Search results for: bivariate interpolation polynomial

Authors: A. Belmeguenai, K. Mansouri, R. Djemili

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This work present a new algorithm based on the nonlinear filter generator for speech encryption and decryption. The proposed algorithm consists on the use a linear feedback shift register (LFSR) whose polynomial is primitive and nonlinear Boolean function. The purpose of this system is to construct Keystream with good statistical properties, but also easily computable on a machine with limited capacity calculated. This proposed speech encryption scheme is very simple, highly efficient, and fast to implement the speech encryption and decryption. We conclude the paper by showing that this system can resist certain known attacks.

Keywords: nonlinear filter generator, stream ciphers, speech encryption, security analysis

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Authors: Ayantika Biswas

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Hypertension still remains one of the most important preventable contributors to adult mortality and morbidity and a major public health challenge worldwide. Studying regional and rural-urban differences in prevalence and assessment of the contributions of different indicators is essential in determining the drivers of this condition. The 2015-16 National Family Health Survey data has been used for the study. Bivariate analysis, multinomial regression analysis, concentration indices and decomposition of concentration indices assessing contribution of factors has been undertaken in the present study. An overall concentration index of 0.003 has been found for hypertensive population, which shows its concentration among the richer wealth quintiles. The contribution of factors like age 45 to 49 years, years of schooling between 5 to 9 years are factors that are important contributors to inequality in hypertension occurrence. Studies should be conducted to find approaches to prevent or delay the onset of the condition.

Keywords: hypertension, decomposition, inequalities, India

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Authors: Sammani Danwawu Abdullahi

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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration

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Authors: Likewin Thomas, M. V. Manoj Kumar, B. Annappa

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The aim of this study was to develop an Artificial Neural Network0 s recommendation model for an online process using the complexity of load, performance, and average servicing time of the resources. Here, the proposed model investigates the resource performance using stochastic gradient decent method for learning ranking function. A probabilistic cost function is implemented to identify the optimal θ values (load) on each resource. Based on this result the recommendation of resource suitable for performing the currently executing task is made. The test result of CoSeLoG project is presented with an accuracy of 72.856%.

Keywords: ADALINE, neural network, gradient decent, process mining, resource behaviour, polynomial regression model

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Authors: Ayesha M. Facey

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The evaluation sought to determine the factors associated with the high failure rate among students taking a first-year introductory statistics course. By utilizing Tyler’s Objective Based Model, the main objectives were: to assess the effectiveness of the lecturer’s teaching strategies; to determine the proportion of students who attends lectures and tutorials frequently and to determine the impact of infrequent attendance on performance; to determine how the assigned activities assisted in students understanding of the course content; to ascertain the possible issues being faced by students in understanding the course material and obtain possible solutions to the challenges and to determine whether the learning outcomes have been achieved based on an assessment of the second in-course examination. A quantitative survey research strategy was employed and the study population was students enrolled in semester one of the academic year 2015/2016. A convenience sampling approach was employed resulting in a sample of 98 students. Primary data was collected using self-administered questionnaires over a one-week period. Secondary data was obtained from the results of the second in-course examination. Data were entered and analyzed in SPSS version 22 and both univariate and bivariate analyses were conducted on the information obtained from the questionnaires. Univariate analyses provided description of the sample through means, standard deviations and percentages while bivariate analyses were done using Spearman’s Rho correlation coefficient and Chi-square analyses. For secondary data, an item analysis was performed to obtain the reliability of the examination questions, difficulty index and discriminant index. The examination results also provided information on the weak areas of the students and highlighted the learning outcomes that were not achieved. Findings revealed that students were more likely to participate in lectures than tutorials and that attendance was high for both lectures and tutorials. There was a significant relationship between participation in lectures and performance on examination. However, a high proportion of students has been absent from three or more tutorials as well as lectures. A higher proportion of students indicated that they completed the assignments obtained from the lectures sometimes while they rarely completed tutorial worksheets. Students who were more likely to complete their assignments were significantly more likely to perform well on their examination. Additionally, students faced a number of challenges in understanding the course content and the topics of probability, binomial distribution and normal distribution were the most challenging. The item analysis also highlighted these topics as problem areas. Problems doing mathematics and application and analyses were their major challenges faced by students and most students indicated that some of the challenges could be alleviated if additional examples were worked in lectures and they were given more time to solve questions. Analysis of the examination results showed that a number of learning outcomes were not achieved for a number of topics. Based on the findings recommendations were made that suggested adjustments to grade allocations, delivery of lectures and methods of assessment.

