Search results for: Saigo's generalized fractional calculus

Authors: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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Authors: Mondher Yahyaoui

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A generalized vortex lattice method for complex lifting surfaces with flap and aileron deflection is formulated. The method is not restricted by the linearized theory assumption and accounts for all standard geometric lifting surface parameters: camber, taper, sweep, washout, dihedral, in addition to flap and aileron deflection. Thickness is not accounted for since the physical lifting body is replaced by a lattice of panels located on the mean camber surface. This panel lattice setup and the treatment of different wake geometries is what distinguish the present work form the overwhelming majority of previous solutions based on the vortex lattice method. A MATLAB code implementing the proposed formulation is developed and validated by comparing our results to existing experimental and numerical ones and good agreement is demonstrated. It is then used to study the accuracy of the widely used classical vortex-lattice method. It is shown that the classical approach gives good agreement in the clean configuration but is off by as much as 30% when a flap or aileron deflection of 30° is imposed. This discrepancy is mainly due the linearized theory assumption associated with the conventional method. A comparison of the effect of four different wake geometries on the values of aerodynamic coefficients was also carried out and it is found that the choice of the wake shape had very little effect on the results.

Keywords: aileron deflection, camber-surface-bound vortices, classical VLM, generalized VLM, flap deflection

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Authors: Jafar Khodagholizadeh

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In this talk, we study the tensor mode equation of perturbation in the presence of nonzero $-\Lambda$ as dark energy, whose dynamic nature depends on the Hubble parameter $ H$ and/or its time derivative. Dark energy, according to the total vacuum contribution, has little effect during the radiation-dominated era, but it reduces the squared amplitude of gravitational waves (GWs) up to $60\%$ for the wavelengths that enter the horizon during the matter-dominated era. Moreover, the observations bound on dark energy models, such as running vacuum model (RVM), generalized running vacuum model (GRVM), and generalized running vacuum subcase (GRVS), are effective in reducing the GWs’ amplitude. Although this effect is less for the wavelengths that enter the horizon at later times, this reduction is stable and permanent.

Keywords: gravitational waves, dark energy, GW's amplitude, all stage universe

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Authors: Noora Al-Shanfari, M. Mazharul Islam

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The cumulative incidence function (CIF) is a fundamental approach for analyzing survival data in the presence of competing risks, which estimates the marginal probability for each competing event. Parametric modeling of CIF has the advantage of fitting various shapes of CIF and estimates the impact of covariates with maximum efficiency. To calculate the total CIF's covariate influence using a parametric model., it is essential to parametrize the baseline of the CIF. As the CIF is an improper function by nature, it is necessary to utilize an improper distribution when applying parametric models. The Gompertz distribution, which is an improper distribution, is limited in its applicability as it only accounts for monotone hazard shapes. The generalized Gompertz distribution, however, can adapt to a wider range of hazard shapes, including unimodal, bathtub, and monotonic increasing or decreasing hazard shapes. In this paper, the generalized Gompertz distribution is used to parametrize the baseline of the CIF, and the parameters of the proposed model are estimated using the maximum likelihood approach. The proposed model is compared with the existing Gompertz model using the Akaike information criterion. Appropriate statistical test procedures and model-fitting criteria will be used to test the adequacy of the model. Both models are applied to the ‘colon’ dataset, which is available in the “biostat3” package in R.

Keywords: competing risks, cumulative incidence function, improper distribution, parametric modeling, survival analysis

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Authors: Tasir Khan, Yejuan Wan, Kalim Ullah

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Hydrological frequency analysis has been conducted to estimate the minimum flow elevation of the Indus River in Pakistan to protect the ecosystem. The Maximum likelihood estimation (MLE) technique is used to estimate the best-fitted distribution for Minimum Ecological Flows at nine stations of the Indus River in Pakistan. The four selected distributions, Generalized Extreme Value (GEV) distribution, Generalized Logistics (GLO) distribution, Generalized Pareto (GPA) distribution, and Pearson type 3 (PE3) are fitted in all sites, usually used in hydro frequency analysis. Compare the performance of these distributions by using the goodness of fit tests, such as the Kolmogorov Smirnov test, Anderson darling test, and chi-square test. The study concludes that the Maximum Likelihood Estimation (MLE) method recommended that GEV and GPA are the most suitable distributions which can be effectively applied to all the proposed sites. The quantiles are estimated for the return periods from 5 to 1000 years by using MLE, estimations methods. The MLE is the robust method for larger sample sizes. The results of these analyses can be used for water resources research, including water quality management, designing irrigation systems, determining downstream flow requirements for hydropower, and the impact of long-term drought on the country's aquatic system.

