Search results for: perturbation analysis

Authors: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

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In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: Fuad Ali Mohammed Al-Yarimi

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Many algorithms have been proposed to provide privacy preserving in data mining. These protocols are based on two main approaches named as: the perturbation approach and the Cryptographic approach. The first one is based on perturbation of the valuable information while the second one uses cryptographic techniques. The perturbation approach is much more efficient with reduced accuracy while the cryptographic approach can provide solutions with perfect accuracy. However, the cryptographic approach is a much slower method and requires considerable computation and communication overhead. In this paper, a new scalable protocol is proposed which combines the advantages of the perturbation and distortion along with cryptographic approach to perform privacy preserving in distributed frequent itemset mining on horizontally distributed data. Both the privacy and performance characteristics of the proposed protocol are studied empirically.

Keywords: anonymity data, data mining, distributed frequent itemset mining, gaussian perturbation, perturbation approach, privacy preserving data mining

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Authors: Soran Aminiaghdam, Christian Rode, Reinhard Blickhan, Astrid Zech

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Despite considerable studies on the impact of imposed trunk posture on human walking, less is known about such locomotion while negotiating changes in ground level. The aim of this study was to investigate the behavior of the VBCOM in response to a two-fold expected perturbation, namely alterations in body posture and in ground level. To this end, the kinematic data and ground reaction forces of twelve able participants were collected. We analyzed the vertical position of the body center of mass (VBCOM) from the ground determined by the body segmental analysis method relative to the laboratory coordinate system at touchdown and toe-off instants during walking across uneven ground — characterized by perturbation contact (a 10-cm visible drop) and pre- and post-perturbation contacts — in comparison to unperturbed level contact while maintaining three postures (regular erect, ~30° and ~50° of trunk flexion from the vertical). The VBCOM was normalized to the distance between the greater trochanter marker and the lateral malleoli marker at the instant of TD. Moreover, we calculated the backward rotation during step-down as the difference of the maximum of the trunk angle in the pre-perturbation contact and the minimal trunk angle in the perturbation contact. Two-way repeated measures ANOVAs revealed contact-specific effects of posture on the VBCOM at touchdown (F = 5.96, p = 0.00). As indicated by the analysis of simple main effects, during unperturbed level and pre-perturbation contacts, no between-posture differences for the VBCOM at touchdown were found. In the perturbation contact, trunk-flexed gaits showed a significant increase of VBCOM as compared to the pre-perturbation contact. In the post-perturbation contact, the VBCOM demonstrated a significant decrease in all gait postures relative to the preceding corresponding contacts with no between-posture differences. Main effects of posture revealed that the VBCOM at toe-off significantly decreased in trunk-flexed gaits relative to the regular erect gait. For the main effect of contact, the VBCOM at toe-off demonstrated changes across perturbation and post-perturbation contacts as compared to the unperturbed level contact. Furthermore, participants exhibited a backward trunk rotation during step-down possibly to control the angular momentum of their whole body. A more pronounced backward trunk rotation (2- to 3-fold compared with level contacts) in trunk-flexed walking contributed to the observed elevated VBCOM during the step-down which may have facilitated drop negotiation. These results may shed light on the interaction between posture and locomotion in able gait, and specifically on the behavior of the body center of mass during perturbed locomotion.

Keywords: center of mass, perturbation, posture, uneven ground, walking

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Authors: Nosratollah Hedayatpour, Hamid Reza Taheri, Mehrdad Fathi

