Search results for: asymptotic expansions

Authors: Ghazi Chabchoub, Mouna Feki, Mohamed Abid, Hammadi Ayadi

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Autoimmune thyroid diseases (AITDs), including Graves’ disease (GD) and Hashimoto’s thyroiditis (HT), are inherited as complex traits. Genetic factors associated with AITDs have been tentatively identified by candidate gene and genome scanning approaches. We analysed three intragenic microsatellite markers in the thyroid hormone receptor associated protein 2 gene (THRAP2), mapped near D12S79 marker, which have a potential role in immune function and inflammation [THRAP2-1(TG)n, THRAP2-2 (AC)n and THRAP2-3 (AC)n]. Our study population concerned 12 patients affected with AITDs belonging to a multiplex Tunisian family with high prevalence of AITDs. Fluorescent genotyping was carried out on ABI 3100 sequencers (Applied Biosystems USA) with the use of GENESCAN for semi-automated fragment sizing and GENOTYPER peak-calling software. Statistical analysis was performed using the non parametric Lod score (NPL) by Merlin software. Merlin outputs non-parametric NPLall (Z) and LOD scores and their corresponding asymptotic P values. The analysis for three intragenic markers in the THRAP2 gene revealed strong evidence for linkage (NPL=3.68, P=0.00012). Our results suggested the possible role of THRAP2 gene in AITDs susceptibility in this family.

Keywords: autoimmunity, autoimmune disease, genetic, linkage analysis

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Authors: Rakibul Islam Sagor, Sadia Ibnat Raisa

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Many nations across the globe, including Dhaka, are facing challenges in meeting the needs for a satisfactory quality of life due to the combination of a growing population and limited land resources. As a result, maximum spaces in modern cities are engulfed by concrete infrastructure, and there are hardly any open spaces in the urban neighborhoods. Although vertical movement has predominantly been employed for residential and commercial applications, the notion of vertical recreational and sports facilities remains unsettled. The primary objective of this study is to explore the feasibility of implementing vertical adaptations in urban recreational spaces, drawing upon the principles of high-rise theory. This article presents an analysis of the open spaces in Gulshan, Dhaka, focusing on the evaluation of the demand for open recreational and sports facilities that adequately cater to the existing population of the region. Initially, the study tried to identify and examine all potential open spaces within the designated area. Following that, an acceptable place is selected utilizing space syntax analysis, which takes into account the most conveniently accessible space for social interactions in the neighborhood. In addition, socioeconomic conditions of the area have been studied in order to determine the feasibility of the area. Finally, the study presented viable options for vertical urban sports facilities in the context of Dhaka, Bangladesh. Additionally, it seeks to develop strategies for maximizing the use of vertical expansions, thereby promoting a healthier and more active lifestyle among the city's residents. This approach aims to effectively handle the issue of limited land availability and enhance the efficiency of recreational areas around the globe.

Keywords: vertical sports, urban open spaces, social interaction, recreational activities

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Authors: Chittana Phompila

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The current increased population pushes increasing demands for natural resources and living space. In Laos, urban areas have been expanding rapidly in recent years. The rapid urbanization can have negative impacts on landscapes, including forest and agriculture lands. The primary objective of this research were to map current urban areas in a large city in Savannakhet province, in Laos, 2) to compare changes in urbanization between 1990 and 2018, and 3) to estimate forest and agriculture areas lost due to expansions of urban areas during the last over twenty years within study area. Landsat 8 data was used and existing GIS data was collected including spatial data on rivers, lakes, roads, vegetated areas and other land use/land covers). GIS data was obtained from the government sectors. Object based classification (OBC) approach was applied in ECognition for image processing and analysis of urban area using. Historical data from other Landsat instruments (Landsat 5 and 7) were used to allow us comparing changes in urbanization in 1990, 2000, 2010 and 2018 in this study area. Only three main land cover classes were focused and classified, namely forest, agriculture and urban areas. Change detection approach was applied to illustrate changes in built-up areas in these periods. Our study shows that the overall accuracy of map was 95% assessed, kappa~ 0.8. It is found that that there is an ineffective control over forest and land-use conversions from forests and agriculture to urban areas in many main cities across the province. A large area of agriculture and forest has been decreased due to this conversion. Uncontrolled urban expansion and inappropriate land use planning can lead to creating a pressure in our resource utilisation. As consequence, it can lead to food insecurity and national economic downturn in a long term.