Keywords: minimum ecological flow, frequency distribution, indus river, maximum likelihood estimation

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Authors: Rasaq Kareem, Jacob Gbadeyan

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In this study, analysis of the entropy generation of an unsteady reactive hydromagnetic generalized couette fluid flow of a two-step exothermic chemical reaction through a channel with isothermal wall temperature under the influence of different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics was investigated. The modelled nonlinear dimensionless equations governing the fluid flow were simplified and solved using the combined Laplace Differential Transform Method (LDTM). The effects of fluid parameters associated with the problem on the fluid temperature, entropy generation rate and Bejan number were discussed and presented through graphs.

Keywords: couette, entropy, exothermic, unsteady

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, decomposition method, generalized thermoelasticity, algorithm

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Authors: A. Abdul-Ameer

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The equations governing the distance, pressure- volume flow relationships for the pipeline transportation of gaseous mixtures, are considered. A derivation based on differential calculus, for an element of this system model, is addressed. Solutions, yielding the input- output response following pressure changes, are reviewed. The technical problems associated with these analytical results are identified. Procedures resolving these difficulties providing thereby an attractive, simple, analysis route are outlined. Computed responses, validating thereby calculated predictions, are presented.

Keywords: pressure, distance, flow, dissipation, models

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Authors: Oren Shtayermman

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The current investigation expended on research among parents caring for a child who is diagnosed with an autism spectrum disorder (ASD). An online web survey was used to collect data from 253 parents caring for a child with a diagnosis of ASD. Both parents reported on elevated levels of parental stress associated with caring for the child on the spectrum. In addition, lower levels of marital satisfaction were found in both parents. About 13% of the parents in the sample met the diagnostic criteria for Major Depressive Disorder and About 15% of the parents met the diagnostic criteria for Generalized Anxiety Disorder. Although the majority of the sample was females (94%) significant differences were found between males and females in relation to meeting the diagnostic criteria for Major Depressive Disorder and for Generalized Anxiety Disorder. Higher levels of stress were associated with higher number of Generalized Anxiety Disorder symptoms and higher number of Major Depressive Disorder symptoms. Findings from this study indicate how vulnerable parents and especially females are in relation to caring to a child diagnosed with ASD. Educational Objectives: At the conclusion of the paper, the readers should be able to: -Identify levels of stress and marital satisfaction among parents caring for a child diagnosed with autism spectrum disorder, -Recognize the impact of stress on the development of mental health issues, -Name the two most common mood and anxiety related disorders associated with caring for a child diagnosed with an autism spectrum disorder.

Keywords: autism, stress, parents, children

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Authors: Arunee Wongkhao, Suparat Niwitpong, Sa-aat Niwitpong

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In this paper, we propose two new confidence intervals for the difference between the inverse of normal means with known coefficients of variation. One of these two confidence intervals for this problem is constructed based on the generalized confidence interval and the other confidence interval is constructed based on the closed form method of variance estimation. We examine the performance of these confidence intervals in terms of coverage probabilities and expected lengths via Monte Carlo simulation.

Keywords: coverage probability, expected length, inverse of normal mean, coefficient of variation, generalized confidence interval, closed form method of variance estimation

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Authors: Vallence Ngabo M., Leonard Atuhaire, Peter Clever Rutayisire

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The main aim of this study was to establish the differences in both the determinants of stunting and the causal mechanism through which the identified determinants influence stunting amongst male and female under-fives in Uganda. Literature shows that male children below the age of five years are at a higher risk of being stunted than their female counterparts. Specifically, studies in Uganda indicate that being a male child is positively associated with stunting, while being a female is negatively associated with stunting. Data for 904 males and 829 females under-fives was extracted form UDHS-2016 survey dataset. Key variables for this study were identified and used in generating relevant models and paths. Structural equation modeling techniques were used in their generalized form (GSEM). The generalized nature necessitated specifying both the family and link functions for each response variable in the system of the model. The sex of the child (b4) was used as a grouping factor and the height for age (HAZ) scores were used to construct the status for stunting of under-fives. The estimated models and path clearly indicated that the set of underlying factors that influence male and female under-fives respectively was different and the path through which they influence stunting was different. However, some of the determinants that influenced stunting amongst male under-fives also influenced stunting amongst the female under-fives. To reduce the stunting problem to the desirable state, it is important to consider the multifaceted and complex nature of the risk factors that influence stunting amongst the under-fives but, more importantly, consider the different sex-specific factors and their causal mechanism or paths through which they influence stunting.