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Introduction: Quadriceps femoris muscle is frequently involved in various movements e.g., jumping, landing) during sport and/or daily activities. During ballistic movement when individuals are faced with unexpected knee perturbation, fast twitch muscle fibers contribute to force production to stabilize knee joint. Fast twitch muscle fiber is more susceptible to fatigue and therefor may reduce the ability of the quadriceps muscle to stabilize knee joint during fast perturbation. Aim: The aim of this study was to investigate the effect of fatigue on postural response of the knee extensor muscles to fast and slow perturbations. Methods: Fatigue was induced to the quadriceps muscle using a KinCom Isokinetic Dynamometer (Chattanooga, TN). Bipolar surface electromyography (EMG) signals were simultaneously recorded from quadriceps components (vastus medialis, rectus femoris, and vastus lateralis) during pre- and post-fatigue postural perturbation performed at two different velocities of 120 ms and 250 mes. Results: One-way ANOVA showed that maximal voluntary knee extension force and time to task failure, and associated EMG activities were significantly reduced after fatiguing knee exercise (P< 0.05). Two-ways ANOVA also showed that ARV of EMG during backward direction was significantly larger than forward direction (P< 0.05), and during fast-perturbation it was significantly higher than slow-perturbation (P< 0.05). Moreover, ARV of EMG was significantly reduced during post fatigue perturbation, with the largest reduction identified for fast-perturbation compared with slow perturbation (P< 0.05). Conclusion: A larger reduction in muscle activity of the quadriceps muscle was observed during post fatigue fast-perturbation to stabilize knee joint, most likely due to preferential recruitment of fast twitch muscle fiber which are more susceptible to fatigue. This may partly explain that why knee injuries is common after fast ballistic movement.

Keywords: electromyography, fast-slow perturbations, fatigue, quadriceps femoris muscle

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Authors: Nicolas Thiers, Romain Gers, Olivier Skurtys

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In this work, we study numerically the effect of a thermal perturbation on the heat transfer in a rectangular differentially heated cavity of aspect ratio 4, filled by air. In order to maintain the center symmetry, the thermal perturbation is imposed by a square wave at both active walls, at the same relative position of the hot or cold boundary layers. The influences of the amplitude and the vertical location of the perturbation are investigated. The air flow is calculated solving the unsteady Boussinesq-Navier-Stokes equations using the PN - PN-2 Spectral Element Method (SEM) programmed in the Nek5000 opencode, at RaH= 9x107, just before the first bifurcation which leads to periodical flow. The results show that the perturbation has a major impact for the highest amplitude, and at about three quarters of the cavity height, upstream, in both hot and cold boundary layers.

Keywords: direct numerical simulation, heat transfer enhancement, localized thermal perturbations, natural convection, rectangular differentially-heated cavity

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Authors: Noufe H. Aljahdaly

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The Laplace homotopy perturbation method (LHPM) is an approximate method that help to compute the approximate solution for partial differential equations. The method has been used for solving several problems in science. It requires the initial condition, so it solves the initial value problem. In physics, when some important terms are taken in account, we may obtain non-integrable partial differential equations that do not have analytical integrals. This type of PDEs do not have exact solution, therefore, we need to compute the solution without initial condition. In this work, we improved the LHPM to be able to solve non-integrable problem, especially the damped PDEs, which are the PDEs that include a damping term which makes the PDEs non-integrable. We improved the LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for damped PDE as the initial condition for non-damped PDE.

Keywords: non-integrable PDEs, modified Kawahara equation;, laplace homotopy perturbation method, damping term

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Authors: Sameena Tarannum, S. Pranesh

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The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: gravity modulation, Oldroyd-b liquid, triple diffusive convection, venezian approach

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

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This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: online data updates, covariance matrix, online principle component analysis, matrix perturbation

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: S. H. Iranmanesh, L. Aliabadi, A. Mollajan

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Integrated resilience engineering (IRE) is capable of returning banking systems to the normal state in extensive economic circumstances. In this study, information system of a large bank (with several branches) is assessed and optimized under severe economic conditions. Data envelopment analysis (DEA) models are employed to achieve the objective of this study. Nine IRE factors are considered to be the outputs, and a dummy variable is defined as the input of the DEA models. A standard questionnaire is designed and distributed among executive managers to be considered as the decision-making units (DMUs). Reliability and validity of the questionnaire is examined based on Cronbach's alpha and t-test. The most appropriate DEA model is determined based on average efficiency and normality test. It is shown that the proposed integrated design provides higher efficiency than the conventional RE design. Results of sensitivity and perturbation analysis indicate that self-organization, fault tolerance, and reporting culture respectively compose about 50 percent of total weight.