Keywords: evaluation, item analysis, Tyler’s objective based model, university statistics

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Authors: Sayed Isahaq Hossain, K. T. Chang, Moustapha Ndour

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Inference of the phreatic line through earth dams is of paramount importance because it could be directly associated with piping phenomena which may lead to the dam failure. Normally in the field, the instrumentations such as ‘diver’ and ‘standpipe’ are to be used to identify the seepage conditions which only provide point data with a fair amount of interpolation or assumption. Here in this paper, we employed high-resolution fiber optic cable sensors (FOCS) based on Raman Scattering in order to obtain a very accurate phreatic line and seepage profile. Unlike the above-mention devices which pinpoint the water level location, this kind of Distributed Fiber Optics Sensing gives us more reliable information due to its inherent characteristics of continuous measurement.

Keywords: standpipe, diver, FOCS, monitoring, Raman scattering

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Authors: Modreck Gomo

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Although the dolomite and calcite carbonates can neutralize Acid Mine Drainage (AMD) and prevent leaching of metals, salinity still remains a huge problem. The study presents a conceptual discussion of geochemical controls of salinity in a typical calcite and dolomite AMD neutralised groundwater systems. Thereafter field evidence is presented to support the conceptual discussions. 1020 field data sets of from a groundwater system reported to be under circumneutral conditions from the neutralization effect of calcite and dolomite is analysed using correlation analysis and bivariate plots. Field evidence indicates that sulphate, calcium and magnesium are strongly and positively correlated to Total Dissolved Solids (TDS) which is used as measure of salinity. In this, a hydrogeochemical system, the dissolution of sulphate, calcium and magnesium form AMD neutralization process contributed 50%, 10% and 5% of the salinity.

Keywords: acid mine drainage, carbonates, neutralization, salinity

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Authors: Bo Wang

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This paper proposes a method that can estimate PM2.5 by the images of GF-1 Satellite that called WFOV images (Wide Field of View). AOD (Aerosol Optical Depth) over land surfaces was retrieved in Shanghai area based on DDV (Dark Dense Vegetation) method. PM2.5 information, gathered from ground monitoring stations hourly, was fitted with AOD using different polynomial coefficients, and then the correlation coefficient between them was calculated. The results showed that, the GF-1 WFOV images can meet the requirement of retrieving AOD, and the correlation coefficient between the retrieved AOD and PM2.5 was high. If more detailed and comprehensive data is provided, the accuracy could be improved and the parameters can be more precise in the future.

Keywords: remote sensing retrieve, PM 2.5, GF-1, aerosol optical depth

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Authors: Thanutch Sukwimolseree, Preeyaphorn Kosa

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Many problems are occurred in watershed due to human activity and economic development. The purpose is to determine the effects of the land use change on surface runoff using land use map on 1980, 2001 and 2008 and daily weather data during January 1, 1979 to September 30, 2010 applied to SWAT. The results can be presented that the polynomial equation is suitable to display that relationship. These equations for land use in 1980, 2001 and 2008 are consisted of y = -0.0076x5 + 0.1914x4–1.6386x3 + 6.6324x2–8.736x + 7.8023(R2 = 0.9255), y = -0.0298x5 + 0.8794x4 - 9.8056x3 + 51.99x2 - 117.04x + 96.797; (R2 = 0.9186) and y = -0.0277x5 + 0.8132x4 - 8.9598x3 + 46.498x2–101.83x +81.108 (R2 = 0.9006), respectively. Moreover, if the agricultural area is the largest area, it is a sensitive parameter to concern surface runoff.

Keywords: land use, runoff, SWAT, upper Mun River basin

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Authors: Negar Riazifar, Nigel G. Stocks

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This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to an alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.

Keywords: alias-free, level crossing sampling, spectrum, trigonometric polynomial

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Authors: Reut Lanyado, David Mendlovic

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Most biological methods for authentication require special equipment and, some of them are easy to fake. We proposed a method for authentication based on hand movement while typing a sentence with a regular camera. This technique uses the full video of the hand, which is harder to fake. In the first phase, we tracked the hand joints in each frame. Next, we represented a single frame for each individual using our Pose Agnostic Rotation and Movement (PARM) dimensional space. Then, we indicated a full video of hand movement in a fixed low dimensional space using this method: Fixed Dimension Video by Interpolation Statistics (FDVIS). Finally, we identified each individual in the FDVIS representation using unsupervised clustering and supervised methods. Accuracy exceeds 96% for 80 individuals by using supervised KNN.

