Search results for: inverse Gaussian distribution

Authors: Mkhinini Maher, Knani Jilani

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We present in this work the performances of a mobile omnidirectional robot through evaluating its management of the redundancy of actuation. Thus we come to the predictive control implemented. The distribution of the wringer on the robot actions, through the inverse pseudo of Moore-Penrose, corresponds to a -geometric- distribution of efforts. We will show that the load on vehicle wheels would not be equi-distributed in terms of wheels configuration and of robot movement. Thus, the threshold of sliding is not the same for the three wheels of the vehicle. We suggest exploiting the redundancy of actuation to reduce the risk of wheels sliding and to ameliorate, thereby, its accuracy of displacement. This kind of approach was the subject of study for the legged robots.

Keywords: mobile robot, actuation, redundancy, omnidirectional, inverse pseudo moore-penrose, reductive control

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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

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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: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

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This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: aeroacoustics, fluid-structure coupling, inverse methods, naval, turbulent flow

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Authors: Jeremie Coullon, Robert J. Webber

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We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Carlos Gonzales, Zaida Quiroz, Marcos Prates

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Several spatial variables collected at the same location that share a common spatial distribution can be modeled simultaneously through a multivariate geostatistical model that takes into account the correlation between these variables and the spatial autocorrelation. The main goal of this model is to perform spatial prediction of these variables in the region of study. Here we focus on a geostatistical multivariate formulation that relies on sharing common spatial random effect terms. In particular, the first response variable can be modeled by a mean that incorporates a shared random spatial effect, while the other response variables depend on this shared spatial term, in addition to specific random spatial effects. Each spatial random effect is defined through a Gaussian process with a valid covariance function, but in order to improve the computational efficiency when the data are large, each Gaussian process is approximated to a Gaussian random Markov field (GRMF), specifically to the block nearest neighbor Gaussian process (Block-NNGP). This approach involves dividing the spatial domain into several dependent blocks under certain constraints, where the cross blocks allow capturing the spatial dependence on a large scale, while each individual block captures the spatial dependence on a smaller scale. The multivariate geostatistical model belongs to the class of Latent Gaussian Models; thus, to achieve fast Bayesian inference, it is used the integrated nested Laplace approximation (INLA) method. The good performance of the proposed model is shown through simulations and applications for massive data.

Keywords: Block-NNGP, geostatistics, gaussian process, GRMF, INLA, multivariate models.

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

Keywords: Gaussian process, nonlinearity distribution, particle filter, system identification

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Authors: Sandeep Kumar, Naveen Gupta

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The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing.

Keywords: non-Gaussian beam, collisional plasma, variational theory, self-focusing

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Authors: Levent Basayigit, Sinan Demir, Yusuf Ucar, Burhan Kara

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Many research projects require accurate delineation of the different land cover type of the agricultural area. Especially it is critically important for the definition of specific plants like cannabis. However, the complexity of vegetation stands structure, abundant vegetation species, and the smooth transition between different seconder section stages make vegetation classification difficult when using traditional approaches such as the maximum likelihood classifier. Most of the time, classification distinguishes only between trees/annual or grain. It has been difficult to accurately determine the cannabis mixed with other plants. In this paper, a mixed distribution models approach is applied to classify pure and mix cannabis parcels using Worldview-2 imagery in the Lakes region of Turkey. Five different land use types (i.e. sunflower, maize, bare soil, and cannabis) were identified in the image. A constrained Gaussian mixture discriminant analysis (GMDA) was used to unmix the image. In the study, 255 reflectance ratios derived from spectral signatures of seven bands (Blue-Green-Yellow-Red-Rededge-NIR1-NIR2) were randomly arranged as 80% for training and 20% for test data. Gaussian mixed distribution model approach is proved to be an effective and convenient way to combine very high spatial resolution imagery for distinguishing cannabis vegetation. Based on the overall accuracies of the classification, the Gaussian mixed distribution model was found to be very successful to achieve image classification tasks. This approach is sensitive to capture the illegal cannabis planting areas in the large plain. This approach can also be used for monitoring and determination with spectral reflections in illegal cannabis planting areas.