Keywords: banking system, Data Envelopment Analysis (DEA), Integrated Resilience Engineering (IRE), performance evaluation, perturbation analysis

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Authors: Myunggon Yoon, Jung-Ho Moon

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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: combustor, dynamics, thermoacoustics, transfer function

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Authors: Susy Thomas, Sajju Thomas, Varghese Vaidyan

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This paper considers SMCs using linear feedback with switched gains and proposes a method which can minimize the pole perturbation. The method is able to enhance the robustness property of the controller. A pre-assigned neighborhood of the ‘nominal’ positions is assigned and the system poles are not allowed to stray out of these bounds even when parameters variations/uncertainties act upon the system. A quasi SMM is maintained within the assigned boundaries of the sliding surface.

Keywords: parameter variations, pole perturbation, sliding mode control, switching surface, robust switching vector

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

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A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: elasto-aerodynamic lubrication, air foil bearing, steady-state deformation, dynamic deformation, stiffness and damping coefficients, perturbation method, fluid-structure interaction, Galerk infinite element method, finite difference method

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

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So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: Hamid Reza Pakzad

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In this paper, the properties of dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma, whose constituents are inertial ions, superthermal electrons, and stationary dust particles, are investigated by employing the reductive perturbation method. The dissipation is taken into account the kinematic viscosity among the plasma constituents. It is shown that the basic features of DIA shock waves are significantly modified by the effects of electron superthermality and ion kinematic viscosity.

Keywords: reductive perturbation method, dust ion acoustic shock wave, superthermal electron, dissipative plasmas

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Song Ni, Junxiang Xu

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This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Mehdi Jalalpour, Mazdak Tootkaboni

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We present a computationally efficient method for reliability-based topology optimization under material properties uncertainty, which is assumed to be lognormally distributed and correlated within the domain. Computational efficiency is achieved through estimating the response statistics with stochastic perturbation of second order, using these statistics to fit an appropriate distribution that follows the empirical distribution of the response, and employing an efficient gradient-based optimizer. The proposed algorithm is utilized for design of new structures and the changes in the optimized topology is discussed for various levels of target reliability and correlation strength. Predictions were verified thorough comparison with results obtained using Monte Carlo simulation.

Keywords: material uncertainty, stochastic perturbation, structural reliability, topology optimization

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Authors: Bandar Alahmadi, Manohar Mareboyana, Lethia Jackson

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Today, there are many applications that are using computer vision models, such as face recognition, image classification, and object detection. The accuracy of these models is very important for the performance of these applications. One challenge that facing the computer vision models is the adversarial examples attack. In computer vision, the adversarial example is an image that is intentionally designed to cause the machine learning model to misclassify it. One of very well-known method that is used to attack the Convolution Neural Network (CNN) is Fast Gradient Sign Method (FGSM). The goal of this method is to find the perturbation that can fool the CNN using the gradient of the cost function of CNN. In this paper, we introduce a novel model that can attack Regional-Convolution Neural Network (R-CNN) that use FGSM. We first extract the regions that are detected by R-CNN, and then we resize these regions into the size of regular images. Then, we find the best perturbation of the regions that can fool CNN using FGSM. Next, we add the resulted perturbation to the attacked region to get a new region image that looks similar to the original image to human eyes. Finally, we placed the regions back to the original image and test the R-CNN with the attacked images. Our model could drop the accuracy of the R-CNN when we tested with Pascal VOC 2012 dataset.

Keywords: adversarial examples, attack, computer vision, image processing

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

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The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method, wire coating die

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Authors: Dingyang Hu, Dan Liu

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DNN (Deep Neural Network) deep learning models are widely used in classification, prediction, and other task scenarios. To address the difficulties of generic adversarial perturbation generation for deep learning models under black-box conditions, a generic adversarial ingestion generation method based on a saliency map (CJsp) is proposed to obtain salient image regions by counting the factors that influence the input features of an image on the output results. This method can be understood as a saliency map attack algorithm to obtain false classification results by reducing the weights of salient feature points. Experiments also demonstrate that this method can obtain a high success rate of migration attacks and is a batch adversarial sample generation method.

