Search results for: approximate arithmetic

Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Hamdi Amroun, Yacine Benziani, Mehdi Ammi

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In this paper, we propose an approach of detecting the behavior of the viewers of a TV program in a non-controlled environment. The experiment we propose is based on the use of three types of connected objects (smartphone, smart watch, and a connected remote control). 23 participants were observed while watching their TV programs during three phases: before, during and after watching a TV program. Their behaviors were detected using an approach based on The Dempster Shafer Theory (DST) in two phases. The first phase is to approximate dynamically the mass functions using an approach based on the correlation coefficient. The second phase is to calculate the approximate mass functions. To approximate the mass functions, two approaches have been tested: the first approach was to divide each features data space into cells; each one has a specific probability distribution over the behaviors. The probability distributions were computed statistically (estimated by empirical distribution). The second approach was to predict the TV-viewing behaviors through the use of classifiers algorithms and add uncertainty to the prediction based on the uncertainty of the model. Results showed that mixing the fusion rule with the computation of the initial approximate mass functions using a classifier led to an overall of 96%, 95% and 96% success rate for the first, second and third TV-viewing phase respectively. The results were also compared to those found in the literature. This study aims to anticipate certain actions in order to maintain the attention of TV viewers towards the proposed TV programs with usual connected objects, taking into account the various uncertainties that can be generated.

Keywords: Iot, TV-viewing behaviors identification, automatic classification, unconstrained environment

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Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif

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This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.

Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function

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Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava

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This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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Authors: Zikiou Nadia, Lahdir Mourad, Ameur Soltane

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In this paper, we propose an effective method for image compression based on SVM Regression (SVR), with three different kernels, and biorthogonal 2D Discrete Wavelet Transform. SVM regression could learn dependency from training data and compressed using fewer training points (support vectors) to represent the original data and eliminate the redundancy. Biorthogonal wavelet has been used to transform the image and the coefficients acquired are then trained with different kernels SVM (Gaussian, Polynomial, and Linear). Run-length and Arithmetic coders are used to encode the support vectors and its corresponding weights, obtained from the SVM regression. The peak signal noise ratio (PSNR) and their compression ratios of several test images, compressed with our algorithm, with different kernels are presented. Compared with other kernels, Gaussian kernel achieves better image quality. Experimental results show that the compression performance of our method gains much improvement.

Keywords: image compression, 2D discrete wavelet transform (DWT-2D), support vector regression (SVR), SVM Kernels, run-length, arithmetic coding

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Authors: Gong Zhilin, Jing Yang, Jian Yin

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The purpose of this paper is to develop a novel system for credit card fraud detection based on sequential modeling of data using hybrid deep learning models. The projected model encapsulates five major phases are pre-processing, imbalance-data handling, feature extraction, optimal feature selection, and fraud detection with an ensemble classifier. The collected raw data (input) is pre-processed to enhance the quality of the data through alleviation of the missing data, noisy data as well as null values. The pre-processed data are class imbalanced in nature, and therefore they are handled effectively with the K-means clustering-based SMOTE model. From the balanced class data, the most relevant features like improved Principal Component Analysis (PCA), statistical features (mean, median, standard deviation) and higher-order statistical features (skewness and kurtosis). Among the extracted features, the most optimal features are selected with the Self-improved Arithmetic Optimization Algorithm (SI-AOA). This SI-AOA model is the conceptual improvement of the standard Arithmetic Optimization Algorithm. The deep learning models like Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), and optimized Quantum Deep Neural Network (QDNN). The LSTM and CNN are trained with the extracted optimal features. The outcomes from LSTM and CNN will enter as input to optimized QDNN that provides the final detection outcome. Since the QDNN is the ultimate detector, its weight function is fine-tuned with the Self-improved Arithmetic Optimization Algorithm (SI-AOA).

Keywords: credit card, data mining, fraud detection, money transactions

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Authors: Nithiya C., Komathi B. J., Praveena N. G., Samuda Prathima

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At present, the ultimate aim in digital system designs, especially at the gate level and lower levels of design abstraction, is power optimization. Adders are a nearly universal component of today's integrated circuits. Most of the research was on the design of high-speed adders to execute addition based on various adder structures. This paper discusses the ideal path for selecting an arithmetic unit for IoT applications. Based on the analysis of eight types of 16-bit adders, we found out Carry Look-ahead (CLA) produces low power. Additionally, multiplier and accumulator (MAC) unit is implemented with the Booth multiplier by using the low power adders in the order of preference. The design is synthesized and verified using Synopsys Design Compiler and VCS. Then it is implemented by using Cadence Encounter. The total power consumed by the CLA based booth multiplier is 0.03527mW, the total area occupied is 11260 um², and the speed is 2034 ps.

