Binomial Approximation Research Articles

Geometrical effective medium model of electric conduction of partially saturated clays

The current existing researches were discussed to assess the advantages and limitations of existing empirical and theoretical models for direct conductivity (DC) prediction. Prior research has demonstrated that an effective medium model may not accurately reflect the actual situation due to the presence of two types of water (bound water and bulk water) in clay-rich materials. Furthermore, the existing models can not satisfy the prediction of electrical conductivity of metal ions adsorbed clay or unsaturated clay. To address this issue, a new Effective Medium Double Water (EMDW) model was proposed based on multiple scattering techniques, which encompasses soil particles, surface-bound water layers, and bulk water and was established by controlled soil types and degrees of saturation. The novel EMDW model includes the Coherent Potential Approximation (CPA), which has consistently demonstrated superior agreement with experimental data when compared to other approximation models. Moreover, the binomial expansion approximation was utilized to simplify the formula and facilitate its use. The developed conductivity model was validated with data from other researchers. In comparison to other well-established conductivity models, the proposed EMDW model has clear physical meaning and can accurately compute matrix conductivity utilizing modified coated particle conductivity and saturation conductivity. The findings suggest that matrix conductivity in clay materials is significantly correlated with electrical-physical parameters, such as porosity, degree of saturation, shape of each discontinuous phase, and conductivity of surface-bound water and bulk water. Consequently, the new EMDW model is a theoretically grounded, physically meaningful, and easy-to-use model for conductivity prediction in clay materials.

A Comparative Analysis of Flooding Methods on Random and Real Network Topologies

The Internet of Things (IoT) is revolutionizing industries by connecting everyday objects, known as smart devices, via the Internet. These devices, embedded with sensors and communication technologies, gather and share data. For the guaranteed gathering of information, the devices share global knowledge with each other, by using dissemination mechanisms in order to broadcast information. This study evaluates four flooding methods for broadcasting information across network nodes, namely: (i) blind flooding; (ii) probabilistic flooding; (iii) m-probabilistic flooding; and (iv) scoped probabilistic flooding, the latter to be introduced here. The evaluation considers random networks that are based on the Burr Type XII distribution and seven real networks. The evaluated flooding methods are studied on three different metrics: (i) coverage achieved; (ii) number of messages exchanged; and (iii) a metric that is based on binomial approximation. The latter is introduced to provide deeper insights into the particulars of the under-evaluation flooding methods. The results show that, under certain conditions, m-probabilistic flooding outperforms probabilistic flooding in terms of coverage, while requiring significantly fewer messages. Additionally, the study revealed that the scoped probabilistic flooding achieves coverage comparable to that of the probabilistic flooding while reducing the number of exchanged messages.

Comparison of probabilistic cruising-for-parking time estimation models

Models of parking search time predominantly rely on the binomial approximation, the calculation of which is dependent solely on the occupancy of the parking network. This paper sheds light on the importance of accounting for competition between parking searchers and the effects of dynamically changing occupancy. To this end, we investigate the accuracy of two probabilistic models, namely the binomial approximation and a model proposed by Cao and Menéndez (CaM). We utilize an agent-based microscopic parking simulation model as a benchmark for comparison purposes. Our findings highlight the significance of considering the competitive dynamics among drivers in the quest for parking spaces and the fluctuations in parking occupancy rates over short time intervals. We highlight the ranges of occupancies for which the binomial approximation and the CaM model provide more reliable estimations of parking search times. The CaM model provides, in general, more accurate estimations of search times since it accounts for various parking network characteristics such as competition and varying occupancy. The binomial approximation underestimates parking search times more substantially at high occupancies with a large number of searching vehicles, whereas the CaM model performs worse for lower spacing between parking spots and lower parking occupancies. Insights from this research are then used to discuss policy implications of accounting for competition and short-term occupancy variations when designing either parking models or parking-related control strategies.