Keywords: authentication, feature extraction, hand recognition, security, signal processing

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Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: array signal processing, direction-of-arrival, antenna arrays, Eigenvalues, Eigenvectors, Lagrange multiplier

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Authors: M. Helaimi, R. Taleb, D. Benyoucef, B. Belmadani

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This paper presents the design of a polynomial controller with coefficient diagram method (CDM). This controller is used to control the output power of high frequency resonant inverter with LLC tank. One of the most important problems associated with the proposed inverter is achieving ZVS operating during the induction heating process. To overcome this problem, asymmetrical voltage cancellation (AVC) control technique is proposed. The phased look loop (PLL) is used to track the natural frequency of the system. The small signal model of the system with the proposed control is obtained using extending describing function method (EDM). The validity of the proposed control is verified by simulation results.

Keywords: induction heating, AVC control, CDM, PLL, resonant inverter

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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Authors: Matteo Gentilucci, Marco Materazzi, Gilberto Pambianchi

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Climate change is an increasingly central issue in the world, because it affects many of human activities. In this context regional studies are of great importance because they sometimes differ from the general trend. This research focuses on a small area of central Italy which overlooks the Adriatic Sea, the province of Macerata. The aim is to analyze space-based climate changes, for precipitation and temperatures, in the last 3 climatological standard normals (1961-1990; 1971-2000; 1981-2010) through GIS software. The data collected from 30 weather stations for temperature and 61 rain gauges for precipitation were subject to quality controls: validation and homogenization. These data were fundamental for the spatialization of the variables (temperature and precipitation) through geostatistical techniques. To assess the best geostatistical technique for interpolation, the results of cross correlation were used. The co-kriging method with altitude as independent variable produced the best cross validation results for all time periods, among the methods analysed, with 'root mean square error standardized' close to 1, 'mean standardized error' close to 0, 'average standard error' and 'root mean square error' with similar values. The maps resulting from the analysis were compared by subtraction between rasters, producing 3 maps of annual variation and three other maps for each month of the year (1961/1990-1971/2000; 1971/2000-1981/2010; 1961/1990-1981/2010). The results show an increase in average annual temperature of about 0.1°C between 1961-1990 and 1971-2000 and 0.6 °C between 1961-1990 and 1981-2010. Instead annual precipitation shows an opposite trend, with an average difference from 1961-1990 to 1971-2000 of about 35 mm and from 1961-1990 to 1981-2010 of about 60 mm. Furthermore, the differences in the areas have been highlighted with area graphs and summarized in several tables as descriptive analysis. In fact for temperature between 1961-1990 and 1971-2000 the most areally represented frequency is 0.08°C (77.04 Km² on a total of about 2800 km²) with a kurtosis of 3.95 and a skewness of 2.19. Instead, the differences for temperatures from 1961-1990 to 1981-2010 show a most areally represented frequency of 0.83 °C, with -0.45 as kurtosis and 0.92 as skewness (36.9 km²). Therefore it can be said that distribution is more pointed for 1961/1990-1971/2000 and smoother but more intense in the growth for 1961/1990-1981/2010. In contrast, precipitation shows a very similar shape of distribution, although with different intensities, for both variations periods (first period 1961/1990-1971/2000 and second one 1961/1990-1981/2010) with similar values of kurtosis (1st = 1.93; 2nd = 1.34), skewness (1st = 1.81; 2nd = 1.62 for the second) and area of the most represented frequency (1st = 60.72 km²; 2nd = 52.80 km²). In conclusion, this methodology of analysis allows the assessment of small scale climate change for each month of the year and could be further investigated in relation to regional atmospheric dynamics.

Keywords: climate change, GIS, interpolation, co-kriging

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Balasaheb Bansode, L. Ladusingh

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The public distribution system is an important component of food security. It is a massive welfare program undertaken by Government of India and implemented by state government since India being a federal state; for achieving multiple objectives like eliminating hunger, reduction in malnutrition and making food consumption affordable. This program reaches at the community level through the various agencies of the government. The paper focuses on the accessibility of PDS at household level and how the present policy framework results in exclusion and inclusion errors. It tries to explore the sanctioned food grain quantity received by differentiated ration cards according to income criterion at household level, and also it has highlighted on the type of corruption in food distribution that is generated by the PDS system. The data used is of secondary nature from NSSO 68 round conducted in 2012. Bivariate and multivariate techniques have been used to understand the working and consumption of food for this paper.

Keywords: calories intake, entitle food quantity, poverty aliviation through PDS, target error

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Authors: Young Hee Geum

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In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.

