Search results for: T1T2-semi star generalized closed sets.
918 Impact of Similarity Ratings on Human Judgement
Authors: Ian A. McCulloh, Madelaine Zinser, Jesse Patsolic, Michael Ramos
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Recommender systems are a common artificial intelligence (AI) application. For any given input, a search system will return a rank-ordered list of similar items. As users review returned items, they must decide when to halt the search and either revise search terms or conclude their requirement is novel with no similar items in the database. We present a statistically designed experiment that investigates the impact of similarity ratings on human judgement to conclude a search item is novel and halt the search. In the study, 450 participants were recruited from Amazon Mechanical Turk to render judgement across 12 decision tasks. We find the inclusion of ratings increases the human perception that items are novel. Percent similarity increases novelty discernment when compared with star-rated similarity or the absence of a rating. Ratings reduce the time to decide and improve decision confidence. This suggests that the inclusion of similarity ratings can aid human decision-makers in knowledge search tasks.
Keywords: Ratings, rankings, crowdsourcing, empirical studies, user studies, similarity measures, human-centered computing, novelty in information retrieval.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 412917 A Force-directed Graph Drawing based on the Hierarchical Individual Timestep Method
Authors: T. Matsubayashi, T. Yamada
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In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.Keywords: visualization, graph drawing, Internet Map
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1852916 Quantification of Aerodynamic Variables Using Analytical Technique and Computational Fluid Dynamics
Authors: Adil Loya, Kamran Maqsood, Muhammad Duraid
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Aerodynamic stability coefficients are necessary to be known before any unmanned aircraft flight is performed. This requires expertise on aerodynamics and stability control of the aircraft. To enable efficacious performance of aircraft requires that a well-defined flight path and aerodynamics should be defined beforehand. This paper presents a study on the aerodynamics of an unmanned aero vehicle (UAV) during flight conditions. Current research holds comparative studies of different parameters for flight aerodynamic, measured using two different open source analytical software programs. These software packages are DATCOM and XLRF5, which help in depicting the flight aerodynamic variables. Computational fluid dynamics (CFD) was also used to perform aerodynamic analysis for which Star CCM+ was used. Output trends of the study demonstrate high accuracies between the two software programs with that of CFD. It can be seen that the Coefficient of Lift (CL) obtained from DATCOM and XFLR is similar to CL of CFD simulation. In the similar manner, other potential aerodynamic stability parameters obtained from analytical software are in good agreement with CFD.
Keywords: XFLR5, DATCOM, computational fluid dynamic, unmanned aero vehicle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 875915 Classification of the Bachet Elliptic Curves y2 = x3 + a3 in Fp, where p ≡ 1 (mod 6) is Prime
Authors: Nazli Yildiz İkikardes, Gokhan Soydan, Musa Demirci, Ismail Naci Cangul
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In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.Keywords: Elliptic curves over finite fields, quadratic residue, cubic residue.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1854914 A Simplified Distribution for Nonlinear Seas
Authors: M. A. Tayfun, M. A. Alkhalidi
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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.
Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2095913 A New Algorithm for Cluster Initialization
Authors: Moth'd Belal. Al-Daoud
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Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the k-means algorithm. Solutions obtained from this technique are dependent on the initialization of cluster centers. In this article we propose a new algorithm to initialize the clusters. The proposed algorithm is based on finding a set of medians extracted from a dimension with maximum variance. The algorithm has been applied to different data sets and good results are obtained.