A negative binomial approximation to the distribution of the sum of maxima of indicator random variables

In a sequence of independent indicator random variables, we consider the sum of maxima of k consecutive indicator random variables that represent a specific type of k-runs in the theory of runs and patterns. Intriguingly, it can be expressed as the sum of locally dependent random variables. Our focus is on employing Stein’s method to provide a negative binomial approximation to the distribution of this specific random variable under certain conditions on moments. The derived bounds exhibit an optimal order, reflecting the precision and efficiency of the proposed approximation.

Binomial Approximation to Locally Dependent Collateralized Debt Obligations

Binomial Approximation to Locally Dependent Collateralized Debt Obligations

Computation of the Distribution of the Sum of Independent Negative Binomial Random Variables

The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series expression by convolution. We compare both methods, as well as a new normalized saddlepoint approximation, and normal and single distribution negative binomial approximations. We show that the exact series expression used lots of memory when the number of random variables was high (>7). The normalized saddlepoint approximation gives an output with a high relative error (around 3–5%), which can be a problem in some situations. The convolution method is a good compromise for applied practitioners, considering the amount of memory used, the computing time, and the precision of the estimates. However, a simplistic implementation of the algorithm could produce incorrect results due to the non-monotony of the convergence rate. The tolerance limit must be chosen depending on the expected magnitude order of the estimate, for which we used the answer generated by the saddlepoint approximation. Finally, the normal and negative binomial approximations should not be used, as they produced outputs with a very low accuracy.

Probabilistic Flooding Performance Analysis Exploiting Graph Spectra Properties

Probabilistic flooding is an efficient information dissemination policy capable of spreading information to the network nodes by sending <i>information messages</i> according to a fixed <i>forwarding probability</i> in a per-hop manner starting from an <i>initiator</i> node. It is a suitable approach, especially in topologies where the number of information messages sent under traditional approaches is significantly increased. The analysis presented in this paper considers graph spectra properties such as the <i>largest eigenvalue</i> <inline-formula> <tex-math notation="LaTeX">$\lambda_1$</tex-math> </inline-formula> of the adjacency matrix, and the <i>eigenvector centrality</i>. Both are analytically investigated and <inline-formula> <tex-math notation="LaTeX">$\frac{4}{\lambda_1}$</tex-math> </inline-formula> is derived as a <i>lower bound</i> of the forwarding probability that allows for <i>global coverage</i>, i.e., all network nodes receive the information message, under certain conditions also investigated here (e.g., the condition of the binomial approximation). It is shown that for any value of the forwarding probability equal to or larger than <inline-formula> <tex-math notation="LaTeX">$\frac{4}{\lambda_1}$</tex-math> </inline-formula>: (i) coverage is proportional to the initiator node&#x2019;s eigenvector centrality; (ii) the probability a node receives the information message is proportional to the node&#x2019;s eigenvector centrality; (iii) <i>termination time</i> decreases as the initiator node&#x2019;s eigenvector centrality increases. If knowledge of <inline-formula> <tex-math notation="LaTeX">$\lambda_1$</tex-math> </inline-formula> is not available, then the <i>average node degree</i> <inline-formula> <tex-math notation="LaTeX">$\bar{d}$</tex-math> </inline-formula> can be used for ensuring global coverage. If knowledge of both <inline-formula> <tex-math notation="LaTeX">$\lambda_1$</tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\bar{d}$</tex-math> </inline-formula> is not available, a dissemination policy is proposed that forwards messages to <inline-formula> <tex-math notation="LaTeX">$m$</tex-math> </inline-formula> (randomly selected) neighbor nodes. It is analytically shown that any value of <inline-formula> <tex-math notation="LaTeX">$m \geq 4$</tex-math> </inline-formula> allows for global coverage. Simulation results demonstrate the effectiveness of the considered analytical approach and the introduced policy.