Keywords: stunting, underfives, sex of the child, GSEM, causal mechanism

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Authors: Naushad Mamode Khan

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The Com-Poisson (CMP) model is one of the most popular discrete generalized linear models (GLMS) that handles both equi-, over- and under-dispersed data. In longitudinal context, an integer-valued autoregressive (INAR(1)) process that incorporates covariate specification has been developed to model longitudinal CMP counts. However, the joint likelihood CMP function is difficult to specify and thus restricts the likelihood based estimating methodology. The joint generalized quasilikelihood approach (GQL-I) was instead considered but is rather computationally intensive and may not even estimate the regression effects due to a complex and frequently ill conditioned covariance structure. This paper proposes a new GQL approach for estimating the regression parameters (GQLIII) that are based on a single score vector representation. The performance of GQL-III is compared with GQL-I and separate marginal GQLs (GQL-II) through some simulation experiments and is proved to yield equally efficient estimates as GQL-I and is far more computationally stable.

Keywords: longitudinal, com-Poisson, ill-conditioned, INAR(1), GLMS, GQL

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Authors: Sujeet Kumar, Arun Prasad

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The present work investigates the effect of multiple parameters on the unconfined compressive strength of the bauxite residue-lime mix. A number of unconfined compressive strength tests considering various curing time, lime content, dry density and moisture content were carried out. The results show that an empirical correlation may be successfully developed using volumetric lime content, porosity, moisture content, curing time unconfined compressive strength for the range of the bauxite residue-lime mix studied. The proposed empirical correlations efficiently predict the strength of bauxite residue-lime mix, and it can be used as a generalized empirical equation to estimate unconfined compressive strength.

Keywords: bauxite residue, curing time, porosity/volumetric lime ratio, unconfined compressive strength

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Authors: Noha Ibrahim, Eman S. Elzanfaly, Said A. Hassan, Ahmed E. El Gendy

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Objectives: The purpose of the study is to develop a sensitive synchronous spectrofluorimetric method with multivariate calibration after studying and optimizing the different variables affecting the native fluorescence intensity of amlodipine and olmesartan implementing an experimental design approach. Method: In the first step, the fractional factorial design used to screen independent factors affecting the intensity of both drugs. The objective of the second step was to optimize the method performance using a Central Composite Face-centred (CCF) design. The optimal experimental conditions obtained from this study were; a temperature of (15°C ± 0.5), the solvent of 0.05N HCl and methanol with a ratio of (90:10, v/v respectively), Δλ of 42 and the addition of 1.48 % surfactant providing a sensitive measurement of amlodipine and olmesartan. The resolution of the binary mixture with a multivariate calibration method has been accomplished mainly by using partial least squares (PLS) model. Results: The recovery percentage for amlodipine besylate and atorvastatin calcium in tablets dosage form were found to be (102 ± 0.24, 99.56 ± 0.10, for amlodipine and Olmesartan, respectively). Conclusion: Method is valid according to some International Conference on Harmonization (ICH) guidelines, providing to be linear over a range of 200-300, 500-1500 ng mL⁻¹ for amlodipine and Olmesartan. The methods were successful to estimate amlodipine besylate and olmesartan in bulk powder and pharmaceutical preparation.

Keywords: amlodipine, central composite face-centred design, experimental design, fractional factorial design, multivariate calibration, olmesartan

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Authors: Mariia Timofeeva, Andrew Ooi, Eric K. W. Poon, Peter Barlis

