calculation of possible variants of using the Amudarya up-stream water resources according to satisfaction of incompatible requirements of the national economics in irrigation and energy generation is proposed.

Keywords: water resources, national economics, irrigation, transboundry, energy generation, optimal solution, program complex, up-stream, down-stream, compensating services.

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Authors: Christian Rathgeber, Franz Winkler, Xiaoyu Kang, Steffen Müller

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In this contribution two approaches for calculating optimal trajectories for highly automated vehicles are presented and compared. The first one is based on a non-linear vehicle model, used for evaluation. The second one is based on a simplified model and can be implemented on a current ECU. In usual driving situations both approaches show very similar results.

Keywords: Trajectory planning, direct method, indirect method, highly automated driving.

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Authors: Gaurav Bhanjana, Ganga Ram Chaudhary, Sandeep Kumar, Neeraj Dilbaghi

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Main sources of endocrine disrupting compounds in the ecosystem are hormones, pesticides, phthalates, flame retardants, dioxins, personal-care products, coplanar polychlorinated biphenyls (PCBs), bisphenol A, and parabens. These endocrine disrupting compounds are responsible for learning disabilities, brain development problems, deformations of the body, cancer, reproductive abnormalities in females and decreased sperm count in human males. Although discharge of these chemical compounds into the environment cannot be stopped, yet their amount can be retarded through proper evaluation and detection techniques. The available techniques for determination of these endocrine disrupting compounds mainly include high performance liquid chromatography (HPLC), mass spectroscopy (MS) and gas chromatography-mass spectrometry (GC–MS). These techniques are accurate and reliable but have certain limitations like need of skilled personnel, time consuming, interference and requirement of pretreatment steps. Moreover, these techniques are laboratory bound and sample is required in large amount for analysis. In view of above facts, new methods for detection of endocrine disrupting compounds should be devised that promise high specificity, ultra sensitivity, cost effective, efficient and easy-to-operate procedure. Nowadays, electrochemical sensors/biosensors modified with nanomaterials are gaining high attention among researchers. Bioelement present in this system makes the developed sensors selective towards analyte of interest. Nanomaterials provide large surface area, high electron communication feature, enhanced catalytic activity and possibilities of chemical modifications. In most of the cases, nanomaterials also serve as an electron mediator or electrocatalyst for some analytes.

Keywords: Sensors, endocrine disruptors, nanoparticles, electrochemical, microscopy.

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Authors: Francisco Aparisi, Marco A. de Luna

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In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.

Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.

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Authors: Vinay Gautam, Vivek Gautam

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With increase in the unauthorized users access, it is required to increase the security in the Near Field Communication (NFC). In the paper we propose a user behavior based enhanced protocol entitled ‘User Behavior based Enhanced Protocol (UBEP)’ to increase the security in NFC enabled devices. The UBEP works on the history of interaction of a user with system.The propose protocol considers four different factors (touch, time and distance & angle) of user behavior to know the authenticity or authorization of the users. These factors can be same for a user during interaction with the system. The UBEP uses two phase user verification system to authenticate a user. Firstly the acquisition phase is used to acquire and store the user interaction with NFC device and the same information is used in future to detect the authenticity of the user. The second phase (recognition) uses analysis of current and previous scenario of user interaction and digital signature verification system to finally authenticate user. The analysis of user based input makes a NFC transaction more advance and secure. This security is very tactical because it is completely depends on usage of the device.

Keywords: Security, Network Field communication, NFC Protocol.

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Authors: Fekkak Bouazza, Menaa Mohamed, Loukriz Abdelhamid, Krim Mohamed L.

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This paper presents modeling and control strategy for the grid connected wind turbine system based on Permanent Magnet Synchronous Generator (PMSG). The considered system is based on back-to-back converter topology. The Grid Side Converter (GSC) achieves the DC bus voltage control and unity power factor. The Machine Side Converter (MSC) assures the PMSG speed control. The PMSG is used as a variable speed generator and connected directly to the turbine without gearbox. The pitch angle control is not either considered in this study. Further, Optimal Tip Speed Ratio (OTSR) based MPPT control strategy is used to ensure the most energy efficiency whatever the wind speed variations. A filter (L) is put between the GSC and the grid to reduce current ripple and to improve the injected power quality. The proposed grid connected wind system is built under MATLAB/Simulink environment. The simulation results show the feasibility of the proposed topology and performance of its control strategies.

Keywords: Wind, grid, PMSG, MPPT, OTSR.

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Authors: Vandana Sharma, Parvinder S. Sandhu, Satwinder Singh, Baljit Saini

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In field of Computer Science and Mathematics, sorting algorithm is an algorithm that puts elements of a list in a certain order i.e. ascending or descending. Sorting is perhaps the most widely studied problem in computer science and is frequently used as a benchmark of a system-s performance. This paper presented the comparative performance study of four sorting algorithms on different platform. For each machine, it is found that the algorithm depends upon the number of elements to be sorted. In addition, as expected, results show that the relative performance of the algorithms differed on the various machines. So, algorithm performance is dependent on data size and there exists impact of hardware also.