Keywords: clustering, k-means, data mining.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2102912 Swarm Navigation in a Complex Environment
Authors: Jai Raj, Jito Vanualailai, Bibhya Sharma, Shonal Singh
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This paper proposes a solution to the motion planning and control problem of car-like mobile robots which is required to move safely to a designated target in a priori known workspace cluttered with swarm of boids exhibiting collective emergent behaviors. A generalized algorithm for target convergence and swarm avoidance is proposed that will work for any number of swarms. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws are demonstrated via computer simulations of an emergent behavior.Keywords: Swarm, practical stability, motion planning, emergent.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1395911 Risk of Occupational Exposure to Cytotoxic Drugs: The Role of Handling Procedures of Hospital Workers
Authors: J. Silva, P. Arezes, R. Schierl, N. Costa
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In order to study environmental contamination by cytostatic drugs in Portugal hospitals, sampling campaigns were conducted in three hospitals in 2015 (112 samples). Platinum containing drugs and fluorouracil were chosen because both were administered in high amounts. The detection limit was 0.01 pg/cm² for platinum and 0.1 pg/cm² for fluorouracil. The results show that spills occur mainly on the patient`s chair, while the most referenced occurrence is due to an inadequately closed wrapper. Day hospitals facilities were detected as having the largest number of contaminated samples and with higher levels of contamination.
Keywords: Antineoplastic, drugs, exposure, surface.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1051910 The Lower and Upper Approximations in a Group
Authors: Zhaohao Wang, Lan Shu
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In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.
Keywords: Lower approximations, Upper approximations, Rough sets, Rough groups, Lagrange
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2217909 dynr.mi: An R Program for Multiple Imputation in Dynamic Modeling
Authors: Yanling Li, Linying Ji, Zita Oravecz, Timothy R. Brick, Michael D. Hunter, Sy-Miin Chow
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Assessing several individuals intensively over time yields intensive longitudinal data (ILD). Even though ILD provide rich information, they also bring other data analytic challenges. One of these is the increased occurrence of missingness with increased study length, possibly under non-ignorable missingness scenarios. Multiple imputation (MI) handles missing data by creating several imputed data sets, and pooling the estimation results across imputed data sets to yield final estimates for inferential purposes. In this article, we introduce dynr.mi(), a function in the R package, Dynamic Modeling in R (dynr). The package dynr provides a suite of fast and accessible functions for estimating and visualizing the results from fitting linear and nonlinear dynamic systems models in discrete as well as continuous time. By integrating the estimation functions in dynr and the MI procedures available from the R package, Multivariate Imputation by Chained Equations (MICE), the dynr.mi() routine is designed to handle possibly non-ignorable missingness in the dependent variables and/or covariates in a user-specified dynamic systems model via MI, with convergence diagnostic check. We utilized dynr.mi() to examine, in the context of a vector autoregressive model, the relationships among individuals’ ambulatory physiological measures, and self-report affect valence and arousal. The results from MI were compared to those from listwise deletion of entries with missingness in the covariates. When we determined the number of iterations based on the convergence diagnostics available from dynr.mi(), differences in the statistical significance of the covariate parameters were observed between the listwise deletion and MI approaches. These results underscore the importance of considering diagnostic information in the implementation of MI procedures.Keywords: Dynamic modeling, missing data, multiple imputation, physiological measures.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 808908 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator
Authors: Lv Yuhua
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In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1428907 Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
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In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2085906 The Extremal Graph with the Largest Merrifield-Simmons Index of (n, n + 2)-graphs
Authors: M. S. Haghighat, A. Dolati, M. Tabari, E. Mohseni
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The Merrifield-Simmons index of a graph G is defined as the total number of its independent sets. A (n, n + 2)-graph is a connected simple graph with n vertices and n + 2 edges. In this paper we characterize the (n, n+2)-graph with the largest Merrifield- Simmons index. We show that its Merrifield-Simmons index i.e. the upper bound of the Merrifield-Simmons index of the (n, n+2)-graphs is 9 × 2n-5 +1 for n ≥ 5.
Keywords: Merrifield-Simmons index, (n, n+2)-graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1259905 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation
Authors: Li Xiguang
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In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1302904 Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems
Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding
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This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.