Keywords: urbanisation, forest cover, agriculture areas, Landsat 8 imagery

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Authors: Rachida Ouysse

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This paper proposes a constrained principal components (CnPC) estimator for efficient estimation of large-dimensional factor models when errors are cross sectionally correlated and the number of cross-sections (N) may be larger than the number of observations (T). Although principal components (PC) method is consistent for any path of the panel dimensions, it is inefficient as the errors are treated to be homoskedastic and uncorrelated. The new CnPC exploits the assumption of bounded cross-sectional dependence, which defines Chamberlain and Rothschild’s (1983) approximate factor structure, as an explicit constraint and solves a constrained PC problem. The CnPC method is computationally equivalent to the PC method applied to a regularized form of the data covariance matrix. Unlike maximum likelihood type methods, the CnPC method does not require inverting a large covariance matrix and thus is valid for panels with N ≥ T. The paper derives a convergence rate and an asymptotic normality result for the CnPC estimators of the common factors. We provide feasible estimators and show in a simulation study that they are more accurate than the PC estimator, especially for panels with N larger than T, and the generalized PC type estimators, especially for panels with N almost as large as T.

Keywords: high dimensionality, unknown factors, principal components, cross-sectional correlation, shrinkage regression, regularization, pseudo-out-of-sample forecasting

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Authors: William Chung

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This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given.

Keywords: approximate subproblem, Dantzig-Wolfe decomposition, large-scale models, multiple subproblems

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Authors: Benson Ade Eniola Afere

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This paper introduces a family of fourth-order hybrid beta polynomial kernels developed for statistical analysis. The assessment of these kernels' performance centers on two critical metrics: asymptotic mean integrated squared error (AMISE) and kernel efficiency. Through the utilization of both simulated and real-world datasets, a comprehensive evaluation was conducted, facilitating a thorough comparison with conventional fourth-order polynomial kernels. The evaluation procedure encompassed the computation of AMISE and efficiency values for both the proposed hybrid kernels and the established classical kernels. The consistently observed trend was the superior performance of the hybrid kernels when compared to their classical counterparts. This trend persisted across diverse datasets, underscoring the resilience and efficacy of the hybrid approach. By leveraging these performance metrics and conducting evaluations on both simulated and real-world data, this study furnishes compelling evidence in favour of the superiority of the proposed hybrid beta polynomial kernels. The discernible enhancement in performance, as indicated by lower AMISE values and higher efficiency scores, strongly suggests that the proposed kernels offer heightened suitability for statistical analysis tasks when compared to traditional kernels.

Keywords: AMISE, efficiency, fourth-order Kernels, hybrid Kernels, Kernel density estimation

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Authors: Peter L. Varkonyi, Andras A. Sipos

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The quasi-static growth of elastic fibers is studied in the presence of distributed contact with an immobile surface, subject to isotropic dry or viscous friction. Unlike classical problems of elastic stability modelled by autonomous dynamical systems with multiple time scales (slowly varying bifurcation parameter, and fast system dynamics), this problem can only be formulated as a non-autonomous system without time scale separation. It is found that the fibers initially converge to a trivial, straight configuration, which is later replaced by divergence reminiscent of buckling phenomena. In order to capture the loss of stability, a new definition of exponential stability against infinitesimal perturbations for systems defined over finite time intervals is developed. A semi-analytical method for the determination of the critical length based on eigenvalue analysis is proposed. The post-critical behavior of the fibers is studied numerically by using variational methods. The emerging post-critical shapes and the asymptotic behavior as length goes to infinity are identified for simple spatial distributions of growth. Comparison with physical experiments indicates reasonable accuracy of the theoretical model. Some applications from modeling plant root growth to the design of soft manipulators in robotics are briefly discussed.