Keywords: carry look-ahead, carry select adder, CSA, internet of things, ripple carry adder, design rule check, power delay product, multiplier and accumulator

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Authors: Michinori Nakata, Hiroshi Sakai

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A rough set, which consists of lower and upper approximations, is formulated in information tables containing possibilistic information. First, lower and upper approximations on the basis of possible world semantics in the same way as Lipski did in the field of incomplete databases are shown in order to clarify fundamentals of rough sets under possibilistic information. Possibility and necessity measures are used, as is done in possibilistic databases. As a result, each object has certain and possible membership degrees to lower and upper approximations, which degrees are the lower and upper bounds. Therefore, the degree that the object belongs to lower and upper approximations is expressed by an interval value. And the complementary property linked with the lower and upper approximations holds, as is valid under complete information. Second, the approach based on indiscernibility relations, which is proposed by Dubois and Prade, are extended in three cases. The first case is that objects used to approximate a set of objects are characterized by possibilistic information. The second case is that objects used to approximate a set of objects with possibilistic information are characterized by complete information. The third case is that objects that are characterized by possibilistic information approximate a set of objects with possibilistic information. The extended approach create the same results as the approach based on possible world semantics. This justifies our extension.

Keywords: rough sets, possibilistic information, possible world semantics, indiscernibility relations, lower approximations, upper approximations

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Helen L. Hein, Joachim Schwarte

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As a pillar of sustainable development, ecology has become an important milestone in research community, especially due to global challenges like climate change. The ecological performance of products can be scientifically conducted with life cycle assessments. In the construction sector, significant amounts of CO₂ emissions are assigned to the energy used for building heating purposes. Therefore, sustainable construction materials for insulating purposes are substantial, whereby aerogels have been explored intensively in the last years due to their low thermal conductivity. Therefore, the WALL-ACE project aims to develop an aerogel-based thermal insulating plaster that would achieve minor thermal conductivities. But as in the early stage of development phases, a lot of information is still missing or not yet accessible, the ecological performance of innovative products bases increasingly on uncertain data that can lead to significant deviations in the results. To be able to predict realistically how meaningful the results are and how viable the developed products may be with regard to their corresponding respective market, these deviations however have to be considered. Therefore, a classification method is presented in this study, which may allow comparing the ecological performance of modern products with already established and competitive materials. In order to achieve this, an alternative calculation method was used that allows computing with lower and upper bounds to consider all possible values without precise data. The life cycle analysis of the considered products was conducted with an interval arithmetic based calculation method. The results lead to the conclusion that the interval solutions describing the possible environmental impacts are so wide that the result usability is limited. Nevertheless, a further optimization in reducing environmental impacts of aerogels seems to be needed to become more competitive in the future.

Keywords: aerogel-based, insulating material, early development phase, interval arithmetic

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Fuyuan Ma, Ying Wang, Xin Wang

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Social networks have become breeding grounds for the rapid spread of rumors and malicious information, posing threats to societal stability and causing significant public harm. Existing research focuses on simulating the spread of information and its impact on users through propagation dynamics and applies methods such as greedy approximation strategies to approximate the optimal control solution at the global scale. However, the greedy strategy at the global scale may fall into locally optimal solutions, and the approximate simulation of information spread may accumulate more errors. Therefore, we propose a multi-scale control model for network group behavior, introducing individual and group scales on top of the greedy strategy’s global scale. At the individual scale, we calculate the propagation influence of nodes based on their structural attributes to alleviate the issue of local optimality. At the group scale, we conduct precise propagation simulations to avoid introducing cumulative errors from approximate calculations without increasing computational costs. Experimental results on three real-world datasets demonstrate the effectiveness of our proposed multi-scale model in controlling network group behavior.

