Polynomial Distribution Research Articles

Bernstein polynomial distribution estimators and the Dvoretzky–Kiefer–Wolfowitz inequality

The problem of nonparametric distribution function estimation using the Bernstein polynomials is investigated. It is proved that the Bernstein polynomial estimator that was most often examined so far does not satisfy the Dvoretzky–Kiefer–Wolfowitz inequal

On the effect of a penetrating recirculation region on the bifurcations of the flow past a permeable sphere

We study the flow past a permeable sphere modeled using homogenization theory. The flow through the porous medium is described by the Darcy law, in which the permeability quantifies the resistance for the fluid to pass through the microstructure. A slip condition on the tangential velocity at the interface between the fluid and porous region is employed to account for the viscous effects in the proximity of the interface. The steady and axisymmetric flow is first characterized under the assumption of a homogenous and isotropic porous medium. In a certain range of permeability, the recirculation region penetrates inside the sphere, resulting in a strong modification of the linear stability properties of the flow and in a decrease in the critical Reynolds numbers for the flow instability. However, for very large permeabilities, a critical permeability value is identified, beyond which the steady and axisymmetric flow remains always linearly stable. The hypothesis of a homogenous porous medium is then relaxed, and the effect of polynomial distributions of permeability inside the body is studied. Interestingly, some macroscopic flow properties do not significantly vary with the permeability distributions, provided that their average is maintained constant. The analysis is concluded by outlining a simplified procedure to retrieve the full-scale structure corresponding to a considered distribution of permeability.

A stiffness degradation model of bolted joint based on fourth polynomial pressure distribution

This paper proposed a new friction mechanical model based on the Coulomb friction law to describe the nonlinear stiffness degradation of bolted joints. Several different contact pressure distributions are analyzed, and the results show that the fourth polynomial distribution has a better effect on characterizing the contact pressure distribution of the bolted interface. Then, a new density function of friction shear stress is obtained through mathematical deduction. There is an interesting discovery that the new density function curve is similar to the truncated power-law spectrum curve. In addition, a method of parameter identification is proposed, and multiple sets of parameters are identified for the subsequent model verification. Finally, the correlation between the theoretical value and the experimental data under different pre-tightening forces is analyzed. The results show the accuracy improvement of the new model compared with the existing model. The new model has better mechanism rationality and can be applied to stiffness degradation analysis.

Chebyshev apodized fiber Bragg gratings.

In this paper, a new apodized fiber Bragg grating (FBG) structure, the Chebyshev apodization, is proposed. The Chebyshev polynomial distribution has been widely used for the optimal design of antennas and filters, but it has not been used for designing FBGs. Unlike the function of traditional Gaussian-apodized FBGs, the Chebyshev polynomial is a discrete function. We demonstrate a new methodology for designing Chebyshev-apodized FBGs: the grating region is divided by discrete n sections with uniform gratings, while the index change is used to express the Chebyshev polynomial. We analyze the Chebyshev-apodized FBGs by using coupled mode theory and the piecewise-uniform approach. The reflection spectrum and the dispersion of Chebyshev-apodized FBGs are calculated and compared with those of Gaussian FBGs. Moreover, a sidelobe suppression level (SSL), a parameter of the Chebyshev polynomial, along with the maximum ac-index change of FBGs are analyzed. Assume that the grating length is 20mm, SSL is 100 dB, the section number is 40, and the maximum ac-index change is 2 × 10-4. The reflection spectrum of Chebyshev apodized FBGs shows flattened sidelobes with an absolute SSL of -95.9 dB (corresponding to SSL=100 dB). The simulation results reveal that at the same full width at half maximum, the Chebyshev FBGs have lower sidelobe suppression than the Gaussian FBGs, but their dispersion is similar. We demonstrate the potential of using Chebyshev-apodized FBGs in optical filters, dispersion compensators, and sensors; Chebyshev apodization can be applied in the design of periodic dielectric waveguides.