Keywords: buckling, elastica, friction, growth

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Authors: Najrullah Khan, Athar Ali Khan

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The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

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Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

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The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a  mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.

Keywords: asymptotic stability, Hartman-Grobman stability criterion, incubation period, Routh-Hurwitz criterion, Runge-Kutta method

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Authors: Ilaria Lucrezia Amerise

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The statistical modelling of precipitation data for a given portion of territory is fundamental for the monitoring of climatic conditions and for Hydrogeological Management Plans (HMP). This modelling is rendered particularly complex by the changes taking place in the frequency and intensity of precipitation, presumably to be attributed to the global climate change. This paper applies the Wakeby distribution (with 5 parameters) as a theoretical reference model. The number and the quality of the parameters indicate that this distribution may be the appropriate choice for the interpolations of the hydrological variables and, moreover, the Wakeby is particularly suitable for describing phenomena producing heavy tails. The proposed estimation methods for determining the value of the Wakeby parameters are the same as those used for density functions with heavy tails. The commonly used procedure is the classic method of moments weighed with probabilities (probability weighted moments, PWM) although this has often shown difficulty of convergence, or rather, convergence to a configuration of inappropriate parameters. In this paper, we analyze the problem of the likelihood estimation of a random variable expressed through its quantile function. The method of maximum likelihood, in this case, is more demanding than in the situations of more usual estimation. The reasons for this lie, in the sampling and asymptotic properties of the estimators of maximum likelihood which improve the estimates obtained with indications of their variability and, therefore, their accuracy and reliability. These features are highly appreciated in contexts where poor decisions, attributable to an inefficient or incomplete information base, can cause serious damages.

Keywords: generalized extreme values, likelihood estimation, precipitation data, Wakeby distribution

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Authors: Nelson Bii, Christopher Ouma, John Odhiambo

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Non-response is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random non-response using auxiliary data. In this study, it is assumed that random non-response occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random non-response. In particular, the auxiliary information is used via an improved Nadaraya-Watson kernel regression technique to compensate for random non-response. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at a 95% coverage rate. The results obtained in this study are useful, for instance, in choosing efficient estimators of the finite population mean in demographic sample surveys.

Keywords: mean squared error, random non-response, two-stage cluster sampling, confidence interval lengths

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Authors: Tomasz Borowski, Dawid Sołoducha, Rafał Rakoczy, Marian Kordas

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The application of magnetic field is essential for a wide range of technologies or processes (i.e., magnetic hyperthermia, bioprocessing). From the practical point of view, bioprocess control is often limited to the regulation of temperature at constant values favourable to microbial growth. The main aim of this study is to determine the effect of various types of electromagnetic fields (i.e., static or alternating) on the heat transfer in a self-designed magnetically assisted reactor. The experimental set-up is equipped with a measuring instrument which controlled the temperature of the liquid inside the container and supervised the real-time acquisition of all the experimental data coming from the sensors. Temperature signals are also sampled from generator of magnetic field. The obtained temperature profiles were mathematically described and analyzed. The parameters characterizing the response to a step input of a first-order dynamic system were obtained and discussed. For example, the higher values of the time constant means slow signal (in this case, temperature) increase. After the period equal to about five-time constants, the sample temperature nearly reached the asymptotic value. This dynamical analysis allowed us to understand the heating effect under the action of various types of electromagnetic fields. Moreover, the proposed mathematical description can be used to compare the influence of different types of magnetic fields on heat transfer operations.