Efficient Posterior Sampling for Bayesian Poisson Regression

ABSTRACT Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient sampling from the posterior distribution of parameters, and standard algorithms, such as random walk Metropolis-Hastings or Hamiltonian Monte Carlo algorithms, are typically used. Herein, we developed an efficient Metropolis-Hastings algorithm and importance sampler to simulate from the posterior distribution of the parameters of Poisson log-linear models under conditional Gaussian priors with superior performance with respect to the state-of-the-art alternatives. The key for both algorithms is the introduction of a proposal density based on a Gaussian approximation of the posterior distribution of parameters. Specifically, our result leverages the negative binomial approximation of the Poisson likelihood and the successful Pólya-gamma data augmentation scheme. Via simulation, we obtained that the time per independent sample of the proposed samplers is competitive with that obtained using the successful Hamiltonian Monte Carlo sampling, with the Metropolis-Hastings showing superior performance in all scenarios considered. Supplementary materials for this article are available online.

Radiotherapy Biological Tumor Control Probability Integral Equation Model with Analytic Determination

The research objective was to obtain a fast/simple analytic solution for previously published Radiotherapy Tumor Control Probability (TCP) Integral Model by other authors. Finding, firstly, is a new/simpler Probability Function than Poisson distribution of survival clonogens which is developed from classical biological model algebraic/numerically modified equation. Solution obtained is this Probability Function alternative based on a Binomial distribution equation approximation from literature. Result, thus, is its use of for developing a fast/analytic solution of the 2D [ α and β biological modelling parameters ] Integral Model Cumulative TCP. The Gaussian Normal distribution convolution is implemented with this Probability Function into the integral model to sort longer/programming numerical methods and determine an analytical solution expression. As a complete result, a formulation for TCP based on Erf functions is obtained. Applications for radiotherapy treatment planning optimization improvements with biological models are explained.

The 1964 US Surgeon General's report on smoking and health.

The 1964 report of the US Surgeon General on smoking and health made an authoritative case that tobacco smoking was a cause of premature deaths from lung cancer and chronic bronchitis. It justified the practice of drawing causal inferences from epidemiological studies, specified influential criteria for doing so, and made use of an early form of meta-analysis.

Improved State-Space All-Digital Filters via Series Approximations

Recently, variable digital filters (VDFs) have become an essential research topic. This paper presents a simple method for the design of infinite impulse response (IIR) VDFs with high tuning accuracy. First, VDFs were created using a state-space model based on a frequency transformation, which requires the inverse matrix and the square root that leads to high computational cost. Then a new algorithm was implemented to generate the same VDFs absent the complex calculations that utilized negative binomial and Taylor series approximations in a simple state-space formulation. This algorithm provides high-accuracy approximations of the inverse matrix and square root compared to other algorithms that have been developed. Thus, the proposed VDFs have high tuning accuracy with respect to finite wordlength effects.

Efficient and Accurate CORDIC Pipelined Architecture Chip Design Based on Binomial Approximation for Biped Robot

Recently, much research has focused on the design of biped robots with stable and smooth walking ability, identical to human beings, and thus, in the coming years, biped robots will accomplish rescue or exploration tasks in challenging environments. To achieve this goal, one of the important problems is to design a chip for real-time calculation of moving length and rotation angle of the biped robot. This paper presents an efficient and accurate coordinate rotation digital computer (CORDIC)-based efficient chip design to calculate the moving length and rotation angle for each step of the biped robot. In a previous work, the hardware cost of the accurate CORDIC-based algorithm of biped robots was primarily limited by the scale-factor architecture. To solve this problem, a binomial approximation was carefully employed for computing the scale-factor. In doing so, the CORDIC-based architecture can achieve similar accuracy but with fewer iterations, thus reducing hardware cost. Hence, incorporating CORDIC-based architecture with binomial approximation, pipelined architecture, and hardware sharing machines, this paper proposes a novel efficient and accurate CORDIC-based chip design by using an iterative pipelining architecture for biped robots. In this design, only low-complexity shift and add operators were used for realizing efficient hardware architecture and achieving the real-time computation of lengths and angles for biped robots. Compared with current designs, this work reduced hardware cost by 7.2%, decreased average errors by 94.5%, and improved average executing performance by 31.5%, when computing ten angles of biped robots.