Assessment of the growing stock and annual increment of Pinus brutia Ten. stands in Kfardebel, Latakia, Syria

The study assessed the growing stock and wood increment of Pinus brutia Ten growing on the Kfardabil-Jabla plantation in Syria. The plantation was created in 1974–1976. Biometric field surveys were carried out over three time periods. In the plantation under study, circular sampling plots with a radius of 11.4 m were made. In the course of the study, we used a polynomial distribution to estimate the height of the measured trees, which makes it possible to predict changes in the plantation growth parameters in the future. There was a substantial increase in the growing stock in the study area: from 197.5 m3 per hectare in 2011 to 213.3 m3 per hectare in 2020. The annual timber increment fell from 2.0 m3 in 2011–2014 to 1.3 m3 per hectare in 2014–2020, which is likely to be associated with age-related changes and excessive stand density. We recommend to remove slow growing trees to reduce the density of the stand and make space for the remaining. The results obtained on the increments and volumes of wood on the Pinus brutia Ten plantation show the potential volume of wood to be harvested in accordance with the principle of sustainable forest management.

Crossings and Nestings Over Some Motzkin Objects and $q$-Motzkin Numbers

We examine the enumeration of certain Motzkin objects according to the numbers of crossings and nestings. With respect to continued fractions, we compute and express the distributions of the statistics of the numbers of crossings and nestings over three sets, namely the set of $4321$-avoiding involutions, the set of $3412$-avoiding involutions, and the set of $(321,3\bar{1}42)$-avoiding permutations. To get our results, we exploit the bijection of Biane restricted to the sets of $4321$- and $3412$-avoiding involutions which was characterized by Barnabei et al. and the bijection between $(321,3\bar{1}42)$-avoiding permutations and Motzkin paths, presented by Chen et al.. Furthermore, we manipulate the obtained continued fractions to get the recursion formulas for the polynomial distributions of crossings and nestings, and it follows that the results involve two new $q$-Motzkin numbers.

Assessment and sensitive analysis of biological water risks in water resources with application of classical mass transfer computations

Due to the urgent need for water in all parts of industrial or developing societies, water supply, and transmission facilities are suitable targets for biological risks. Given that even a short interruption in water supply and water supply operations has a great impact on daily activities in the community, the deliberate contamination of urban water resources has irreparable consequences in the field of public health, and the economy of society will follow. Unfortunately, most officials in the public health control departments in our country have received limited training in detecting accidental or intentional contamination of water resources and dealing with the spread of waterborne diseases both naturally and intentionally. For this reason, there is low preparedness in the responsible agencies to deal with waterborne diseases during biological risks. In the first step of this research, a review study has been conducted on water biological risks and operational strategies to deal with them. In the following, it has studied how Escherichia coli (E. coli) bacteria spread in aqueous media. In this regard, the kinetic model of the studied microorganism was analyzed based on the implementation of (Fick Law) in polar coordinates and the combination of (Dirac Distribution) with (Legendre polynomial) distribution. Finally, after studying the factors affecting the microbial pollutant emission coefficient, the effects of all three factors of linear velocity, linear motion time period, and angle of motion on the pollutant emission flux and biofilm diffusion time in the water supply network environment were investigated. Studies have shown that the linear velocity parameter of Escherichia coli with a nonlinear relationship has the greatest effects on the release of microbial contaminants.

Developing an innovative bimodal model to characterize the dynamic radar cross section of aircrafts