Keywords: influence blocking maximization, competitive linear threshold model, social networks, network group behavior

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Hyun-Ho Lee, Kee-Won Kim

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The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: finite field, Montgomery multiplication, systolic array, cryptography

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: Shareefa Abdullah Al-Maqtari, Ruzaika Omar Basaree, Rafeah Legino

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A pictorial representation of hybrid forms in science-art collaboration has become a crucial issue in the course of exploring a new painting technique development. This is straight related to the reception of an invisible-recognition phenomenology. In hybrid pictorial representation of invisible-recognition phenomenology, the challenging issue is how to depict the pictorial features of indescribable objects from its mental source, modality and transparency. This paper proposes the hybrid technique of painting Demonstrate, Resemble, and Synthesize (DRS) through a combination of the hybrid aspect-recognition representation of understanding picture, demonstrative mod, the number theory, pattern in the modular arithmetic system, and the coherence theory of visual attention in the dynamic scenes representation. Multi-methods digital gaze data analyses, pattern-modular table operation design, and rotation parameter were used for the visualization. In the scientific processes, Eye-trackingvideo-sections based was conducted using Tobii T60 remote eye tracking hardware and TobiiStudioTM analysis software to collect and analyze the eye movements of ten participants when watching the video clip, Alexander Paulikevitch’s performance’s ‘Tajwal’. Results: we found that correlation of fixation count in section one was positively and moderately correlated with section two Person’s (r=.10, p < .05, 2-tailed) as well as in fixation duration Person’s (r=.10, p < .05, 2-tailed). However, a paired-samples t-test indicates that scores were significantly higher for the section one (M = 2.2, SD = .6) than for the section two (M = 1.93, SD = .6) t(9) = 2.44, p < .05, d = 0.87. In the visual process, the exported data of gaze number N was resembled the hybrid forms of visuospatial attention using the table-mod-analyses operation. The explored hybrid guideline was simply applicable, and it could be as alternative approach to the sustainability of contemporary visual arts.

Keywords: science-art collaboration, hybrid forms, pictorial representation, visuospatial attention, modular arithmetic

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Authors: Juliana A. Knocikova

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Methods of nonlinear signal analysis are based on finding that random behavior can arise in deterministic nonlinear systems with a few degrees of freedom. Considering the dynamical systems, entropy is usually understood as a rate of information production. Changes in temporal dynamics of physiological data are indicating evolving of system in time, thus a level of new signal pattern generation. During last decades, many algorithms were introduced to assess some patterns of physiological responses to external stimulus. However, the reflex responses are usually characterized by short periods of time. This characteristic represents a great limitation for usual methods of nonlinear analysis. To solve the problems of short recordings, parameter of approximate entropy has been introduced as a measure of system complexity. Low value of this parameter is reflecting regularity and predictability in analyzed time series. On the other side, increasing of this parameter means unpredictability and a random behavior, hence a higher system complexity. Reduced neurophysiological data complexity has been observed repeatedly when analyzing electroneurogram and electromyogram activities during defence reflex responses. Quantitative phrenic neurogram changes are also obvious during severe hypoxia, as well as during airway reflex episodes. Concluding, the approximate entropy parameter serves as a convenient tool for analysis of reflex behavior characterized by short lasting time series.

Keywords: approximate entropy, neurophysiological data, nonlinear dynamics, reflex

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Authors: Sebastian Andersen, Peter N. Poulsen

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The use of basis projection in the structural dynamic analysis is frequently applied. The purpose of the method is to improve the computational efficiency, while maintaining a high solution accuracy, by projection the governing equations onto a small set of carefully selected basis vectors. The present work considers basis projection in kinematic nonlinear systems with a focus on two widely used basis vectors; the system mode shapes and their modal derivatives. Particularly the latter basis vectors are given special attention since only approximate modal derivatives have been used until now. In the present work the complete modal derivatives, derived from perturbation methods, are presented and compared to the previously applied approximate modal derivatives. The correctness of the complete modal derivatives is illustrated by use of an example of a harmonically loaded kinematic nonlinear structure modeled by beam elements.