Keywords: basin of attraction, conjugacy, fourth-order, multiple-root finder

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Authors: H. Gonzalez-Rivera, J. L. Palmeros-Torres

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This paper describes the application of traditional computer vision techniques as a procedure for automatic measurement of the secondary dendrite arm spacing (SDAS) from microscopic images. The algorithm is capable of finding the lineal or curve-shaped secondary column of the main microstructure, measuring its length size in a micro-meter and counting the number of spaces between dendrites. The automatic characterization was compared with a set of 1728 manually characterized images, leading to an accuracy of −0.27 µm for the length size determination and a precision of ± 2.78 counts for dendrite spacing counting, also reducing the characterization time from 7 hours to 2 minutes.

Keywords: dendrite arm spacing, microstructure inspection, pattern recognition, polynomial regression

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Varsha Hemant Patil, Swati A. Bhavsar, Abolee H. Patil

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Image quality assessment plays an important role in image evaluation. This paper aims to present an investigation of classic techniques in use for image quality assessment, especially for super-resolution imaging. Researchers have contributed a lot towards the development of super-resolution imaging techniques. However, not much attention is paid to the development of metrics for testing the performance of developed techniques. In this paper, the study report of existing image quality measures is given. The paper classifies reviewed approaches according to functionality and suitability for super-resolution imaging. Probable modifications and improvements of these to suit super-resolution imaging are presented. The prime goal of the paper is to provide a comprehensive reference source for researchers working towards super-resolution imaging and suggest a better framework for measuring the performance of super-resolution imaging techniques.

Keywords: interpolation, MSE, PSNR, SSIM, super resolution

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Authors: Francky Fouedjio

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Multivariate geostatistical data have become omnipresent in the geosciences and pose substantial analysis challenges. One of them is the grouping of data locations into spatially contiguous clusters so that data locations within the same cluster are more similar while clusters are different from each other, in some sense. Spatially contiguous clusters can significantly improve the interpretation that turns the resulting clusters into meaningful geographical subregions. In this paper, we develop an agglomerative hierarchical clustering approach that takes into account the spatial dependency between observations. It relies on a dissimilarity matrix built from a non-parametric kernel estimator of the spatial dependence structure of data. It integrates existing methods to find the optimal cluster number and to evaluate the contribution of variables to the clustering. The capability of the proposed approach to provide spatially compact, connected and meaningful clusters is assessed using bivariate synthetic dataset and multivariate geochemical dataset. The proposed clustering method gives satisfactory results compared to other similar geostatistical clustering methods.

Keywords: clustering, geostatistics, multivariate data, non-parametric

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Authors: Alexis Aldo Mendoza Villarroel, Ademir Clemente Villena Zevallos, Cristian Jose Lopez Del Alamo

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With the advancement of technology it is now possible to scan entire objects and obtain their digital representation by using point clouds or polygon meshes. However, some objects may be broken or have missing parts; thus, several methods focused on this problem have been proposed based on Geometric Deep Learning, such as GCNN, ACNN, PointNet, among others. In this article an approach from a different paradigm is proposed, using metric data structures to index global descriptors in the spectral domain and allow the recovery of a set of similar models in polynomial time; to later use the Iterative Close Point algorithm and recover the parts of the incomplete model using the geometry and topology of the model with less Hausdorff distance.

Keywords: 3D reconstruction method, point cloud completion, shape completion, similarity search

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Authors: Kalpana Dahiya

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This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers, and a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem of different sizes validates the efficiency of the proposed algorithm.

Keywords: global optimization, hierarchical optimization, transportation problem, concave minimization

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Authors: N. F. M. Mokhtar, N. Z. A. Hamid

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This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

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Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

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Authors: Ankit Shai

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CRC or Cyclic Redundancy Check is one of the most common, and one of the most powerful error-detecting codes implemented on modern computers. Most of the modern communication protocols use some error detection algorithms in digital networks and storage devices to detect accidental changes to raw data between transmission and reception. Cyclic Redundancy Check, or CRC, is the most popular one among these error detection codes. CRC properties are defined by the generator polynomial length and coefficients. The aim of this project is to implement an efficient FPGA based CRC-8 that accepts a 32 bit input, taking into consideration optimal chip area and high performance, using VHDL. The proposed architecture is implemented on Xilinx ISE Simulator. It is designed while keeping in mind the hardware design, complexity and cost factor.

Keywords: cyclic redundancy checker, CRC-8, 32-bit input, FPGA, VHDL, ModelSim, Xilinx

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Ishapathik Das, Sumen Sen, N. Rao Chaganty, Pooja Sengupta

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Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models.

Keywords: copula, Gaussian copula, multivariate distributions, inflated distributios

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