Big data ordination towards intensive care event count cases using fast computing GLLVMS

BackgroundIn heart data mining and machine learning, dimension reduction is needed to remove multicollinearity. Meanwhile, it has been proven to improve the interpretation of the parameter model. In addition, dimension reduction can also increase the time of computing in high dimensional data.MethodsIn this paper, we perform high dimensional ordination towards event counts in intensive care hospital for Emergency Department (ED 1), First Intensive Care Unit (ICU1), Second Intensive Care Unit (ICU2), Respiratory Care Intensive Care Unit (RICU), Surgical Intensive Care Unit (SICU), Subacute Respiratory Care Unit (RCC), Trauma and Neurosurgery Intensive Care Unit (TNCU), Neonatal Intensive Care Unit (NICU) which use the Generalized Linear Latent Variable Models (GLLVM’s).ResultsDuring the analysis, we measure the performance and calculate the time computing of GLLVM by employing variational approximation and Laplace approximation, and compare the different distributions, including Negative Binomial, Poisson, Gaussian, ZIP, and Tweedie, respectively. GLLVMs (Generalized Linear Latent Variable Models), an extended version of GLMs (Generalized Linear Models) with latent variables, have fast computing time. The major challenge in latent variable modelling is that the function fleft(varTheta right)=int fleft(uvarTheta right)hleft(uright)du is not trivial to solve since the marginal likelihood involves integration over the latent variable u.ConclusionsIn a nutshell, GLLVMs lead as the best performance reaching the variance of 98% comparing other methods. We get the best model negative binomial and Variational approximation, which provides the best accuracy by accuracy value of AIC, AICc, and BIC. In a nutshell, our best model is GLLVM-VA Negative Binomial with AIC 7144.07 and GLLVM-LA Negative Binomial with AIC 6955.922.

Quantitative and Qualitative Analysis of Emergency Physician Performed Biparietal Diameter Estimate for Gestational Age.

An accurate estimation of fetal gestational age is essential for the management of pregnant patients who present to the emergency department (ED). Point-of-care-ultrasound (POCUS) is an integral part of emergency medicine training and includes measurement of fetal gestational age by the biparietal diameter (BPD) method. In this study we performed a quantitative assessment of emergency physician (EP)-performed BPD estimate of gestational age to identify the percentage of studies performed in our department that had an estimated gestational age within 14 days of an adjusted radiological or obstetrical estimation. We performed a chart review of our ED ultrasound database and electronic medical records for cases where a BPD measurement was performed by an EP. We recorded the ED gestational age estimate in days and the radiological or obstetrical estimate of gestational age in days. We then calculated the difference in days between the two examinations. We used a normal binomial approximation to calculate 95% confidence intervals. A secondary analysis looked at the quality of the images based on measurement placement and the view obtained. Seventy-four cases met eligibility criteria; of those, 67 (91%) had a gestational age estimation within 14 days of the adjusted radiological or obstetrical estimate (95% confidence interval 81-96%). This study shows that EP-performed BPD measurements for gestational age are quantitatively accurate, with 91% of estimates within 14 days of a standard radiological or obstetrical estimation.

Integration of Small Productive Processes Into an Energy Management System for Microgrids

Small productive processes (SPPs) have recently emerged as attractive alternatives to contribute to the socio-economic development of communities, primarily in rural contexts. However, SPPs have a complicated electrical behavior involving the interaction between various types of loads, such as, conventional, and complex ones. Further, the SPPs generally include voltage-dependent loads, which may increase/decrease the load consumption. Thus, these characteristics make the integration of the SPPs into energy management systems (EMSs) for microgrids (MGs) a challenging task. This work proposes a novel integration of the SPPs into an EMS considering the SPPs&#x2019; voltage sensitivity and complexity. For this purpose, we extended a previously proposed multi-zone ZIP load model (EMZ-ZIP) to be integrated into a convex AC multi-nodal EMS approach. The latter was formulated based on invertible nonlinear convex transformations and a binomial approximation method. The associated framework was assessed using a modified 9-bus test system with the characteristics of a low-voltage isolated MG with the integration of an SPP. The results demonstrate that the MG operation exhibits better technical and economic performance when the EMZ-ZIP model is an integral part of the EMS. In addition to an operating cost reduction of approximately 5% when considering voltage dependency, relevant practical advantage in scenarios of work shift and solar radiation variability are also presented. These results were compared with those obtained using other approaches like the time-variant ZIP and the constant power model.