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Atherosclerotic plaque build-up, commonly known as stenosis, limits blood flow and hence oxygen and nutrient supplies to the heart muscle. Thus, assessment of its severity is of great interest to health professionals. Numerical simulation of the fractional flow reserve (FFR) has proved to be well correlated with invasively measured FFR used for physiological assessment of the severity of coronary stenosis in arteries. Atherosclerosis may impact the diseased artery in several locations causing serial stenoses, which is a complicated subset of coronary artery disease that requires careful treatment planning. However, hemodynamic of the serial sequential stenoses in coronary arteries has not been extensively studied. The hemodynamics of the serial stenoses is complex because the stenoses in the series interact and affect the flow through each other. To address this, serial stenoses in a 3.4 mm left anterior descending (LAD) artery are examined in this study. Two diameter stenoses (DS) are considered, 30 and 50 percent of the reference diameter. Serial stenoses configurations are divided into three groups based on the order of the stenoses in the series, spacing between them, and deviation of the stenoses’ symmetry (eccentricity). A patient-specific pulsatile waveform is used in the simulations. Blood flow within the stenotic artery is assumed to be laminar, Newtonian, and incompressible. Results for the FFR are reported. Based on the simulation results, it can be deduced that the larger drop in pressure (smaller value of the FFR) is expected when the percentage of the second stenosis in the series is bigger. Varying the distance between the stenoses affects the location of the maximum drop in the pressure, while the minimal FFR in the artery remains unchanged. Eccentric serial stenoses are characterized by a noticeably larger decrease in pressure through the stenoses and by the development of the chaotic flow downstream of the stenoses. The largest drop in the pressure (about 4% difference compared to the axisymmetric case) is obtained for the serial stenoses, where both the stenoses are highly eccentric with the centerlines deflected to the different sides of the LAD. In conclusion, varying configuration of the sequential serial stenoses results in a different distribution of FFR through the LAD. Results presented in this study provide insight into the clinical assessment of the severity of the coronary serial stenoses, which is proved to depend on the relative position of the stenoses and the deviation of the stenoses’ symmetry.

Keywords: computational fluid dynamics, coronary artery, fractional flow reserve, serial stenoses

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Authors: Jonathan D. Moore, Mark G. Reith, David S. Long

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Serious games (SGs) have been shown to be an effective teaching tool in many contexts. Because of the success of SGs, several design frameworks have been created to expedite the process of making original serious games to teach specific learning objectives (LOs). Even with these frameworks, the time required to create a custom SG from conception to implementation can range from months to years. Furthermore, it is even more difficult to design a game framework that allows an instructor to create customized game variants supporting multiple LOs within the same field. This paper proposes a refactoring methodology to apply the theoretical principles from well-established design frameworks to a pre-existing serious game. The expected result is a generalized game that can be quickly customized to teach LOs not originally targeted by the game. This methodology begins by describing the general components in a game, then uses a combination of two SG design frameworks to extract the teaching elements present in the game. The identified teaching elements are then used as the theoretical basis to determine the range of LOs that can be taught by the game. This paper evaluates the proposed methodology by presenting a case study of refactoring the serious game Battlespace Next (BSN) to teach joint military capabilities. The range of LOs that can be taught by the generalized BSN are identified, and examples of creating custom LOs are given. Survey results from users of the generalized game are also provided. Lastly, the expected impact of this work is discussed and a road map for future work and evaluation is presented.

Keywords: serious games, learning objectives, game design, learning theory, game framework

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Authors: Mohadeseh Shojaei Shahrokhabadi, Ding-Geng (Din) Chen

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Positive continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical cost data. To jointly model semi-continuous longitudinal cost data and survival data and to provide marginalized covariate effect estimates, a marginalized two-part joint model (MTJM) has been developed for outcome variables with lognormal distributions. In this paper, we propose MTJM models for outcome variables from a generalized gamma (GG) family of distributions. The GG distribution constitutes a general family that includes approximately all of the most frequently used distributions like the Gamma, Exponential, Weibull, and Log Normal. In the proposed MTJM-GG model, the conditional mean from a conventional two-part model with a three-parameter GG distribution is parameterized to provide the marginal interpretation for regression coefficients. In addition, MTJM-gamma and MTJM-Weibull are developed as special cases of MTJM-GG. To illustrate the applicability of the MTJM-GG, we applied the model to a set of real electronic health record data recently collected in Iran, and we provided SAS code for application. The simulation results showed that when the outcome distribution is unknown or misspecified, which is usually the case in real data sets, the MTJM-GG consistently outperforms other models. The GG family of distribution facilitates estimating a model with improved fit over the MTJM-gamma, standard Weibull, or Log-Normal distributions.

