Search results for: non-linear exponential (NLINEX) loss function

Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: covariation reasoning, exponential function, modeling, representations

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Authors: Nicolò Vaiana, Giorgio Serino

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The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: C. Pislaru, A. Shebani

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This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the K-Means clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: system identification, nonlinear systems, neural networks, radial basis function, K-means clustering algorithm

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

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This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: Bina Kumari, Subir K. Sarkar, Pradipta Bandyopadhyay

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The autocorrelation function of the density fluctuation is studied in each of the two phases in a Gibbs Ensemble Monte Carlo (GEMC) simulation of the problem of phase separation for a square well potential with various values of its range. We find that the normalized autocorrelation function is described very well as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of (α, τ₁, τ₂) on the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We also analyse the issue of how to choose the parameters of the GEMC simulation optimally.

Keywords: autocorrelation function, density fluctuation, GEMC, simulation

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Authors: Sule Sahin, Basak Bulut Karageyik

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This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

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Authors: Grienggrai Rajchakit

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This paper is concerned with the exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, time-varying delays, lyapunov-krasovskii functional, leibniz-newton's formula

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Keywords: base isolation, hardening behavior, nonlinear exponential model, seismic isolators, softening behavior

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: Swapan Maiti, Dipanwita Roy Chowdhury

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Nonlinear functions are essential in different cryptoprimitives as they play an important role on the security of the cipher designs. Rule 30 was identified as a powerful nonlinear function for cryptographic applications. However, an attack (MS attack) was mounted against Rule 30 Cellular Automata (CA). Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide maximum length cycle as well as better cryptographic primitives and they are also secure against MS attack.

Keywords: cellular automata, maximum period nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: grey relational degree, multiple linear regression, membership function, nonlinear programming

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

Abstract:

The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Keywords: base-isolated structures, earthquake engineering, mixed time integration, nonlinear exponential model

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Authors: S. Olyaee, M. Seifouri, A. Nikoosohbat, M. Shams Esfand Abadi

Abstract:

Photonic Crystal Fibers (PCFs) can be used in optical communications as transmission lines. For this reason, the PCFs with low confinement loss, low chromatic dispersion, and low nonlinear effects are highly suitable transmission media. In this paper, we introduce a new design of index-guiding photonic crystal fiber (IG-PCF) with ultra-low chromatic dispersion, low nonlinearity effects, and low confinement loss. Relatively low dispersion is achieved in the wavelength range of 1200 to 1600 nm using the proposed design. According to the new structure of IG-PCF presented in this study, the chromatic dispersion slope is -30(ps/km.nm) and the confinement loss reaches below 10-7 dB/km. While in the wavelength range mentioned above at the same time an effective area of more than 50.2μm2 is obtained.

Keywords: optical communication systems, index-guiding, dispersion, confinement loss, photonic crystal fiber

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Authors: Minas Balyan

Abstract:

Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Hao Chen, Bo Guo, Ping Jiang

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Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: Yoonsuh Jung, Steven N. MacEachern

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Check loss function is used to define quantile regression. In the prospect of cross validation, it is also employed as a validation function when underlying truth is unknown. However, our empirical study indicates that the validation with check loss often leads to choosing an over estimated fits. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. It has a large effect of guarding against over fitted model in some extent. Through various simulation settings of linear and non-linear regressions, the improvement of check loss by L2 adjustment is empirically examined. This adjustment is devised to shrink to zero as sample size grows.

Keywords: cross-validation, model selection, quantile regression, tuning parameter selection

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Authors: Haowen Xi

Abstract:

We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

Abstract:

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: artificial immune system, breast cancer diagnosis, Euclidean function, Gaussian function

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Authors: S. Olyaee, M. Seifouri, A. Nikoosohbat, M. Shams Esfand Abadi

Abstract:

Photonic Crystal Fibers (PCFs) can be used in optical communications as transmission lines. For this reason, the PCFs with low confinement loss, low chromatic dispersion, and low nonlinear effects are highly suitable transmission media. In this paper, we introduce a new design of index-guiding nanostructured photonic crystal fiber (IG-NPCF) with ultra-low chromatic dispersion, low nonlinearity effects, and low confinement loss. Relatively low dispersion is achieved in the wavelength range of 1200 to 1600nm using the proposed design. According to the new structure of nanostructured PCF presented in this study, the chromatic dispersion slope is -30(ps/km.nm) and the confinement loss reaches below 10-7 dB/km. While in the wavelength range mentioned above at the same time an effective area of more than 50.2μm2 is obtained.

Keywords: optical communication systems, nanostructured, index-guiding, dispersion, confinement loss, photonic crystal fiber

Procedia PDF Downloads 533

Authors: Yehjune Heo

Abstract:

As biometric systems become widely deployed, the security of identification systems can be easily attacked by various spoof materials. This paper contributes to finding a reliable and practical anti-spoofing method using Convolutional Neural Networks (CNNs) based on the types of loss functions and optimizers. The types of CNNs used in this paper include AlexNet, VGGNet, and ResNet. By using various loss functions including Cross-Entropy, Center Loss, Cosine Proximity, and Hinge Loss, and various loss optimizers which include Adam, SGD, RMSProp, Adadelta, Adagrad, and Nadam, we obtained significant performance changes. We realize that choosing the correct loss function for each model is crucial since different loss functions lead to different errors on the same evaluation. By using a subset of the Livdet 2017 database, we validate our approach to compare the generalization power. It is important to note that we use a subset of LiveDet and the database is the same across all training and testing for each model. This way, we can compare the performance, in terms of generalization, for the unseen data across all different models. The best CNN (AlexNet) with the appropriate loss function and optimizers result in more than 3% of performance gain over the other CNN models with the default loss function and optimizer. In addition to the highest generalization performance, this paper also contains the models with high accuracy associated with parameters and mean average error rates to find the model that consumes the least memory and computation time for training and testing. Although AlexNet has less complexity over other CNN models, it is proven to be very efficient. For practical anti-spoofing systems, the deployed version should use a small amount of memory and should run very fast with high anti-spoofing performance. For our deployed version on smartphones, additional processing steps, such as quantization and pruning algorithms, have been applied in our final model.

Keywords: anti-spoofing, CNN, fingerprint recognition, loss function, optimizer

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Authors: Mrinal Jana, Geetanjali Panda

Abstract:

In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

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Authors: John Knight, Fuchun Li, Yan Xu

Abstract:

Based on a new method of the nonparametric estimator of the drift function, we propose a consistent test for the parametric specification of the drift function in the short rate diffusion process using observations from a panel of yields. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric drift function is correctly specified, and converges to infinity under the alternative. Taking the daily 7-day European rates as a proxy of the short rate, we use our test to examine whether the drift of the short rate diffusion process is linear or nonlinear, which is an unresolved important issue in the short rate modeling literature. The testing results indicate that none of the drift functions in this literature adequately captures the dynamics of the drift, but nonlinear specification performs better than the linear specification.

Keywords: diffusion process, nonparametric estimation, derivative security price, drift function and volatility function

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Authors: Owolabi Kolade Matthew

Abstract:

In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

Procedia PDF Downloads 386