Keywords: adversarial sample, gradient, probability, black box

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Authors: Azam Zare

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Separation flow control for performance enhancement over airfoils at high incidence angle has become an increasingly important topic. This work details the characteristics of an efficient feedback control of the turbulent subsonic flow over NACA23012 airfoil using forced reduced‐order model based on the proper orthogonal decomposition/Galerkin projection and perturbation method on the compressible Reynolds Averaged Navier‐Stokes equations. The forced reduced‐order model is used in the optimal control of the turbulent separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 5×106, and high incidence angle of 24° using blowing/suction controlling jets. The Spallart-Almaras turbulence model is implemented for high Reynolds number calculations. The main shortcoming of the POD/Galerkin projection on flow equations for controlling purposes is that the blowing/suction controlling jet velocity does not show up explicitly in the resulting reduced order model. Combining perturbation method and POD/Galerkin projection on flow equations introduce a forced reduced‐order model that can predict the time-varying influence of the blowing/suction controlling jet velocity. An optimal control theory based on forced reduced‐order system is used to design a control law for a nonlinear reduced‐order model, which attempts to minimize the vorticity content in the turbulent flow field over NACA23012 airfoil. Numerical simulations were performed to help understand the behavior of the controlled suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. Analysis of streamline profiles indicates that the blowing/suction jets are efficient in removing separation bubbles and increasing the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate Manner.

Keywords: flow control, POD, Galerkin projection, separation

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Authors: E. I. Ugwu

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Theoretical analysis of the optical and Solid State properties of ZnS thin film using beam propagation technique in which a scalar wave is propagated through the material thin film deposited on a substrate with the assumption that the dielectric medium is section into a homogenous reference dielectric constant term, and a perturbed dielectric term, representing the deposited thin film medium is presented in this work. These two terms, constitute arbitrary complex dielectric function that describes dielectric perturbation imposed by the medium of for the system. This is substituted into a defined scalar wave equation in which the appropriate Green’s Function was defined on it and solved using series technique. The green’s value obtained from Green’s Function was used in Dyson’s and Lippmann Schwinger equations in conjunction with Born approximation method in computing the propagated field for different input regions of field wavelength during which the influence of the dielectric constants and mesh size of the thin film on the propagating field were depicted. The results obtained from the computed field were used in turn to generate the data that were used to compute the band gaps, solid state and optical properties of the thin film such as reflectance, Transmittance and reflectance with which the band gap obtained was found to be in close approximate to that of experimental value.

Keywords: scalar wave, optical and solid state properties, thin film, dielectric medium, perturbation, Lippmann Schwinger equations, Green’s Function, propagation

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Authors: Diego F. Camacho, Cristian J. Mejia, Carlos Duque-Daza