Keywords: marginalized two-part model, zero-inflated, right-skewed, semi-continuous, generalized gamma

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for 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, K-functional, mixed modulus of smoothness

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Nikk Leavitt, Peter Kellett, Cheryl Currie, Richard Larouche

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Background: Masculinity has been associated with poor mental health outcomes in adult men and is colloquially referred to as toxic. Masculinity is traditionally measured using the Male Role Norms Inventory, which examines behaviors that may be common in men but that are themselves associated with poor mental health regardless of gender (e.g., aggressiveness). The purpose of this study was to examine if masculinity is associated with generalized anxiety among men using this inventory vs. a man’s personal definition of it. Method: An online survey collected data from 1,200 men aged 18-65 across Canada in July 2022. Masculinity was measured using: 1) the Male Role Norms Inventory Short Form and 2) by asking men to self-define what being masculine means. Men were then asked to rate the extent they perceived themselves to be masculine on a scale of 1 to 10 based on their definition of the construct. Generalized anxiety disorder was measured using the GAD-7. Multiple linear regression was used to examine associations between each masculinity score and anxiety score, adjusting for confounders. Results: The masculinity score measured using the inventory was positively associated with increased anxiety scores among men (β = 0.02, p < 0.01). Masculinity subscales most strongly correlated with higher anxiety were restrictive emotionality (β = 0.29, p < 0.01) and dominance (β = 0.30, p < 0.01). When traditional masculinity was replaced by a man’s self-rated masculinity score in the model, the reverse association was found, with increasing masculinity resulting in a significantly reduced anxiety score (β = -0.13, p = 0.04). Discussion: These findings highlight the need to revisit the ways in which masculinity is defined and operationalized in research to better understand its impacts on men’s mental health. The findings also highlight the importance of allowing participants to self-define gender-based constructs, given they are fluid and socially constructed.

Keywords: masculinity, generalized anxiety disorder, race, intersectionality

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Authors: Devinder Singh, Rajneesh Kumar, Arvind Kumar

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The present investigation deals with generalized model of the equations for a homogeneous isotropic microstretch thermoelastic half space with mass diffusion medium. Theories of generalized thermoelasticity Lord-Shulman (LS) Green-Lindsay (GL) and Coupled Theory (CT) theories are applied to investigate the problem. The stresses in the considered medium have been studied due to normal force and tangential force. The normal mode analysis technique is used to calculate the normal stress, shear stress, couple stresses and microstress. A numerical computation has been performed on the resulting quantity. The computed numerical results are shown graphically.

Keywords: microstretch, thermoelastic, normal mode analysis, normal and tangential force, microstress force

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Authors: Timothy Kayode Samson, Adedoyin Isola Lawal

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The past five years have shown a sharp increase in public interest in the crypto market, with its market capitalization growing from $100 billion in June 2017 to $2158.42 billion on April 5, 2022. Despite the outrageous nature of the volatility of cryptocurrencies, the use of skewed error innovation distributions in modelling the volatility behaviour of these digital currencies has not been given much research attention. Hence, this study models the volatility of 5 largest cryptocurrencies by market capitalization (Bitcoin, Ethereum, Tether, Binance coin, and USD Coin) using four variants of GARCH models (GJR-GARCH, sGARCH, EGARCH, and APARCH) estimated using three skewed error innovation distributions (skewed normal, skewed student- t and skewed generalized error innovation distributions). Daily closing prices of these currencies were obtained from Yahoo Finance website. Finding reveals that the Binance coin reported higher mean returns compared to other digital currencies, while the skewness indicates that the Binance coin, Tether, and USD coin increased more than they decreased in values within the period of study. For both Bitcoin and Ethereum, negative skewness was obtained, meaning that within the period of study, the returns of these currencies decreased more than they increased in value. Returns from these cryptocurrencies were found to be stationary but not normality distributed with evidence of the ARCH effect. The skewness parameters in all best forecasting models were all significant (p<.05), justifying of use of skewed error innovation distributions with a fatter tail than normal, Student-t, and generalized error innovation distributions. For Binance coin, EGARCH-sstd outperformed other volatility models, while for Bitcoin, Ethereum, Tether, and USD coin, the best forecasting models were EGARCH-sstd, APARCH-sstd, EGARCH-sged, and GJR-GARCH-sstd, respectively. This suggests the superiority of skewed Student t- distribution and skewed generalized error distribution over the skewed normal distribution.