The distribution of aircraft dynamic radar cross section (RCS) varies at different course short-cuts and heights and can behave as a bimodal shape. Classical models, such as the Weibull distribution, the chi-square distribution, and lognormal distribution, fit poorly with bimodal RCS distributions and are unable to accurately describe the statistical characteristics of aircraft dynamic RCS. In order to overcome the shortcoming of the classical models, we propose an exponential polynomial distribution model as the probability density function for studying the RCS statistical characteristics. The model parameters were acquired through the linear least-square method. Based on the RCS statistical data, the proposed distribution model was validated through simulation experiments. We calculated the fitting error between the new model and the RCS statistical distribution and determined the optimal exponential polynomial distribution model. We then computed the coefficients of the determination to evaluate the proposed model. The Kolmogorov–Smirnov test showed that the proposed approach yielded smaller values compared to conventional distribution models. For all the analyzed cases, the exponential polynomial model can fit very well against the RCS distribution data with bimodal shape, and the fitting effect is significantly better than the results of the three classical models. The advantages of the proposed model are further demonstrated by comparing it with the Gaussian mixture distribution model from fitting error, determination coefficient, goodness-of-fit, mean error and variance error. The results suggest that the exponential polynomial distribution model provides a more effective alternative in describing the fluctuation characteristics of aircraft dynamic RCS at the different course short-cuts and heights. Given the advantages exhibited by the exponential polynomial distribution model in this study, the methodology and findings in this study can be used to improve in early warning detection of radar targets and as a theoretical basis to enhance the overall performance of radars. 2009 Elsevier Ltd. All rights reserved.

Elliptical harmonic method for gravity forward modelling of 2D bodies

The elliptical harmonic method for gravity forward computation of two-dimensional (2D) bodies with constant, polynomial and exponential density distributions is presented. This paper gives the elliptical harmonic expansions for the gravity field of 2D bodies mainly including the gravitational attractions and gradients, and the conversions from the surface integral expressions of the elliptical harmonic coefficients and the surface integral of the density function into line integrals using Gauss divergence theorem for evaluation of the gravity field. Due to the requirements of the Gauss divergence and Stokes theorems that the boundary surface or curve of the body is piecewise smooth and the vector field as well as its first-order partial derivatives are continuous, the effects of the discontinuities of the elliptical coordinates on the integral conversion using Gauss divergence and Stokes theorems are considered. The integrands of the converted line integrals are the analytical expressions with respect to the coordinates of the internal point of the 2D body for the constant and polynomial density models, but are not elementary functions for the exponential density model that the integrands can be solved by approximating the density function with polynomial function. The numerical experiments with two tested bodies including a rectangular cylinder body with quadratic density contrast varying with depth and a 26-sided polygon body with quadratic density contrast varying in both horizontal and vertical directions show the convergence, accuracy and stability of the elliptical harmonic algorithm. Compared with the circular harmonic approach, the elliptical harmonic approach has smaller non-convergence region between the boundary of the 2D body and the reference ellipse and is convergent faster for most of the external observation points.

Modified Genetic Algorithm and Polynomial Distribution Based Convolutional Neural Network for Asthma Disease Diagnosis

Prevention is considered to be the key solution for asthma rather than treatment for the same. Generally, asthma starts initially at early life, hence primary asthma determination in young children is regarded as significant life saving activity. In prevailing scheme, classification necessitates extra time for task completion as well disease prediction cannot be accomplished precisely using enormous samples for evaluation. Modified Genetic Algorithm and Polynomial distribution based Convolutional Neural Network (MGA+PCNN) algorithm is greatly utilized for mitigating these issues and this methodology encompasses key steps such as normalization, pre-processing, feature selection and classification process. Improved Variance Stabilizing Normalization (IVSN) is exploited for dataset accuracy improvement. Pre-processing is achieved using logistic regression clustering algorithm which helps in increasing asthma patient’s attributes significance and these pre-processed features are considered for feature selection process. MGA algorithm is suggested for highest f-measure features selection from specified dataset via best global and local fitness values. Subsequently, PCNN algorithm is deployed for accurate outcome classification for asthma disease identification. It is thereby validated that suggested MGA+PCNN algorithm offers improved True Positive Rate (TPR), False Positive Rate (FPR), F-measure and accuracy than prevailing approaches.