Keywords: Impulsive systems, switched systems, quadratic stabilization, robust stabilization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1535903 Exponentially Weighted Simultaneous Estimation of Several Quantiles
Authors: Valeriy Naumov, Olli Martikainen
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In this paper we propose new method for simultaneous generating multiple quantiles corresponding to given probability levels from data streams and massive data sets. This method provides a basis for development of single-pass low-storage quantile estimation algorithms, which differ in complexity, storage requirement and accuracy. We demonstrate that such algorithms may perform well even for heavy-tailed data.Keywords: Quantile estimation, data stream, heavy-taileddistribution, tail index.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1531902 Sensitivity and Removed THD of a Phase- Cutting Dimmer
Authors: H. Fathabadi
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In this paper, we consider a designed and implemented phase-cutting dimmer. In fact, the dimmer is closed loop and a microcontroller calculates and then regulates the firing delay angles of each channel. Depending on the firing angle, the harmonic distortion in the input current will not comply with international standards, such as IEC 61000-3-2 (class C equipments). For solving this problem, eight harmonic compensators have been added to the dimmer. So, the proposed dimmer has a little harmonic distortion in the input current whereas conventional phase-cutting dimmers are not so. Sensitivity and removed THD of the proposed dimmer will be presented.Keywords: Dimmer, compensator, harmonic, dimming.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1499901 Study of Unsteady Swirling Flow in a Hydrodynamic Vortex Chamber
Authors: Sergey I. Shtork, Aleksey P. Vinokurov, Sergey V. Alekseenko
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The paper reports on the results of experimental and numerical study of nonstationary swirling flow in an isothermal model of vortex burner. It has been identified that main source of the instability is related to a precessing vortex core (PVC) phenomenon. The PVC induced flow pulsation characteristics such as precession frequency and its variation as a function of flowrate and swirl number have been explored making use of acoustic probes. Additionally pressure transducers were used to measure the pressure drops on the working chamber and across the vortex flow. The experiments have been included also the mean velocity measurements making use of a laser-Doppler anemometry. The features of instantaneous flowfield generated by the PVC were analyzed employing a commercial CFD code (Star-CCM+) based on Detached Eddy Simulation (DES) approach. Validity of the numerical code has been checked by comparison calculated flowfield data with the obtained experimental results. It has been confirmed particularly that the CFD code applied correctly reproduces the flow features.Keywords: Acoustic probes, detached eddy simulation (DES), laser-Doppler anemometry (LDA), precessing vortex core (PVC).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2270900 Sample-Weighted Fuzzy Clustering with Regularizations
Authors: Miin-Shen Yang, Yee-Shan Pan
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Although there have been many researches in cluster analysis to consider on feature weights, little effort is made on sample weights. Recently, Yu et al. (2011) considered a probability distribution over a data set to represent its sample weights and then proposed sample-weighted clustering algorithms. In this paper, we give a sample-weighted version of generalized fuzzy clustering regularization (GFCR), called the sample-weighted GFCR (SW-GFCR). Some experiments are considered. These experimental results and comparisons demonstrate that the proposed SW-GFCR is more effective than the most clustering algorithms.
Keywords: Clustering; fuzzy c-means, fuzzy clustering, sample weights, regularization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1764899 Oscillation Theorems for Second-order Nonlinear Neutral Dynamic Equations with Variable Delays and Damping
Authors: Da-Xue Chen, Guang-Hui Liu
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In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples.
Keywords: Oscillation theorem, second-order nonlinear neutral dynamic equation, variable delay, damping, Riccati transformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1364898 Observer Design for Chaos Synchronization of Time-delayed Power Systems
Authors: Jui-Sheng Lin, Yi-Sung Yang, Meei-Ling Hung, Teh-Lu Liao, Jun-Juh Yan
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The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.
Keywords: Chaos, Synchronization, Quadratic stability theory, Observer
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1720897 Intuitionistic Fuzzy Subalgebras (Ideals) with Thresholds (λ, μ) of BCI-Algebras
Authors: Shaoquan Sun, Qianqian Li
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Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed.
Keywords: BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds (λ, μ).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4085896 Relationship between Sums of Squares in Linear Regression and Semi-parametric Regression
Authors: Dursun Aydın, Bilgin Senel
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In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1853895 Robust Disturbance Rejection for Left Invertible Singular Systems with Nonlinear Uncertain Structure
Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi
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The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.