Keywords: basis projection, finite element method, kinematic nonlinearities, modal derivatives

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Authors: Dimitri Golenko-Ginzburg

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A CPM network project with deterministic activity durations, in which activities require homogenous resources with fixed capacities, is considered. The problem is to determine the optimal schedule of starting times for all network activities within their maximal allowable limits (in order not to exceed the network's critical time) to minimize the maximum required resources for the project at any point in time. In case when a non-critical activity may start only at discrete moments with the pregiven time span, the problem becomes NP-complete and an optimal solution may be obtained via a look-over algorithm. For the case when a look-over requires much computational time an approximate algorithm is suggested. The algorithm's performance ratio, i.e., the relative accuracy error, is determined. Experimentation has been undertaken to verify the suggested algorithm.

Keywords: resource smoothing problem, CPM network, lookover algorithm, lexicographical order, approximate algorithm, accuracy estimate

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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Selvakumar Ulaganathan, Ivo Couckuyt, Francesco Ferranti, Tom Dhaene, Eric Laermans

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Variable-fidelity surrogate modelling offers an efficient way to approximate function data available in multiple degrees of accuracy each with varying computational cost. In this paper, a Kriging-based variable-fidelity surrogate modelling approach is introduced to approximate such deterministic data. Initially, individual Kriging surrogate models, which are enhanced with gradient data of different degrees of accuracy, are constructed. Then these Gradient enhanced Kriging surrogate models are strategically coupled using a recursive CoKriging formulation to provide an accurate surrogate model for the highest fidelity data. While, intuitively, gradient data is useful to enhance the accuracy of surrogate models, the primary motivation behind this work is to investigate if it is also worthwhile incorporating gradient data of varying degrees of accuracy.

Keywords: Kriging, CoKriging, Surrogate modelling, Variable- fidelity modelling, Gradients

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Authors: Jianhong Xiang, Hao Xiang, Linyu Wang

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Compressed sensing (CS) has a wide range of applications in sparse signal reconstruction. Aiming at the problems of low recovery accuracy and long reconstruction time of existing reconstruction algorithms in medical imaging, this paper proposes a corrected smoothing L0 algorithm based on compressed sensing (CSL0). First, an approximate hyperbolic tangent function (AHTF) that is more similar to the L0 norm is proposed to approximate the L0 norm. Secondly, in view of the "sawtooth phenomenon" in the steepest descent method and the problem of sensitivity to the initial value selection in the modified Newton method, the use of the steepest descent method and the modified Newton method are jointly optimized to improve the reconstruction accuracy. Finally, the CSL0 algorithm is simulated on various images. The results show that the algorithm proposed in this paper improves the reconstruction accuracy of the test image by 0-0. 98dB.

Keywords: smoothed L0, compressed sensing, image processing, sparse reconstruction

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Authors: Alexander N. Savostyanov, Tatyana A. Dolgorukova, Elena A. Esipenko, Mikhail S. Zaleshin, Margherita Malanchini, Anna V. Budakova, Alexander E. Saprygin, Yulia V. Kovas

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The present study compared spectral-power indexes and cortical topography of brain activity in a sample characterized by different levels of trait and mathematical anxiety. 52 healthy Russian-speakers (age 17-32; 30 males) participated in the study. Participants solved an error recognition task under 3 conditions: A lexical condition (simple sentences in Russian), and two numerical conditions (simple arithmetic and complicated algebraic problems). Trait and mathematical anxiety were measured using self-repot questionnaires. EEG activity was recorded simultaneously during task execution. Event-related spectral perturbations (ERSP) were used to analyze spectral-power changes in brain activity. Additionally, sLORETA was applied in order to localize the sources of brain activity. When exploring EEG activity recorded after tasks onset during lexical conditions, sLORETA revealed increased activation in frontal and left temporal cortical areas, mainly in the alpha/beta frequency ranges. When examining the EEG activity recorded after task onset during arithmetic and algebraic conditions, additional activation in delta/theta band in the right parietal cortex was observed. The ERSP plots reveled alpha/beta desynchronizations within a 500-3000 ms interval after task onset and slow-wave synchronization within an interval of 150-350 ms. Amplitudes of these intervals reflected the accuracy of error recognition, and were differently associated with the three (lexical, arithmetic and algebraic) conditions. The level of trait anxiety was positively correlated with the amplitude of alpha/beta desynchronization. The level of mathematical anxiety was negatively correlated with the amplitude of theta synchronization and of alpha/beta desynchronization. Overall, trait anxiety was related with an increase in brain activation during task execution, whereas mathematical anxiety was associated with increased inhibitory-related activity. We gratefully acknowledge the support from the №11.G34.31.0043 grant from the Government of the Russian Federation.