Keywords: heat transfer, magnetically assisted reactor, dynamical analysis, transient function

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Authors: Karan Kamboj, Vikramjeet Singh, Vinod Kumar

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Considering blood to be a non-Newtonian Carreau liquid, this indirect numerical model investigates the pulsatile blood flow in a constricted restricted conduit that has numerous gentle stenosis inside the view of an increasing body speed. Asymptotic answers are obtained for the flow rate, pressure inclination, speed profile, sheer divider pressure, and longitudinal impedance to stream after the use of the twofold irritation approach to the problem of the succeeding non-straight limit esteem. It has been observed that the speed of the blood increases when there is an increase in the point of tightening of the conduit, the body speed increase, and the power regulation file. However, this rheological manner of behaving changes to one of longitudinal impedance to stream and divider sheer pressure when each of the previously mentioned boundaries increases. It has also been seen that the sheer divider pressure in the bloodstream greatly increases when there is an increase in the maximum depth of the stenosis but that it significantly decreases when there is an increase in the pulsatile Reynolds number. This is an interesting phenomenon. The assessments of the amount of growth in the longitudinal resistance to flow increase overall with the increment of the maximum depth of the stenosis and the Weissenberg number. Additionally, it is noted that the average speed of blood increases noticeably with the growth of the point of tightening of the corridor, and body speed increases border. This is something that can be observed.

Keywords: geometry of artery, pulsatile blood flow, numerous stenosis

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Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

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A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, Nonlocal Strain Gradient Theory, velocity gradient

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Lamia Bourdache, Amar Djema

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The effect of non-Newtonian property (power law index n) on traveling waves of thin layer of power law fluid flowing over an inclined plane is investigated. For this, a simplified second-order two-equation model (SM) is used. The complete model is second-order four-equation (CM). It is derived by combining the weighted residual integral method and the lubrication theory. This is due to the fact that at the beginning of the instability waves, a very small number of waves is observed. Using a suitable set of test functions, second order terms are eliminated from the calculus so that the model is still accurate to the second order approximation. Linear, spatial, and temporal stabilities are studied. For travelling waves, a particular type of wave form that is steady in a moving frame, i.e., that travels at a constant celerity without changing its shape is studied. This type of solutions which are characterized by their celerity exists under suitable conditions, when the widening due to dispersion is balanced exactly by the narrowing effect due to the nonlinearity. Changing the parameter of celerity in some range allows exploring the entire spectrum of asymptotic behavior of these traveling waves. The (SM) model is converted into a three dimensional dynamical system. The result is that the model exhibits bifurcation scenarios such as heteroclinic, homoclinic, Hopf, and period-doubling bifurcations for different values of the power law index n. The influence of the non-Newtonian parameter on the nonlinear development of these travelling waves is discussed. It is found at the end that the qualitative characters of bifurcation scenarios are insensitive to the variation of the power law index.

Keywords: inclined plane, nonlinear stability, non-Newtonian, thin film

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

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The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: control, limits cycle, robot, stability

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Authors: Yemane Hailu Fissuh, Zhongzhan Zhang

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An estimating equation technique is an alternative method of the widely used maximum likelihood methods, which enables us to ease some complexity due to the complex characteristics of time-varying covariates. In the situations, when both the time-varying covariates and left-truncation are considered in the model, the maximum likelihood estimation procedures become much more burdensome and complex. To ease the complexity, in this study, the modified estimating equations those have been given high attention and considerations in many researchers under semiparametric transformation model was proposed. The purpose of this article was to develop the modified estimating equation under flexible and general class of semiparametric transformation models for left-truncated and right censored survival data with time-varying covariates. Besides the commonly applied Cox proportional hazards model, such kind of problems can be also analyzed with a general class of semiparametric transformation models to estimate the effect of treatment given possibly time-varying covariates on the survival time. The consistency and asymptotic properties of the estimators were intuitively derived via the expectation-maximization (EM) algorithm. The characteristics of the estimators in the finite sample performance for the proposed model were illustrated via simulation studies and Stanford heart transplant real data examples. To sum up the study, the bias for covariates has been adjusted by estimating density function for the truncation time variable. Then the effect of possibly time-varying covariates was evaluated in some special semiparametric transformation models.