Egeria densa Allelopathy on Microcystis aeruginosa Under Different Light Intensities and Preliminary Insight into Inter-Parameter Relationships

Egeria densa release allelochemicals harmful to other species, including cyanobacteria. Under natural conditions, E. densa and Microcystis aeruginosa can be found in various aquatic systems with different light levels. The effect that the coexistence of E. densa has on M. aeruginosa was tested under different photosynthetically active radiation (PAR) intensities. The growth, chlorophyll-a, oxidative stress, and antioxidant activities of M. aeruginosa were quantified after 7 days of coexistence with E. densa. A control experiment without E. densa was conducted for M. aeruginosa under the same conditions to distinguish the effect of the PAR intensity from the allelopathic effect. The allelopathy of E. densa on M. aeruginosa is significantly influenced by the PAR intensity. PAR intensities lower or higher than the favorable range further suppressed M. aeruginosa under coexistence. Research has revealed that the allelopathic effect of E. densa can be utilized to biologically suppress M. aeruginosa under various light conditions. Strong second-order polynomial distributions between the optical density (OD) and cellular H2O2 content of M. aeruginosa were found for both the control and coexistence conditions. In the practical application of E. densa allelopathy, OD can be adopted as a convenient method to obtain an approximate stress status on M. aeruginosa.

Autism Spectrum Disorder Identification Using Polynomial Distribution based Convolutional Neural Network

One main psychiatric disorder found in humans is ASD (Autistic Spectrum Disorder). The disease manifests in a mental disorder that restricts humans from communications, language, speech in terms of their individual abilities. Even though its cure is complex and literally impossible, its early detection is required for mitigating its intensity. ASD does not have a pre-defined age for affecting humans. A system for effectively predicting ASD based on MLTs (Machine Learning Techniques) is proposed in this work. Hybrid APMs (Autism Prediction Models) combining multiple techniques like RF (Random Forest), CART (Classification and Regression Trees), RF-ID3 (RF-Iterative Dichotomiser 3) perform well, but face issues in memory usage, execution times and inadequate feature selections. Taking these issues into account, this work overcomes these hurdles in this proposed work with a hybrid technique that combines MCSO (Modified Chicken Swarm Optimization) and PDCNN (Polynomial Distribution based Convolution Neural Network) algorithms for its objective. The proposed scheme’s experimental results prove its higher levels of accuracy, precision, sensitivity, specificity, FPRs (False Positive Rates) and lowered time complexity when compared to other methods.

Gradient porosity distribution of adsorbent bed for efficient adsorption cooling

Adsorption cooling is an emerging, environment-friendly and energy-saving refrigeration technology. In conventional studies, the spatial distribution of the porosity of the adsorbent bed has never been considered, which could impact the heat and mass transfer in adsorption process, thus the cooling performance of the adsorption cooling systems. Here the influence of the spatial gradient porosity distribution (stepwise and continuous polynomial distributions) of the adsorbent bed on the adsorption process and cooling performance is systematically explored with average bed porosity kept constant. Results reveal that the cooling performance is significantly impacted by the spatial porosity distribution in the z direction. Provided the bed porosity increases from the cooling side to the steam side, the overall heat transfer performance is improved, which reduces the adsorption temperature that contributes to the adsorption uptake and the specific cooling power (SCP). Under the continuous polynomial distribution of the bed porosity, a SCP of 0.348 kW kg−1 is obtained, 9.5% larger than that under the uniform distribution of the bed porosity. A desired bed porosity distribution of the adsorbent bed is that the porosity gradient increases from the cooling side to the steam side.

A pure boundary element analysis of Reissner's shear deformable plates subjected to higher-order polynomial loading

In this paper, a direct Boundary Element Method (BEM) solution without load domain integrals for Reissner's plates subjected to higher-order polynomial loads is derived. To this end, the Multiple Reciprocity Method (MRM), which consists to transform original domain integrals into a series of equivalent boundary integrals using Green's second identity in a recursive way, is used. Moreover, higher-order fundamental solutions of thick plates in bending, which are essential in MRM technique, are also derived and presented in an explicit form for all terms of the series. Despite this present approach deals directly with higher-order polynomial distribution load, this boundary element solution can be also applied to other load distribution functions, since it is possible to expand them in a polynomial series. Numerical results are presented for differing cases of boundary conditions and load functions, such as linear, double quadratic, exponential, and double sinusoidal distributions. The BEM results are compared to analytical solutions showing good agreement among them.