Keywords: skewed generalized error distribution, skewed normal distribution, skewed student t- distribution, APARCH, EGARCH, sGARCH, GJR-GARCH

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Authors: Muhammad Nouman Qureshi, Muhammad Hanif

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Adaptive cluster sampling (ACS) is specifically developed for the estimation of highly clumped populations and applied to a wide range of situations like animals of rare and endangered species, uneven minerals, HIV patients and drug users. In this paper, we proposed a generalized semi-exponential estimator with two auxiliary variables under the framework of ACS design. The expressions of approximate bias and mean square error (MSE) of the proposed estimator are derived. Theoretical comparisons of the proposed estimator have been made with existing estimators. A numerical study is conducted on real and artificial populations to demonstrate and compare the efficiencies of the proposed estimator. The results indicate that the proposed generalized semi-exponential estimator performed considerably better than all the adaptive and non-adaptive estimators considered in this paper.

Keywords: auxiliary information, adaptive cluster sampling, clustered populations, Hansen-Hurwitz estimation

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Authors: Riadh Zorgati, Thomas Triboulet

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In quite diverse application areas such as astronomy, medical imaging, geophysics or nondestructive evaluation, many problems related to calibration, fitting or estimation of a large number of input parameters of a model from a small amount of output noisy data, can be cast as inverse problems. Due to noisy data corruption, insufficient data and model errors, most inverse problems are ill-posed in a Hadamard sense, i.e. existence, uniqueness and stability of the solution are not guaranteed. A wide class of inverse problems in physics relates to the Fredholm equation of the first kind. The ill-posedness of such inverse problem results, after discretization, in a very ill-conditioned linear system of equations, the condition number of the associated matrix can typically range from 109 to 1018. This condition number plays the role of an amplifier of uncertainties on data during inversion and then, renders the inverse problem difficult to handle numerically. Similar problems appear in other areas such as numerical optimization when using interior points algorithms for solving linear programs leads to face ill-conditioned systems of linear equations. Devising efficient solution approaches for such system of equations is therefore of great practical interest. Efficient iterative algorithms are proposed for solving a system of linear equations. The approach is based on a preconditioning of the initial matrix of the system with an approximation of a generalized inverse leading to a stochastic preconditioned matrix. This approach, valid for non-negative matrices, is first extended to hermitian, semi-definite positive matrices and then generalized to any complex rectangular matrices. The main results obtained are as follows: 1) We are able to build a generalized inverse of any complex rectangular matrix which satisfies the convergence condition requested in iterative algorithms for solving a system of linear equations. This completes the (short) list of generalized inverse having this property, after Kaczmarz and Cimmino matrices. Theoretical results on both the characterization of the type of generalized inverse obtained and the convergence are derived. 2) Thanks to its properties, this matrix can be efficiently used in different solving schemes as Richardson-Tanabe or preconditioned conjugate gradients. 3) By using Lp norms, we propose generalized Kaczmarz’s type matrices. We also show how Cimmino's matrix can be considered as a particular case consisting in choosing the Euclidian norm in an asymmetrical structure. 4) Regarding numerical results obtained on some pathological well-known test-cases (Hilbert, Nakasaka, …), some of the proposed algorithms are empirically shown to be more efficient on ill-conditioned problems and more robust to error propagation than the known classical techniques we have tested (Gauss, Moore-Penrose inverse, minimum residue, conjugate gradients, Kaczmarz, Cimmino). We end on a very early prospective application of our approach based on stochastic matrices aiming at computing some parameters (such as the extreme values, the mean, the variance, …) of the solution of a linear system prior to its resolution. Such an approach, if it were to be efficient, would be a source of information on the solution of a system of linear equations.

Keywords: conditioning, generalized inverse, linear system, norms, stochastic matrix

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Authors: Ren Moses, Emmanuel Kidando, Eren Ozguven, Yassir Abdelrazig

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This study applied traffic speed and occupancy to develop clustering models that identify different traffic conditions. Particularly, these models are based on the Dirichlet Process Mixture of Generalized Linear regression (DML) and change-point regression (CR). The model frameworks were implemented using 2015 historical traffic data aggregated at a 15-minute interval from an Interstate 295 freeway in Jacksonville, Florida. Using the deviance information criterion (DIC) to identify the appropriate number of mixture components, three traffic states were identified as free-flow, transitional, and congested condition. Results of the DML revealed that traffic occupancy is statistically significant in influencing the reduction of traffic speed in each of the identified states. Influence on the free-flow and the congested state was estimated to be higher than the transitional flow condition in both evening and morning peak periods. Estimation of the critical speed threshold using CR revealed that 47 mph and 48 mph are speed thresholds for congested and transitional traffic condition during the morning peak hours and evening peak hours, respectively. Free-flow speed thresholds for morning and evening peak hours were estimated at 64 mph and 66 mph, respectively. The proposed approaches will facilitate accurate detection and prediction of traffic congestion for developing effective countermeasures.