Keywords: Gaussian mixture discriminant analysis, spectral mixture model, Worldview-2, land parcels

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Authors: Lina Pan

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In non-Gaussian clutter of a spherically invariant random vector, in the cases that a certain estimated covariance matrix could become singular, the adaptive target detection of high-range-resolution radar is addressed. Firstly, the restricted maximum likelihood (RML) estimates of unknown covariance matrix and scatterer amplitudes are derived for non-Gaussian clutter. And then the RML estimate of texture is obtained. Finally, a novel detector is devised. It is showed that, without secondary data, the proposed detector outperforms the existing Kelly binary integrator.

Keywords: non-Gaussian clutter, covariance matrix estimation, target detection, maximum likelihood

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue

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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

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Authors: Muhammad Farooq, Ahtasham Gul

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To meet the desired standard, it is important to monitor and analyze different engineering processes to get desired output. The bivariate distributions got a lot of attention in recent years to describe the randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed using two independent models developed by the nesting approach to study the effect of each component on reliability for better understanding. Further, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution, like mean median and quantile function, are discussed. We use inverse Gamma prior to study its frequentist properties by conducting Monte Carlo Markov Chain (MCMC) sampling scheme.

Keywords: reliability, system availability Weibull, inverse Lomax, Monte Carlo Markov Chain, Bayesian

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Authors: Abhisek Sinha, Debobrata Rajak, Shilpa Rani, Ram Gopal, Vandana Sharma

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The interaction of femtosecond laser pulses with metallic tips has been studied extensively, and they have proved to be a very good source of ultrashort electron pulses. A study of the interaction of femtosecond Laguerre-Gaussian (LG) laser modes with Tungsten tips is presented here. Laser pulses of 35 fs pulse durations were incident on Tungsten tips, and their electron emission rates were studied for LG (l=1, p=0) and Gaussian modes. A change in the order of the interaction for LG beams is reported, and the difference in the order of interaction is attributed to ponderomotive shifts in the energy levels corresponding to the enhanced near-field intensity supported by numerical simulations.

Keywords: femtosecond, Laguerre-Gaussian, OAM, tip

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Authors: N. Jinesh, K. Shankar

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This article presents a method of using the one dimensional piezo-electric patch on beam model for structural identification. A hybrid element constituted of one dimensional beam element and a PZT sensor is used with reduced material properties. This model is convenient and simple for identification of beams. Accuracy of this element is first verified against a corresponding 3D finite element model (FEM). The structural identification is carried out as an inverse problem whereby parameters are identified by minimizing the deviation between the predicted and measured voltage response of the patch, when subjected to excitation. A non-classical optimization algorithm Particle Swarm Optimization is used to minimize this objective function. The signals are polluted with 5% Gaussian noise to simulate experimental noise. The proposed method is applied on beam structure and identified parameters are stiffness and damping. The model is also validated experimentally.

Keywords: inverse problem, particle swarm optimization, PZT patches, structural identification

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Authors: Keunhong Chae, Seokho Yoon

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This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.

Keywords: frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM

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Authors: An Chengrui, Yin Zi, Wu Bingbing, Ma Yuanzhu, Jin Kaixiu, Chen Xiao, Ouyang Hongwei