Practical evaluation of flows due to arbitrary singularity distributions in the 3D theory of ship motions in regular waves at [formula omitted

The Green-function and boundary-element method, widely used in ship and offshore hydrodynamics, requires accurate and efficient numerical evaluation of flows created by (typically polynomial) distributions of singularities (sources and dipoles) over (flat or curved) panels of various shapes (notably quadrilateral or triangular) that approximate the surface of a ship or offshore structure. This crucial core-element of the Green-function and boundary-element method is considered for the 3D theory of ship motions in regular waves in the regime 0.3≤τ≡Vω∕g where V and ω denote the ship speed and the (encounter) wave frequency, and g is the acceleration of gravity. In this regime, the dispersion relation yields two dispersion curves in the Fourier plane (α,β) that are conveniently defined in the Cartesian form α=α∗(β) with −∞<β<∞, whereas the polar representation k=k∗(γ) where k≡α2+β2 and −π≤γ≤π is convenient and used in a related study to represent the three dispersion curves associated with ship motions in the regime τ<1∕4. The complementary analytical representations given in this study for 0.3≤τ and previously for τ<1∕4 provide simple and practical expressions for the flow due to an arbitrary compact distribution of singularities that are suited for accurate and efficient numerical evaluation for all values of τ outside the relatively narrow range 0.25≤τ<0.3.

Analytical solution of kth price auction

We provide an exact analytical solution of the Nash equilibrium for the kth price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.

Lightweight Noninteractive Membership Authentication and Group Key Establishment for WSNs

Wireless sensor networks (WSNs) exhibit their potential capacity in the next generation of mobile communication networks and wireless systems (5G). Collected data in WSNs are different from most data transmitted in digital communication applications. Most collected data in WSNs contain only few bits of information. Conventional protocols are not suitable for WSNs since this environment needs more flexible and lightweight protocols for secure group communications. Hence, how to realize the mutual secure and lightweight communication is a big challenge for WSNs. User authentication and key establishment are two fundamental security services in secure communications for WSNs. In this paper, we propose a novel design which embeds the function of membership authentication and group key establishment in WSNs. By using an asymmetric bivariate polynomial, membership authentication and pairwise shared keys distribution are realized. Then, each member mixes his/her input with pairwise shared keys with other members and releases the encrypted value in a broadcast channel. After collecting all released values, each member can compute the group key efficiently. Our proposal is noninteractive and lightweight. As it enjoys low computation and communication costs compared with the state-of-the-art cryptographic solutions, this design is more suitable for efficient membership authentication and group key establishment in WSNs.

Physical training in patients with chronic heart failure: level of involvement, as well as psychosocial, anamnestic and iatrogenic factors that determine the motivation to practice