Keywords: System theory, uncertain systems, robust control, singular systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1478894 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation
Authors: Li Xiguang
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In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1413893 A Kernel Classifier using Linearised Bregman Iteration
Authors: K. A. D. N. K Wimalawarne
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In this paper we introduce a novel kernel classifier based on a iterative shrinkage algorithm developed for compressive sensing. We have adopted Bregman iteration with soft and hard shrinkage functions and generalized hinge loss for solving l1 norm minimization problem for classification. Our experimental results with face recognition and digit classification using SVM as the benchmark have shown that our method has a close error rate compared to SVM but do not perform better than SVM. We have found that the soft shrinkage method give more accuracy and in some situations more sparseness than hard shrinkage methods.Keywords: Compressive sensing, Bregman iteration, Generalisedhinge loss, sparse, kernels, shrinkage functions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1376892 Cognitive Relaying in Interference Limited Spectrum Sharing Environment: Outage Probability and Outage Capacity
Authors: Md Fazlul Kader, Soo Young Shin
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In this paper, we consider a cognitive relay network (CRN) in which the primary receiver (PR) is protected by peak transmit power ¯PST and/or peak interference power Q constraints. In addition, the interference effect from the primary transmitter (PT) is considered to show its impact on the performance of the CRN. We investigate the outage probability (OP) and outage capacity (OC) of the CRN by deriving closed-form expressions over Rayleigh fading channel. Results show that both the OP and OC improve by increasing the cooperative relay nodes as well as when the PT is far away from the SR.Keywords: Cognitive relay, outage, interference limited, decode-and-forward (DF).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1907891 An Intelligent Text Independent Speaker Identification Using VQ-GMM Model Based Multiple Classifier System
Authors: Cheima Ben Soltane, Ittansa Yonas Kelbesa
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Speaker Identification (SI) is the task of establishing identity of an individual based on his/her voice characteristics. The SI task is typically achieved by two-stage signal processing: training and testing. The training process calculates speaker specific feature parameters from the speech and generates speaker models accordingly. In the testing phase, speech samples from unknown speakers are compared with the models and classified. Even though performance of speaker identification systems has improved due to recent advances in speech processing techniques, there is still need of improvement. In this paper, a Closed-Set Tex-Independent Speaker Identification System (CISI) based on a Multiple Classifier System (MCS) is proposed, using Mel Frequency Cepstrum Coefficient (MFCC) as feature extraction and suitable combination of vector quantization (VQ) and Gaussian Mixture Model (GMM) together with Expectation Maximization algorithm (EM) for speaker modeling. The use of Voice Activity Detector (VAD) with a hybrid approach based on Short Time Energy (STE) and Statistical Modeling of Background Noise in the pre-processing step of the feature extraction yields a better and more robust automatic speaker identification system. Also investigation of Linde-Buzo-Gray (LBG) clustering algorithm for initialization of GMM, for estimating the underlying parameters, in the EM step improved the convergence rate and systems performance. It also uses relative index as confidence measures in case of contradiction in identification process by GMM and VQ as well. Simulation results carried out on voxforge.org speech database using MATLAB highlight the efficacy of the proposed method compared to earlier work.Keywords: Feature Extraction, Speaker Modeling, Feature Matching, Mel Frequency Cepstrum Coefficient (MFCC), Gaussian mixture model (GMM), Vector Quantization (VQ), Linde-Buzo-Gray (LBG), Expectation Maximization (EM), pre-processing, Voice Activity Detection (VAD), Short Time Energy (STE), Background Noise Statistical Modeling, Closed-Set Tex-Independent Speaker Identification System (CISI).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1880890 Mean Square Stability of Impulsive Stochastic Delay Differential Equations with Markovian Switching and Poisson Jumps
Authors: Dezhi Liu
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In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.
Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1557889 Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method
Authors: Nemat Abazari, Reza Abazari
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In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.
Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2557