Keywords: EM algorithm, estimating equation, semiparametric transformation models, time-to-event outcomes, time varying covariate

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Authors: Shabadini Sampath, Jinglang Feng

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With huge kinetic energy, space debris poses a major threat to astronauts’ space activities and spacecraft in orbit if a collision happens. The active removal of space debris is required in order to avoid frequent collisions that would occur. In addition, the amount of space debris will increase uncontrollably, posing a threat to the safety of the entire space system. But the safe and reliable removal of large-scale space debris has been a huge challenge to date. While capturing and deorbiting space debris, the space manipulator has to achieve high control precision. However, due to uncertainties and unknown disturbances, there is difficulty in coordinating the control of the space manipulator. To address this challenge, this paper focuses on developing a robust and intelligent control algorithm that controls joint movement and restricts it on the sliding manifold by reducing uncertainties. A neural network adaptive sliding mode controller (NNASMC) is applied with the objective of finding the control law such that the joint motions of the space manipulator follow the given trajectory. A computed torque control (CTC) is an effective motion control strategy that is used in this paper for computing space manipulator arm torque to generate the required motion. Based on the Lyapunov stability theorem, the proposed intelligent controller NNASMC and CTC guarantees the robustness and global asymptotic stability of the closed-loop control system. Finally, the controllers used in the paper are modeled and simulated using MATLAB Simulink. The results are presented to prove the effectiveness of the proposed controller approach.

Keywords: GNC, active removal of space debris, AI controllers, MatLabSimulink

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Authors: A. M. Pashayev, A. S. Samedov, T. B. Usubaliyev, N. Sh. Yusifov

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Different types of coating technologies are widely used for gas turbine blades. Thermal barrier coatings, consisting of ceramic top coat, thermally grown oxide and a metallic bond coat are used in applications for thermal protection of hot section components in gas turbine engines. Operational characteristics and longevity of high-temperature turbine blades substantially depend on a right choice of composition of the protective thermal barrier coatings. At a choice of composition of a coating and content of the basic elements it is necessary to consider following factors, as minimum distinctions of coefficients of thermal expansions of elements, level of working temperatures and composition of the oxidizing environment, defining the conditions for the formation of protective layers, intensity of diffusive processes and degradation speed of protective properties of elements, extent of influence on the fatigue durability of details during operation, using of elements with high characteristics of thermal stability and satisfactory resilience of gas corrosion, density, hardness, thermal conduction and other physical characteristics. Forecasting and a choice of a thermal barrier coating composition, all above factors at the same time cannot be considered, as some of these characteristics are defined by experimental studies. The implemented studies and investigations show that one of the main failures of coatings used on gas turbine blades is related to not fully taking the physical-chemical features of elements into consideration during the determination of the composition of alloys. It leads to the formation of more difficult spatial structure, composition which also changes chaotically in some interval of concentration that doesn't promote thermal and structural firmness of a coating. For the purpose of increasing the thermal and structural resistant of gas turbine blade coatings is offered a new approach to forecasting of composition on the basis of analysis of physical-chemical characteristics of alloys taking into account the size factor, electron configuration, type of crystal lattices and Darken-Gurry method. As a result, of calculations and experimental investigations is offered the new four-component metallic bond coat on the basis of chrome for the gas turbine blades.