Introduction Physical exercise (PE) is a necessary part in the treatment of patients with chronic heart failure (CHF), which is stated in the European Society of Cardiology guidelines and the Russian Heart Failure Society guidelines. However, this type of non-drug treatment is still not sufficiently used in HF patients in Russia.Aim To study the current involvement of HF patients in PT and to describe psychosocial factors that influence the patients' willingness to exercise and potential barriers and motivations for PE.Methods This study was designed as an in-moment survey. Patients with CHF who visited clinics in 7 cities of the Russian Federation in 2018 as a part of European Heart Failure Awareness Days were provided with a self-administered questionnaire containing questions about their social and educational status, attitude to PT as a method of treatment, and factors motivating and demotivating them to participation in training sessions. The survey participants were also asked a question about their source of information about exercise in HF. Physicians filled in the items describing HF clinical manifestations (left ventricular ejection fraction (EF) and HF functional class (FC)). Code numbers were used for further identification of the participants and to protect their confidentiality. Statistical analysis was performed with the StatXcat-8 program. Limits of exact confidence intervals (CIs) were provided both for fractions and parameters of polynomial distribution. CI limits for differences and fractions were calculated using MOVER. Age was analyzed using the PAST program.Results The study included 560 patients with HF; 52 % of them were women (mean age, 64; 95 % CI: 63-65 years). Women were 3 years older than men (95 % CI: 1.3-4.9 years). 501 (89.5 %) patients had FC II-III; 265 (49 %) patients had HF with low EF. 350 (62 %) patients had comorbidities: 41.4 % of patients had diabetes mellitus and 25.4 % of patients had arthritis. Only 91 (17 %) patients reported exercising. Patients younger than 65 exercised significantly more frequently than older ones (odds ratio (OR), 1.7, 95 % CI: 1.0-2.7, р&lt;0.001). Patients with higher education had better chances to be involved in PT or were more anxious to start training (OR, 2.7; 95 % CI: 1.6-4.7, р&lt;0.001). The capability for influencing the disease was the major motivation for PT for both sexes. Probability of this answer was 48 % (95 % CI: 33-61) for men and 46 % (95 % CI: 29-63) for women. 62 % of patients indicated poor health as the major barrier for participation in PT. Only 55 % of patients knew that PT could be a method for HF treatment, and only 50 % were informed about that by their physician.Conclusion The factors that positively influence the willingness to exercise include male sex, higher level of education, younger age, and better perception of the own health condition. 62 % of patients indicated poor health as the major barrier for participation in training. On the whole, the awareness of patients about PT benefits for health in HF was low. To our opinion, this was a serious factor of the extremely low involvement of patients in PT. Only 55 % of patients knew that PT could be a method for HF treatment, and, furthermore, only 50 % of patients received this information from their physicians.

Additive Genetic Behavior of Stem Solidness in Wheat (Triticum aestivum L.)

Stem solidness in wheat is an important architectural trait to support the erect behavior of the plant. The varieties with high yield potential due to increased sink strength tend to lodge either because of poor anchorage or weak stem. The solid stem can partially counter the tradeoff between biomass driven yield gain irrespective of the plant height. Stem solidness being a complex trait with highly variable expressivity, understanding its genetic behavior in different genetic backgrounds is highly essential to integrate this trait in the breeding program. In this study, the expressivity of a solid stem in different internodes was investigated in nine F2 populations selected from 34 F1s (solid stem × hollow stem and hollow stem × hollow stem). The progeny of solid stem type F1 plants from hollow stem parents indicated the complementation of favorable alleles dispersed among the parents. Non-confirmation to digenic complementary (9:7) model of inheritance and polynomial distribution of the trait in all F2 populations indicates multiple factors complementation in the additive fashion for stem solidness.

An improved methodology for evaluating availability of multistate series–parallel systems using the polynomial distribution function

PurposeThis paper employs new methods to evaluate the availability of multistate series–parallel systems, in which a number of similar components are available in each subsystem.Design/methodology/approachIn this paper, polynomial distribution function (PDF) is combined with universal generating function (UGF) and recursive algorithm (RA) methods to evaluate the availability of multistate series–parallel systems. To achieve this goal, the PDF is initially used to determine the performance rates and the probabilities corresponding to the performance states of the similar components in a subsystem. The obtained results are used to evaluate the system availability via the UGF and RA methods.FindingsIt is shown that the combined UGF and PDF (UGF-PDF) and also the combined RA and PDF (RA-PDF) methods require less computational time than did the UGF and RA methods, respectively.Originality/valueIn the UGF and RA methods, there is no difference in system availability evaluation time when considering similar or different components in each subsystem. But the proposed methods in this article do not have this restrictions; therefore, these methods can be used to evaluate system availability in optimal redundancy allocation problems. As a result, using these methods reduces the optimization time of those problems.