Keywords: Algorithm, Analysis, Complexity, Sorting.

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Authors: Chiou-Yng Lee, Wen-Yo Lee, Chieh-Tsai Wu, Cheng-Chen Yang

Abstract:

Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit level and digi -level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba schemes, and used that to derive a novel scalable multiplier architecture. Analytical results show that the proposed multiplier provides a trade-off between space and time complexities. Our proposed multiplier is modular, regular, and suitable for very large scale integration (VLSI) implementations. It involves less area complexity compared to the multipliers based on traditional decomposition methods. It is therefore, more suitable for efficient hardware implementation of pairing based cryptography and elliptic curve cryptography (ECC) in constraint driven applications.

Keywords: Digit-serial systolic multiplier, elliptic curve cryptography (ECC), Karatsuba algorithm (KA), shifted polynomial basis (SPB), pairing computation.

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Authors: X. Vecino, J. M. Cruz, A. Moldes

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The disposal and the treatment of sewage sludge is an expensive and environmentally complex problem. In this work, a lipopeptide biosurfactant extracted from corn steep liquor was used as ecofriendly and cost-competitive alternative for the mobilization and bioremediation of fluorene in sewage sludge. Results have demonstrated that this biosurfactant has the capability to mobilize fluorene to the aqueous phase, reducing the amount of fluorene in the sewage sludge from 484.4 mg/Kg up to 413.7 mg/Kg and 196.0 mg/Kg after 1 and 27 days respectively. Furthermore, once the fluorene was extracted the lipopeptide biosurfactant contained in the aqueous phase allowed the biodegradation, up to 40.5% of the initial concentration of this polycyclic aromatic hydrocarbon.

Keywords: Fluorene, lipopeptide biosurfactant, mobilization, sewage sludge.

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Authors: Insaf Ajili, Malik Mallem, Jean-Yves Didier

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Motion recognition from videos is actually a very complex task due to the high variability of motions. This paper describes the challenges of human motion recognition, especially motion representation step with relevant features. Our descriptor vector is inspired from Laban Movement Analysis method. We propose discriminative features using the Random Forest algorithm in order to remove redundant features and make learning algorithms operate faster and more effectively. We validate our method on MSRC-12 and UTKinect datasets.

Keywords: Human motion recognition, Discriminative LMA features, random forest, features reduction.

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Authors: Mikako Nishimuko

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This paper aims to argue that religion and Faith-based Organizations (FBOs) contribute to building democratic process through the provision of education in Sierra Leone. Sierra Leone experienced a civil war from 1991 to 2002 and about 70 percent of the population lives in poverty. While the government has been in the process of rebuilding the nation, many forms of Civil Society Organizations (CSOs), including FBOs, have played a significant role in promoting social development. Education plays an important role in supporting people-s democratic movements through knowledge acquisition, spiritual enlightenment and empowerment. This paper discusses religious tolerance in Sierra Leone and how FBOs have contributed to the provision of primary education in Sierra Leone. This study is based on the author-s field research, which involved interviews with teachers and development stakeholders, notably government officials, Non-governmental Organizations (NGOs) and FBOs, as well as questionnaires completed by pupils, parents and teachers.

Keywords: Civil society, democracy, faith-based organizations (FBOs), religious tolerance, universal primary education (UPE)

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Authors: Mikako Nishimuko

Abstract:

This paper aims to argue that religion and Faith-based Organizations (FBOs) contribute to building democratic process through the provision of education in Sierra Leone. Sierra Leone experienced a civil war from 1991 to 2002 and about 70 percent of the population lives in poverty. While the government has been in the process of rebuilding the nation, many forms of Civil Society Organizations (CSOs), including FBOs, have played a significant role in promoting social development. Education plays an important role in supporting people-s democratic movements through knowledge acquisition, spiritual enlightenment and empowerment. This paper discusses religious tolerance in Sierra Leone and how FBOs have contributed to the provision of primary education in Sierra Leone. This study is based on the author-s field research, which involved interviews with teachers and development stakeholders, notably government officials, Non-governmental Organizations (NGOs) and FBOs, as well as questionnaires completed by pupils, parents and teachers.

Keywords: Civil society, democracy, faith-based organizations (FBOs), religious tolerance, universal primary education (UPE).