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Single cell RNA sequence (scRNA-seq) is one of the effective tools to study transcriptomics of biological processes. Recently, similarity measurement of cells is Euclidian distance or its derivatives. However, the process of scRNA-seq is a multi-variate Bernoulli event model, thus we hypothesize that it would be more efficient when the divergence between cells is valued with relative entropy than Euclidian distance. In this study, we compared the performances of Euclidian distance, Spearman correlation distance and Relative Entropy using scRNA-seq data of the early, medial and late stage of limb development generated in our lab. Relative Entropy is better than other methods according to cluster potential test. Furthermore, we developed KL-SNE, an algorithm modifying t-SNE whose definition of divergence between cells Euclidian distance to Kullback–Leibler divergence. Results showed that KL-SNE was more effective to dissect cell heterogeneity than t-SNE, indicating the better performance of relative entropy than Euclidian distance. Specifically, the chondrocyte expressing Comp was clustered together with KL-SNE but not with t-SNE. Surprisingly, cells in early stage were surrounded by cells in medial stage in the processing of KL-SNE while medial cells neighbored to late stage with the process of t-SNE. This results parallel to Heatmap which showed cells in medial stage were more heterogenic than cells in other stages. In addition, we also found that results of KL-SNE tend to follow Gaussian distribution compared with those of the t-SNE, which could also be verified with the analysis of scRNA-seq data from another study on human embryo development. Therefore, it is also an effective way to convert non-Gaussian distribution to Gaussian distribution and facilitate the subsequent statistic possesses. Thus, relative entropy is potentially a better way to determine the divergence of cells in scRNA-seq data analysis.

Keywords: Single cell RNA sequence, Similarity measurement, Relative Entropy, KL-SNE, t-SNE

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Alexander N. Pisarchik, Parth Chholak

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Intrinsic brain noise was estimated via magneto-encephalograms (MEG) recorded during perception of flickering visual stimuli with frequencies of 6.67 and 8.57 Hz. First, we measured the mean phase difference between the flicker signal and steady-state event-related field (SSERF) in the occipital area where the brain response at the flicker frequencies and their harmonics appeared in the power spectrum. Then, we calculated the probability distribution of the phase fluctuations in the regions of frequency locking and computed its kurtosis. Since kurtosis is a measure of the distribution’s sharpness, we suppose that inverse kurtosis is related to intrinsic brain noise. In our experiments, the kurtosis value varied among subjects from K = 3 to K = 5 for 6.67 Hz and from 2.6 to 4 for 8.57 Hz. The majority of subjects demonstrated leptokurtic kurtosis (K < 3), i.e., the distribution tails approached zero more slowly than Gaussian. In addition, we found a strong correlation between kurtosis and brain complexity measured as the correlation dimension, so that the MEGs of subjects with higher kurtosis exhibited lower complexity. The obtained results are discussed in the framework of nonlinear dynamics and complex network theories. Specifically, in a network of coupled oscillators, phase synchronization is mainly determined by two antagonistic factors, noise, and the coupling strength. While noise worsens phase synchronization, the coupling improves it. If we assume that each neuron and each synapse contribute to brain noise, the larger neuronal network should have stronger noise, and therefore phase synchronization should be worse, that results in smaller kurtosis. The described method for brain noise estimation can be useful for diagnostics of some brain pathologies associated with abnormal brain noise.

Keywords: brain, flickering, magnetoencephalography, MEG, visual perception, perception time

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Authors: Ngo Thi Thu, Kazuo Tanaka, Masahiro Tanaka, Dao Ngoc Chien

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Nanometric superfocusing of optical intensity near the tip of partially metal- coated dielectric conical probe of the convergent surface plasmon polariton wave is investigated by the volume integral equation method. It is possible to perform nanofocusing using this probe by using both linearly and radially polarized Gaussian beams as the incident waves. Strongly localized and enhanced optical near-fields can be created on the tip of this probe for the cases of both incident Gaussian beams. However the intensity distribution near the probe tip was found to be very sensitive to the shape of the probe tip.

Keywords: waveguide, surface plasmons, electromagnetic theory

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Authors: A. Didaoui, N. Benhalima, M. Elkeurti, A. Chouaih, F. Hamzaoui

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The monomer and dimer structures of the title molecule have been obtained from density functional theory (DFT) B3LYP method with 6-31G (d,p) as basis set calculations. The optimized geometrical parameters obtained by B3LYP/6-31G (d,p) method show good agreement with xperimental X-ray data. The polarizability and first order hyperpolarizabilty of the title molecule were calculated and interpreted. the intermolecular N–H•••O hydrogen bonds are discussed in dimer structure of the molecule. The vibrational wave numbers and their assignments were examined theoretically using the Gaussian 03 set of quantum chemistry codes. The predicted frontier molecular orbital energies at B3LYP/6-31G(d,p) method set show that charge transfer occurs within the molecule. The frontier molecular orbital calculations clearly show the inverse relationship of HOMO–LUMO gap with the total static hyperpolarizability. The results also show that N-(2-Methylphenyl)-2-nitrobenzenesulfonamide molecule may have nonlinear optical (NLO) comportment with non-zero values.