Keywords: anxiety, EEG, lexical and numerical error-recognition tasks, alpha/beta desynchronization

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Authors: Jingling Li, Yi Zhang, Wei Liang, Tao Cui, Jun Li

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Compared with terrestrial network, the traffic of spatial information network has both self-similarity and short correlation characteristics. By studying its traffic prediction method, the resource utilization of spatial information network can be improved, and the method can provide an important basis for traffic planning of a spatial information network. In this paper, considering the accuracy and complexity of the algorithm, the spatial information network traffic is decomposed into approximate component with long correlation and detail component with short correlation, and a time series hybrid prediction model based on wavelet decomposition is proposed to predict the spatial network traffic. Firstly, the original traffic data are decomposed to approximate components and detail components by using wavelet decomposition algorithm. According to the autocorrelation and partial correlation smearing and truncation characteristics of each component, the corresponding model (AR/MA/ARMA) of each detail component can be directly established, while the type of approximate component modeling can be established by ARIMA model after smoothing. Finally, the prediction results of the multiple models are fitted to obtain the prediction results of the original data. The method not only considers the self-similarity of a spatial information network, but also takes into account the short correlation caused by network burst information, which is verified by using the measured data of a certain back bone network released by the MAWI working group in 2018. Compared with the typical time series model, the predicted data of hybrid model is closer to the real traffic data and has a smaller relative root means square error, which is more suitable for a spatial information network.

Keywords: spatial information network, traffic prediction, wavelet decomposition, time series model

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Authors: Wanhyun Cho, Soonja Kang, Sanggoon Kim, Soonyoung Park

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We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered an efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, importance sampling, approximate posterior distribution, marginal likelihood evidence

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: K. Sanjayani, C. Saraswathy, S. Sreenivasan, S. Sudhahar, D. Suganya, K. S. Neelukumari, N. Vijayarangan

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Double Base Number System (DBNS) is an imminent system of representing a number using two bases namely 2 and 3, which has its application in Elliptic Curve Cryptography (ECC) and Digital Signature Algorithm (DSA).The previous binary method representation included only base 2. DBNS uses an approximation algorithm namely, Greedy Algorithm. By using this algorithm, the number of digits required to represent a larger number is less when compared to the standard binary method that uses base 2 algorithms. Hence, the computational speed is increased and time being reduced. The standard binary method uses binary digits 0 and 1 to represent a number whereas the DBNS method uses binary digit 1 alone to represent any number (canonical form). The greedy algorithm uses two ways to represent the number, one is by using only the positive summands and the other is by using both positive and negative summands. In this paper, arithmetic operations are used for elliptic curve cryptography. Elliptic curve discrete logarithm problem is the foundation for most of the day to day elliptic curve cryptography. This appears to be a momentous hard slog compared to digital logarithm problem. In elliptic curve digital signature algorithm, the key generation requires 160 bit of data by usage of standard binary representation. Whereas, the number of bits required generating the key can be reduced with the help of double base number representation. In this paper, a new technique is proposed to generate key during encryption and extraction of key in decryption.

Keywords: cryptography, double base number system, elliptic curve cryptography, elliptic curve digital signature algorithm

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Authors: Sanaa Chafik, Imane Daoudi, Mounim A. El Yacoubi, Hamid El Ouardi

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Locality Sensitive Hashing (LSH) is one of the most promising techniques for solving nearest neighbour search problem in high dimensional space. Euclidean LSH is the most popular variation of LSH that has been successfully applied in many multimedia applications. However, the Euclidean LSH presents limitations that affect structure and query performances. The main limitation of the Euclidean LSH is the large memory consumption. In order to achieve a good accuracy, a large number of hash tables is required. In this paper, we propose a new hashing algorithm to overcome the storage space problem and improve query time, while keeping a good accuracy as similar to that achieved by the original Euclidean LSH. The Experimental results on a real large-scale dataset show that the proposed approach achieves good performances and consumes less memory than the Euclidean LSH.

Keywords: approximate nearest neighbor search, content based image retrieval (CBIR), curse of dimensionality, locality sensitive hashing, multidimensional indexing, scalability

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