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Authors: Jixiao Tao, Xiaoqiao He

Abstract:

The present study deals with the finite element (FE) analysis of thermally-induced bistable plate using various plate elements. The quadrilateral plate elements include the 4-node conforming plate element based on the classical laminate plate theory (CLPT), the 4-node and 9-node Mindlin plate element based on the first-order shear deformation laminated plate theory (FSDT), and a displacement-based 4-node quadrilateral element (RDKQ-NL20). Using the von-Karman’s large deflection theory and the total Lagrangian (TL) approach, the nonlinear FE governing equations for plate under thermal load are derived. Convergence analysis for four elements is first conducted. These elements are then used to predict the stable shapes of thermally-induced bistable plate. Numerical test shows that the plate element based on FSDT, namely the 4-node and 9-node Mindlin, and the RDKQ-NL20 plate element can predict two stable cylindrical shapes while the 4-node conforming plate predicts a saddles shape. Comparing the simulation results with ABAQUS, the RDKQ-NL20 element shows the best accuracy among all the elements.

Keywords: Finite element method, geometrical nonlinearity, bistable, quadrilateral plate elements.

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Authors: B. Rajkumarsingh, S. Goolaup, A. Galleegadoo

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Laboratory classes in Electrical Engineering are often hampered by safety issues, as students have to work on high voltage lines. One solution is to make use of virtual laboratory simulations, to help students understand the concepts taught in their coursework. In this context, we have conceived and implemented virtual lab experiments in connection with the study of earthing arrangements. In this work, software was developed, which aid student in understanding the working of a residual current device (RCD) in a TT earthing system. Various parameters, such as the earthing resistances, leakage currents and harmonics were included for a TT system with RCD connection.

Keywords: TT system, RCD, LabVIEW, Learning aids.

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Authors: Yun-Yao Chi, Chieh-Kai Tsai, Dai-Ling Li

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In this paper, a method of fast 3D topography modeling using the high-resolution camera images is studied based on the characteristics of Unmanned Aerial Vehicle (UAV) system for low altitude aerial photogrammetry and the need of three dimensional (3D) urban landscape modeling. Firstly, the existing high-resolution digital camera with special design of overlap images is designed by reconstructing and analyzing the auto-flying paths of UAVs, which improves the self-calibration function to achieve the high precision imaging by software, and further increased the resolution of the imaging system. Secondly, several-angle images including vertical images and oblique images gotten by the UAV system are used for the detail measure of urban land surfaces and the texture extraction. Finally, the aerial photography and 3D topography construction are both developed in campus of Chang-Jung University and in Guerin district area in Tainan, Taiwan, provide authentication model for construction of 3D topography based on combined UAV-based camera images from system. The results demonstrated that the UAV system for low altitude aerial photogrammetry can be used in the construction of 3D topography production, and the technology solution in this paper offers a new, fast, and technical plan for the 3D expression of the city landscape, fine modeling and visualization.

Keywords: 3D, topography, UAV, images.

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Authors: Zhen Cheng, Xinyu Dai, Shujian Huang, Jiajun Chen

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Recently, explanatory natural language inference has attracted much attention for the interpretability of logic relationship prediction, which is also known as explanation generation for Natural Language Inference (NLI). Existing explanation generators based on discriminative Encoder-Decoder architecture have achieved noticeable results. However, we find that these discriminative generators usually generate explanations with correct evidence but incorrect logic semantic. It is due to that logic information is implicitly encoded in the premise-hypothesis pairs and difficult to model. Actually, logic information identically exists between premise-hypothesis pair and explanation. And it is easy to extract logic information that is explicitly contained in the target explanation. Hence we assume that there exists a latent space of logic information while generating explanations. Specifically, we propose a generative model called Variational Explanation Generator (VariationalEG) with a latent variable to model this space. Training with the guide of explicit logic information in target explanations, latent variable in VariationalEG could capture the implicit logic information in premise-hypothesis pairs effectively. Additionally, to tackle the problem of posterior collapse while training VariaztionalEG, we propose a simple yet effective approach called Logic Supervision on the latent variable to force it to encode logic information. Experiments on explanation generation benchmark—explanation-Stanford Natural Language Inference (e-SNLI) demonstrate that the proposed VariationalEG achieves significant improvement compared to previous studies and yields a state-of-the-art result. Furthermore, we perform the analysis of generated explanations to demonstrate the effect of the latent variable.

Keywords: Natural Language Inference, explanation generation, variational auto-encoder, generative model.

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Authors: Asterios Leonidis, George Margetis, Margherita Antona, Constantine Stephanidis

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Ambient Intelligence (AmI) environments bring significant potential to exploit sophisticated computer technology in everyday life. In particular, the educational domain could be significantly enhanced through AmI, as personalized and adapted learning could be transformed from paper concepts and prototypes to real-life scenarios. In this paper, an integrated framework is presented, named ClassMATE, supporting ubiquitous computing and communication in a school classroom. The main objective of ClassMATE is to enable pervasive interaction and context aware education in the technologically augmented classroom of the future.