Keywords: gas turbine blades, thermal barrier coating, metallic bond coat, strategic metals, physical-chemical features

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Authors: Khanh To Duc, Monica Chiogna, Gianfranco Adimari

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With three diagnostic categories, assessment of the performance of diagnostic tests is achieved by the analysis of the receiver operating characteristic (ROC) surface, which generalizes the ROC curve for binary diagnostic outcomes. The volume under the ROC surface (VUS) is a summary index usually employed for measuring the overall diagnostic accuracy. When the true disease status can be exactly assessed by means of a gold standard (GS) test, unbiased nonparametric estimators of the ROC surface and VUS are easily obtained. In practice, unfortunately, disease status verification via the GS test could be unavailable for all study subjects, due to the expensiveness or invasiveness of the GS test. Thus, often only a subset of patients undergoes disease verification. Statistical evaluations of diagnostic accuracy based only on data from subjects with verified disease status are typically biased. This bias is known as verification bias. Here, we consider the problem of correcting for verification bias when continuous diagnostic tests for three-class disease status are considered. We assume that selection for disease verification does not depend on disease status, given test results and other observed covariates, i.e., we assume that the true disease status, when missing, is missing at random. Under this assumption, we discuss several solutions for ROC surface analysis based on imputation and re-weighting methods. In particular, verification bias-corrected estimators of the ROC surface and of VUS are proposed, namely, full imputation, mean score imputation, inverse probability weighting and semiparametric efficient estimators. Consistency and asymptotic normality of the proposed estimators are established, and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations using real datasets are also given.

Keywords: imputation, missing at random, inverse probability weighting, ROC surface analysis

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Authors: Gulcan Ozerim, Gunay Anlas

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In shape memory alloys, upon loading, stress increases around crack tip and a martensitic phase transformation occurs in early stages. In many studies the stress distribution in the vicinity of the crack tip is represented by using linear elastic fracture mechanics (LEFM) although the pseudo-elastic behavior results in a nonlinear stress-strain relation. In this study, the HRR singularity (Hutchinson, Rice and Rosengren), that uses Rice’s path independent J-integral, is tried to formulate the stress distribution around the crack tip. In HRR approach, the Ramberg-Osgood model for the stress-strain relation of power-law hardening materials is used to represent the elastic-plastic behavior. Although it is recoverable, the inelastic portion of the deformation in martensitic transformation (up to the end of transformation) resembles to that of plastic deformation. To determine the constants of the Ramberg-Osgood equation, the material’s response is simulated in ABAQUS using a UMAT based on ZM (Zaki-Moumni) thermo-mechanically coupled model, and the stress-strain curve of the material is plotted. An edge cracked shape memory alloy (Nitinol) plate is loaded quasi-statically under mode I and modeled using ABAQUS; the opening stress values ahead of the cracked tip are calculated. The stresses are also evaluated using the asymptotic equations of both LEFM and HRR. The results show that in the transformation zone around the crack tip, the stress values are much better represented when the HRR singularity is used although the J-integral does not show path independent behavior. For the nodes very close to the crack tip, the HRR singularity is not valid due to the non-proportional loading effect and high-stress values that go beyond the transformation finish stress.

Keywords: crack, HRR singularity, shape memory alloys, stress distribution

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Authors: Nir Schreiber, Reuven Cohen, Simi Haber

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The Potts model has been widely explored in the literature for the last few decades. While many analytical and numerical results concern with the traditional two site interaction model in various geometries and dimensions, little is yet known about models where more than two spins simultaneously interact. We consider a ferromagnetic four site interaction Potts model on the square lattice (FFPS), where the four spins reside in the corners of an elementary square. Each spin can take an integer value 1,2,...,q. We write the partition function as a sum over clusters consisting of monochromatic faces. When the number of faces becomes large, tracing out spin configurations is equivalent to enumerating large lattice animals. It is known that the asymptotic number of animals with k faces is governed by λᵏ, with λ ≈ 4.0626. Based on this observation, systems with q < 4 and q > 4 exhibit a second and first order phase transitions, respectively. The transition nature of the q = 4 case is borderline. For any q, a critical giant component (GC) is formed. In the finite order case, GC is simple, while it is fractal when the transition is continuous. Using simple equilibrium arguments, we obtain a (zero order) bound on the transition point. It is claimed that this bound should apply for other lattices as well. Next, taking into account higher order sites contributions, the critical bound becomes tighter. Moreover, for q > 4, if corrections due to contributions from small clusters are negligible in the thermodynamic limit, the improved bound should be exact. The improved bound is used to relate the critical point to the finite correlation length. Our analytical predictions are confirmed by an extensive numerical study of FFPS, using the Wang-Landau method. In particular, the q=4 marginal case is supported by a very ambiguous pseudo-critical finite size behavior.