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The recent widespread use of Unmanned Aerial Vehicles (UAVs) has fueled a renewed interest in efficiency and performance of airfoils, particularly for applications at low and moderate Reynolds numbers, typical of this kind of vehicles. Most of previous efforts in the aeronautical industry, regarding aerodynamic efficiency, had been focused on high Reynolds numbers applications, typical of commercial airliners and large size aircrafts. However, in order to increase the levels of efficiency and to boost the performance of these UAV, it is necessary to explore new alternatives in terms of airfoil design and application of drag reduction techniques. The objective of the present work is to carry out the analysis and comparison of performance levels between a standard NACA0012 profile against another one featuring a wall protuberance or surface perturbation. A computational model, based on the finite volume method, is employed to evaluate the effect of the presence of geometrical distortions on the wall. The performance evaluation is achieved in terms of variations of drag and lift coefficients for the given profile. In particular, the aerodynamic performance of the new design, i.e. the airfoil with a surface perturbation, is examined under conditions of incompressible and subsonic flow in transient state. The perturbation considered is a shaped protrusion prescribed as a small surface deformation on the top wall of the aerodynamic profile. The ultimate goal by including such a controlled smooth artificial roughness was to alter the turbulent boundary layer. It is shown in the present work that such a modification has a dramatic impact on the aerodynamic characteristics of the airfoil, and if properly adjusted, in a positive way. The computational model was implemented using the unstructured, FVM-based open source C++ platform OpenFOAM. A number of numerical experiments were carried out at Reynolds number 5x104, based on the length of the chord and the free-stream velocity, and angles of attack 6° and 12°. A Large Eddy Simulation (LES) approach was used, together with the dynamic Smagorinsky approach as subgrid scale (SGS) model, in order to account for the effect of the small turbulent scales. The impact of the surface perturbation on the performance of the airfoil is judged in terms of changes in the drag and lift coefficients, as well as in terms of alterations of the main characteristics of the turbulent boundary layer on the upper wall. A dramatic change in the whole performance can be appreciated, including an arguably large level of lift-to-drag coefficient ratio increase for all angles and a size reduction of laminar separation bubble (LSB) for a twelve-angle-of-attack.

Keywords: CFD, LES, Lift-to-drag ratio, LSB, NACA 0012 airfoil

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Authors: James Jr. Mashiyane, Risuna Nkolele, Stephanie J. Müller, Gciniwe S. Dlamini, Rebone L. Meraba, Darlington S. Mapiye

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When performing language tasks in natural language processing (NLP), the dimensionality of word embeddings is chosen either ad-hoc or is calculated by optimizing the Pairwise Inner Product (PIP) loss. The PIP loss is a metric that measures the dissimilarity between word embeddings, and it is obtained through matrix perturbation theory by utilizing the unitary invariance of word embeddings. Unlike in natural language, in genomics, especially in genome sequence processing, unlike in natural language processing, there is no notion of a “word,” but rather, there are sequence substrings of length k called k-mers. K-mers sizes matter, and they vary depending on the goal of the task at hand. The dimensionality of word embeddings in NLP has been studied using the matrix perturbation theory and the PIP loss. In this paper, the sufficiency and reliability of applying word-embedding algorithms to various genomic sequence datasets are investigated to understand the relationship between the k-mer size and their embedding dimension. This is completed by studying the scaling capability of three embedding algorithms, namely Latent Semantic analysis (LSA), Word2Vec, and Global Vectors (GloVe), with respect to the k-mer size. Utilising the PIP loss as a metric to train embeddings on different datasets, we also show that Word2Vec outperforms LSA and GloVe in accurate computing embeddings as both the k-mer size and vocabulary increase. Finally, the shortcomings of natural language processing embedding algorithms in performing genomic tasks are discussed.

Keywords: word embeddings, k-mer embedding, dimensionality reduction

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Authors: Orhun Aydin, Mark V. Janikas, Rodrigo Alves, Renato Assuncao

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In this paper, a tree-based perturbation methodology for regionalization inference is presented. Regionalization is a constrained optimization problem that aims to create groups with similar attributes while satisfying spatial contiguity constraints. Similar to any constrained optimization problem, the spatial constraint may hinder convergence to some global minima, resulting in spatially contiguous members of a group with dissimilar attributes. This paper presents a general methodology for rigorously perturbing spatial constraints through the use of random spanning trees. The general framework presented can be used to quantify the effect of the spatial constraints in the overall regionalization result. We compare several types of stochastic spanning trees used in inference problems such as fuzzy regionalization and determining the number of regions. Performance of stochastic spanning trees is juxtaposed against the traditional permutation-based hypothesis testing frequently used in spatial statistics. Inference results for fuzzy regionalization and determining the number of regions is presented on the Local Area Personal Incomes for Texas Counties provided by the Bureau of Economic Analysis.

Keywords: regionalization, constrained clustering, probabilistic inference, fuzzy clustering

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Authors: A. Jawahar

Abstract:

In this paper, the dependence of soliton pulses with respect to phase in a 10 Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the I also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point I.

Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system

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