Keywords: traffic congestion, multistate speed distribution, traffic occupancy, Dirichlet process mixtures of generalized linear model, Bayesian change-point detection

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Authors: Carla Silva

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The aim of this research is to study the relationship between the performance of humanities students in different statistics classes and their performance in their specific courses. Several factors are been studied, such as gender and final grades in statistics and math. Participants of this study comprised a sample of students at a Lisbon University during their academic year. A significant relationship tends to appear between these factors and the performance of these students. However this relationship tends to be stronger with students who had previous studied calculus and math.

Keywords: education, performance, statistic, humanities

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Habshah Midi, Mohammed A. Mohammed, Sohel Rana

Abstract:

Multicollinearity occurs when two or more independent variables in a multiple linear regression model are highly correlated. The ridge regression is the commonly used method to rectify this problem. However, the ridge regression cannot handle the problem of multicollinearity which is caused by high leverage collinearity enhancing observation (HLCEO). Since high leverage points (HLPs) are responsible for inducing multicollinearity, the effect of HLPs needs to be reduced by using Generalized M estimator. The existing GM6 estimator is based on the Minimum Volume Ellipsoid (MVE) which tends to swamp some low leverage points. Hence an improvised GM (MGM) estimator is presented to improve the precision of the GM6 estimator. Numerical example and simulation study are presented to show how HLPs can cause multicollinearity. The numerical results show that our MGM estimator is the most efficient method compared to some existing methods.

Keywords: identification, high leverage points, multicollinearity, GM-estimator, DRGP, DFFITS

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Authors: Saba Riaz, Syed A. Hussain

Abstract:

This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

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Authors: Olga I. Moskalenko, Vladislav A. Khanadeev, Anastasya D. Koloskova, Alexey A. Koronovskii, Anatoly A. Pivovarov

Abstract:

Generalized synchronization is one of the most intricate phenomena in nonlinear science. It can be observed both in systems with a unidirectional and mutual type of coupling including the complex networks. Such a phenomenon has a number of practical applications, for example, for the secure information transmission through the communication channel with a high level of noise. Known methods for the secure information transmission needs in the increase of the privacy of data transmission that arises a question about the observation of such phenomenon in systems with a complex topology of chaotic attractor possessing two or more positive Lyapunov exponents. The present report is devoted to the study of such phenomenon in two unidirectionally and mutually coupled dynamical systems being in chaotic (with one positive Lyapunov exponent) and hyperchaotic (with two or more positive Lyapunov exponents) regimes, respectively. As the systems under study, we have used two mutually coupled modified Lorenz oscillators and two unidirectionally coupled time-delayed generators. We have shown that in both cases the generalized synchronization regime can be detected by means of the calculation of Lyapunov exponents and phase tube approach whereas due to the complex topology of attractor the nearest neighbor method is misleading. Moreover, the auxiliary system approaches being the standard method for the synchronous regime observation, for the mutual type of coupling results in incorrect results. To calculate the Lyapunov exponents in time-delayed systems we have proposed an approach based on the modification of Gram-Schmidt orthogonalization procedure in the context of the time-delayed system. We have studied in detail the mechanisms resulting in the generalized synchronization regime onset paying a great attention to the field where one positive Lyapunov exponent has already been become negative whereas the second one is a positive yet. We have found the intermittency here and studied its characteristics. To detect the laminar phase lengths the method based on a calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been verified using the example of two unidirectionally coupled Rössler systems being in the band chaos regime. We have revealed the main characteristics of intermittency, i.e. the distribution of the laminar phase lengths and dependence of the mean length of the laminar phases on the criticality parameter, for all systems studied in the report. This work has been supported by the Russian President's Council grant for the state support of young Russian scientists (project MK-531.2018.2).

Keywords: complex topology of attractor, generalized synchronization, hyperchaos, Lyapunov exponents

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