Keywords: DFT, Gaussian 03, NLO, N-(2-Methylphenyl)-2-nitrobenzenesulfonamide

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Authors: A. Didaoui, N. Benhalima, M. Elkeurti, A. Chouaih, F. Hamzaoui

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The monomer and dimer structures of the title molecule have been obtained from density functional theory (DFT) B3LYP method with 6-31G(d,p) as basis set calculations. The optimized geometrical parameters obtained by B3LYP/6-31G(d,p) method show good agreement with experimental X-ray data. The polarizability and first order hyperpolarizability of the title molecule were calculated and interpreted. The intermolecular N–H•••O hydrogen bonds are discussed in dimer structure of the molecule. The vibrational wave numbers and their assignments were examined theoretically using the Gaussian 03 set of quantum chemistry codes. The predicted frontier molecular orbital energies at B3LYP/6-31G(d,p) method set show that charge transfer occurs within the molecule. The frontier molecular orbital calculations clearly show the inverse relationship of HOMO–LUMO gap with the total static hyperpolarizability. The results also show that N-(2-Methylphenyl)-2-nitrobenzenesulfonamide molecule may have nonlinear optical (NLO) comportment with non-zero values.

Keywords: DFT, Gaussian 03, NLO, N-(2-Methylphenyl)-2-nitrobenzenesulfonamide, polarizability

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Authors: Lakshmi Prayaga, Chandra Prayaga. Aaron Wade, Gopi Shankar Mallu, Harsha Satya Pola

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Synthetic data generated by Generative Adversarial Networks and Autoencoders is becoming more common to combat the problem of insufficient data for research purposes. However, generating synthetic data is a tedious task requiring extensive mathematical and programming background. Open-source platforms such as the Synthetic Data Vault (SDV) and Mostly AI have offered a platform that is user-friendly and accessible to non-technical professionals to generate synthetic data to augment existing data for further analysis. The SDV also provides for additions to the generic GAN, such as the Gaussian copula. We present the results from two synthetic data sets (CTGAN data and CTGAN with Gaussian Copula) generated by the SDV and report the findings. The results indicate that the ROC and AUC curves for the data generated by adding the layer of Gaussian copula are much higher than the data generated by the CTGAN.

Keywords: synthetic data generation, generative adversarial networks, conditional tabular GAN, Gaussian copula

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: Rafida M. Elobaid

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Most of the literature on goodness-of-fit test try to provide a theoretical basis for studying empirical distribution functions. Such goodness-of-fit tests are Kolmogorove-Simirnov and Crumer-Von Mises Type tests. However, it is likely that most of literature has not focused in details on the relationship of the values of the test statistics and skewness or kurtosis. The aim of this study is to investigate the behavior of the values of the χ2 test statistic with the variation of the skewness of right skewed distribution. A simulation study is conducted to generate random numbers from Weibull distribution. For a fixed sample sizes, different levels of skewness are considered, and the corresponding values of the χ2 test statistic are calculated. Using different sample sizes, the results show an inverse relationship between the value of χ2 test and the level of skewness for Wiebull distribution, i.e the value of χ2 test statistic decreases as the value of skewness increases. The research results also show that with large values of skewness we are more confident that the data follows the assumed distribution. Nonparametric Kendall τ test is used to confirm these results.