Keywords: entropic sampling, lattice animals, phase transitions, Potts model

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Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: Satish Kumar, Spandan Sahu, Sarjati Sahoo, K. K. Khatua

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An experimental investigation has been carried out in a tilting flume of 2 m wide, 13 m long, and 0.3 m deep to study the effect of flow on the formation of braided channel pattern. Sediment flow is recirculated through the flume, which passes from the headgate to the sediment/water collecting tank through the tailgate. Further, without altering the geometry of the sand bed channel, the discharge is varied to study the effect of the formation of the braided pattern with time. Then the flow rate is varied to study the effect of flow on the formation of the braided pattern. Sediment transport rate is highly variable and was found to be a nonlinear function of flow rate, aspect ratio, longitudinal slope, and time. Total braided intensity (BIT) for each discharge case is found to be more than the active braided intensity (BIA). Both the parameters first increase and then decrease as the time progresses following a similar pattern for all the observed discharge cases. When the flow is increased, the movement of sediment also increases since the active braided intensity is found to adjust quickly. The measurement of velocity and boundary shear helps to study the erosion and sedimentation processes in the channel and formation of small meandering channels and then the braided channel for different discharge conditions of a sediment river. Due to regime properties of rivers, both total braided Intensity and active braided intensity become stable for a given channel and flow conditions. In the present case, the trend of the ratio of BIA to BIT is found to be asymptotic against the time with a value of 0.4. After the particular time elapses off the flow, new small channels are also found to be formed with changes in the sinuosity of the active channels, thus forming the braided network. This is due to the continuous erosion and sedimentation processes occurring for the flow process for the flow and sediment conditions.

Keywords: active braided intensity, bed load, sediment transport, shear stress, total braided intensity

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Authors: Daniel Fundi Murithi

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Data from economic, social, clinical, and industrial studies are in some way incomplete or incorrect due to censoring. Such data may have adverse effects if used in the estimation problem. We propose the use of Maximum Likelihood Estimation (MLE) under a progressive type-II censoring scheme to remedy this problem. In particular, maximum likelihood estimates (MLEs) for the location (µ) and scale (λ) parameters of two Parameter Rayleigh distribution are realized under a progressive type-II censoring scheme using the Expectation-Maximization (EM) and the Newton-Raphson (NR) algorithms. These algorithms are used comparatively because they iteratively produce satisfactory results in the estimation problem. The progressively type-II censoring scheme is used because it allows the removal of test units before the termination of the experiment. Approximate asymptotic variances and confidence intervals for the location and scale parameters are derived/constructed. The efficiency of EM and the NR algorithms is compared given root mean squared error (RMSE), bias, and the coverage rate. The simulation study showed that in most sets of simulation cases, the estimates obtained using the Expectation-maximization algorithm had small biases, small variances, narrower/small confidence intervals width, and small root of mean squared error compared to those generated via the Newton-Raphson (NR) algorithm. Further, the analysis of a real-life data set (data from simple experimental trials) showed that the Expectation-Maximization (EM) algorithm performs better compared to Newton-Raphson (NR) algorithm in all simulation cases under the progressive type-II censoring scheme.