Keywords: Ambient intelligence, smart classroom, pervasivecomputing, education.

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Authors: Sandra Ondrušová, Jaroslav Polec

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Arbitrarily shaped video objects are an important concept in modern video coding methods. The techniques presently used are not based on image elements but rather video objects having an arbitrary shape. In this paper, spatial shape error concealment techniques to be used for object-based image in error-prone environments are proposed. We consider a geometric shape representation consisting of the object boundary, which can be extracted from the α-plane. Three different approaches are used to replace a missing boundary segment: Bézier interpolation, Bézier approximation and NURBS approximation. Experimental results on object shape with different concealment difficulty demonstrate the performance of the proposed methods. Comparisons with proposed methods are also presented.

Keywords: error concealment, shape coding, object-based image, NURBS, Bézier curves.

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Authors: Wang Yunhong

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The present paper is preoccupied with the different styles of three translators in their translating a Chinese classical novel Shuihu Zhuan. Based on a parallel corpus, it adopts a target-oriented approach to look into whether and what stylistic differences and shifts the three translations have revealed. The findings show that the three translators demonstrate different styles concerning their word choices and sentence preferences, which implies that identification of recurrent textual patterns may be a basic step for investigating the style of a translator.

Keywords: Corpus, lexical choices, sentence characteristics, style.

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Authors: Essam Al-Daoud

Abstract:

A New features are extracted and compared to improve the prediction of protein-protein interactions. The basic idea is to select and use the best set of features from the Tensor matrices that are produced by the frequency vectors of the protein sequences. Three set of features are compared, the first set is based on the indices that are the most common in the interacting proteins, the second set is based on the indices that tend to be common in the interacting and non-interacting proteins, and the third set is constructed by using random indices. Moreover, three encoding strategies are compared; that are based on the amino asides polarity, structure, and chemical properties. The experimental results indicate that the highest accuracy can be obtained by using random indices with chemical properties encoding strategy and support vector machine.

Keywords: protein-protein interactions, random indices, encoding strategies, support vector machine.

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Authors: S. Golmohammadi, M. Noorian Bidgoli

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Tunneling progress is a key parameter in the blasting method of tunneling. Taking measures to enhance tunneling advance can limit the progress distance without a supporting system, subsequently reducing or eliminating the risk of damage. This paper focuses on modeling tunneling progress using three main groups of parameters (tunneling geometry, blasting pattern, and rock mass specifications) based on the Rock Engineering Systems (RES) methodology. In the proposed models, four main effective parameters on tunneling progress are considered as inputs (RMR, Q-system, Specific charge of blasting, Area), with progress as the output. Data from 86 blasts conducted at the tailrace tunnel in the Azad Dam, western Iran, were used to evaluate the progress value for each blast. The results indicated that, for the 86 blasts, the progress of the estimated model aligns mostly with the measured progress. This paper presents a method for building the interaction matrix (statistical base) of the RES model. Additionally, a comparison was made between the results of the new RES-based model and a Multi-Linear Regression (MLR) analysis model. In the RES-based model, the effective parameters are RMR (35.62%), Q (28.6%), q (specific charge of blasting) (20.35%), and A (15.42%), respectively, whereas for MLR analysis, the main parameters are RMR, Q (system), q, and A. These findings confirm the superior performance of the RES-based model over the other proposed models.

Keywords: Rock Engineering Systems, tunneling progress, Multi Linear Regression, Specific charge of blasting.

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Authors: A. Buzzanca, G. Castellano, A.M. Fanelli

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In this paper we address the problem of musical style classification, which has a number of applications like indexing in musical databases or automatic composition systems. Starting from MIDI files of real-world improvisations, we extract the melody track and cut it into overlapping segments of equal length. From these fragments, some numerical features are extracted as descriptors of style samples. We show that a standard Bayesian classifier can be conveniently employed to build an effective musical style classifier, once this set of features has been extracted from musical data. Preliminary experimental results show the effectiveness of the developed classifier that represents the first component of a musical audio retrieval system

Keywords: Musical style, Bayesian classifier.

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Authors: Dong-Woo Lim, Chang-Jae Chun, Hyung-Myung Kim

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We consider a two-way relay network where two sources exchange information. A relay helps the two sources exchange information using the decode-and-XOR-forward protocol. We investigate the power minimization problem with minimum rate constraints. The system needs two time slots and in each time slot the required rate pair should be achievable. The power consumption is minimized in each time slot and we obtained the closed form solution. The simulation results confirm that the proposed power allocation scheme consumes lower total power than the conventional schemes.

Keywords: Decode-and-XOR-forward, power minimization, two-way relay

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Authors: Fangfang Meng, Shuang Cong

Abstract:

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.

Keywords: Implicit Lyapunov control, state error, degenerate cases, convergence.

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