Keywords: goodness-of-fit test, chi-square test, simulation, continuous right skewed distributions

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Authors: Petr Gurný

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One of the most important tasks in the risk management is the correct determination of probability of default (PD) of particular financial subjects. In this paper a possibility of determination of financial institution’s PD according to the credit-scoring models is discussed. The paper is divided into the two parts. The first part is devoted to the estimation of the three different models (based on the linear discriminant analysis, logit regression and probit regression) from the sample of almost three hundred US commercial banks. Afterwards these models are compared and verified on the control sample with the view to choose the best one. The second part of the paper is aimed at the application of the chosen model on the portfolio of three key Czech banks to estimate their present financial stability. However, it is not less important to be able to estimate the evolution of PD in the future. For this reason, the second task in this paper is to estimate the probability distribution of the future PD for the Czech banks. So, there are sampled randomly the values of particular indicators and estimated the PDs’ distribution, while it’s assumed that the indicators are distributed according to the multidimensional subordinated Lévy model (Variance Gamma model and Normal Inverse Gaussian model, particularly). Although the obtained results show that all banks are relatively healthy, there is still high chance that “a financial crisis” will occur, at least in terms of probability. This is indicated by estimation of the various quantiles in the estimated distributions. Finally, it should be noted that the applicability of the estimated model (with respect to the used data) is limited to the recessionary phase of the financial market.

Keywords: credit-scoring models, multidimensional subordinated Lévy model, probability of default

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Authors: H. Hajimolahoseini, J. Hashemi, D. Redfearn

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Background: Catheter ablation is an effective therapy for symptomatic atrial fibrillation (AF). The intracardiac electrocardiogram (IEGM) collected during this procedure contains precious information that has not been explored to its full capacity. Novel processing techniques allow looking at these recordings from different perspectives which can lead to improved therapeutic approaches. In our previous study, we showed that variation in amplitude measured through Shannon Entropy could be used as an AF recurrence risk stratification factor in patients who received Ibutilide before the electrograms were recorded. The aim of this study is to further investigate the effect of Ibutilide on characteristics of the recorded signals from the left atrium (LA) of a patient with persistent AF before and after administration of the drug. Methods: The IEGMs collected from different intra-atrial sites of 12 patients were studied and compared before and after Ibutilide administration. First, the before and after Ibutilide IEGMs that were recorded within a Euclidian distance of 3 mm in LA were selected as pairs for comparison. For every selected pair of IEGMs, the Probability Distribution Function (PDF) of the amplitude in time domain and magnitude in frequency domain was estimated using the regression analysis. The PDF represents the relative likelihood of a variable falling within a specific range of values. Results: Our observations showed that in time domain, the PDF of amplitudes was fitted to a Gaussian distribution while in frequency domain, it was fitted to a Rayleigh distribution. Our observations also revealed that after Ibutilide administration, the IEGMs would have significantly narrower short-tailed PDFs both in time and frequency domains. Conclusion: This study shows that the PDFs of the IEGMs before and after administration of Ibutilide represents significantly different properties, both in time and frequency domains. Hence, by fitting the PDF of IEGMs in time domain to a Gaussian distribution or in frequency domain to a Rayleigh distribution, the effect of Ibutilide can easily be tracked using the statistics of their PDF (e.g., standard deviation) while this is difficult through the waveform of IEGMs itself.

Keywords: atrial fibrillation, catheter ablation, probability distribution function, time-frequency characteristics

Procedia PDF Downloads 138

Authors: Reza Nasrollahpour, Mohamad Hidayat Bin Jamal, Zulhilmi Bin Ismail

Abstract:

Density currents are generated when the fluid of one density is released into another fluid with a different density. These currents occur in a variety of natural and man-made environments, and this emphasises the importance of studying them. In most practical cases, the density currents flow over the surfaces which are not plane; however, there have been limited investigations in this regard. This study uses laboratory experiments to analyse the influence of bottom roughness on the velocity distribution within these dense underflows. The currents are analysed over a plane surface and three different configurations of beam-roughened beds. The velocity profiles are collected using Acoustic Doppler Velocimetry technique, and the distribution of velocity within these currents is formulated for the tested beds. The results indicate that the empirical power and Gaussian relations can describe the velocity distribution in the inner and outer regions of the profiles, respectively. Moreover, it is found that the bottom roughness is the primary controlling parameter in the inner region.

Keywords: density currents, velocity profiles, Acoustic Doppler Velocimeter, bed roughness

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