Keywords: expectation-maximization algorithm, maximum likelihood estimation, Newton-Raphson method, two-parameter Rayleigh distribution, progressive type-II censoring

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Authors: K. Al Ammari, B. G. Clarke

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Soil improvement using vibro stone column techniques consists of two main parts: (1) the installed load bearing columns of well-compacted, coarse-grained material and (2) the improvements to the surrounding soil due to vibro compaction. Extensive research work has been carried out over the last 20 years to understand the improvement in the composite foundation performance due to the second part mentioned above. Nevertheless, few of these studies have tried to quantify some of the key design parameters, namely the changes in the stiffness and stress state of the treated soil, or have consider these parameters in the design and calculation process. Consequently, empirical and conservative design methods are still being used by ground improvement companies with a significant variety of results in engineering practice. Two-dimensional finite element study to develop an axisymmetric model of a single stone column reinforced foundation was performed using PLAXIS 2D AE to quantify the effect of the vibro installation of this column in soft saturated clay. Settlement and bearing performance were studied as an essential part of the design and calculation of the stone column foundation. Particular attention was paid to the large deformation in the soft clay around the installed column caused by the lateral expansion. So updated mesh advanced option was taken in the analysis. In this analysis, different degrees of stone column lateral expansions were simulated and numerically analyzed, and then the changes in the stress state, stiffness, settlement performance and bearing capacity were quantified. It was found that application of radial expansion will produce a horizontal stress in the soft clay mass that gradually decrease as the distance from the stone column axis increases. The excess pore pressure due to the undrained conditions starts to dissipate immediately after finishing the column installation, allowing the horizontal stress to relax. Changes in the coefficient of the lateral earth pressure K ٭, which is very important in representing the stress state, and the new stiffness distribution in the reinforced clay mass, were estimated. More encouraging results showed that increasing the expansion during column installation has a noticeable effect on improving the bearing capacity and reducing the settlement of reinforced ground, So, a design method should include this significant effect of the applied lateral displacement during the stone column instillation in simulation and numerical analysis design.

Keywords: bearing capacity, design, installation, numerical analysis, settlement, stone column

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Authors: Lukas Reznak, Maria Reznakova

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Recession of an economy has a profound negative effect on all involved stakeholders. It follows that timely prediction of recessions has been of utmost interest both in the theoretical research and in practical macroeconomic modelling. Current mainstream of recession prediction is based on standard OLS models of continuous GDP using macroeconomic data. This approach is not suitable for two reasons: the standard continuous models are proving to be obsolete and the macroeconomic data are unreliable, often revised many years retroactively. The aim of the paper is to explore a different branch of recession forecasting research theory and verify the findings on real data of the Czech Republic and Germany. In the paper, the authors present a family of discrete choice probit models with parameters estimated by the method of maximum likelihood. In the basic form, the probits model a univariate series of recessions and expansions in the economic cycle for a given country. The majority of the paper deals with more complex model structures, namely dynamic and bivariate extensions. The dynamic structure models the autoregressive nature of recessions, taking into consideration previous economic activity to predict the development in subsequent periods. Bivariate extensions utilize information from a foreign economy by incorporating correlation of error terms and thus modelling the dependencies of the two countries. Bivariate models predict a bivariate time series of economic states in both economies and thus enhance the predictive performance. A vital enabler of timely and successful recession forecasting are reliable and readily available data. Leading indicators, namely the yield curve and the stock market indices, represent an ideal data base, as the pieces of information is available in advance and do not undergo any retroactive revisions. As importantly, the combination of yield curve and stock market indices reflect a range of macroeconomic and financial market investors’ trends which influence the economic cycle. These theoretical approaches are applied on real data of Czech Republic and Germany. Two models for each country were identified – each for in-sample and out-of-sample predictive purposes. All four followed a bivariate structure, while three contained a dynamic component.

Keywords: bivariate probit, leading indicators, recession forecasting, Czech Republic, Germany

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Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

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Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

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Authors: Avinash Nayak, Debopam Das

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

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

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