Reliability Test Plan Based on Logistic-Exponential Distribution and Its Application

In this article, a reliability test plan is developed for Logistic-exponential distribution (LoED) under time truncated life test scheme. The distribution has been chosen because it can used to model lifetime of several reliability phenomenon and it performs better than many well known existing distributions. With the discussions of statistical properties of the aforesaid model, the reliability test plan has been established under the assumption of median quality characteristics when minimum confidence level P* is given. To quench the objective of the paper i.e; to serve as a guiding aid to the emerging practitioners, minimum sample sizes have been obtained by using binomial approximation and Poisson approximation for the proposed plan. Further, operating characteristic (OC) values for the various choices of quality level are placed. Also, minimum ratio of true median life to specified life has been presented for specified producer’s risk. Important findings of the proposed reliability test plan are given for considered value of k=0.75,1,2. To demonstrate the appropriateness of suggested reliability test plan is achieved using four real life situation.

Reliability Test Plan Based on Logistic-Exponential Distribution and Its Application

In this article, a reliability test plan is developed for Logistic-exponential distribution (LoED) under time truncated life test scheme. The distribution has been chosen because it can used to model lifetime of several reliability phenomenon and it performs better than many well known existing distributions. With the discussions of statistical properties of the aforesaid model, the reliability test plan has been established under the assumption of median quality characteristics when minimum confidence level P* is given. To quench the objective of the paper i.e; to serve as a guiding aid to the emerging practitioners, minimum sample sizes have been obtained by using binomial approximation and Poisson approximation for the proposed plan. Further, operating characteristic (OC) values for the various choices of quality level are placed. Also, minimum ratio of true median life to specified life has been presented for specified producer’s risk. Important findings of the proposed reliability test plan are given for considered value of k=0.75,1,2. To demonstrate the appropriateness of suggested reliability test plan is achieved using four real life situation.

A Proposed Binomial Approximation for the Ellipsoid Gravity and Presentation on gravity anomaly from constants and standardized model &amp; reference to the Sea level bouguer effect.

A Proposed Binomial Approximation for the Ellipsoid Gravity and Presentation on gravity anomaly from constants and standardized model &amp; reference to the Sea level bouguer effect.

MIMO-SAR 3-D Imaging Based on Range Wavenumber Decomposing

Multiple-input-multiple-output synthetic aperture radar (MIMO-SAR) technology is an effective scheme to achieve there-dimensional (3-D) imaging in millimeter wave and terahertz band. Compared with the 2-D array, the system complexity and the number of array elements are greatly reduced. In this paper, an efficient image reconstruction algorithm in wavenumber domain based on phase shift migration (PSM) was proposed for MIMO-SAR 3-D real-time imaging application. By decomposing the range-wavenumber based on binomial approximation theory, the PSM operation can be achieved only by matrix multiplication and Fourier transform (FT) algorithm without time-consuming wavenumber accumulation. Proof-of-principle experiments were also carried out in 0.1THz band based on a MIMO-SAR prototype system. Both simulation and experimental results of different targets show that the image quality of the proposed algorithm is comparable to that of back-projection algorithm (BPA). The partial enlarged images of the imaging results validate that compared with the range migration algorithm (RMA) the proposed algorithm can achieve higher reconstruction accuracy with comparable efficiency.

On Approximation of the Panjer Distribution by the Poisson and Binomial Distributions

The aim of this paper is to approximate the panjer distribution by the poisson and binomial distributions, where each bound is obtained by using the z-function and the Stein-Chen identity. For these bounds, it is indicated that a result of each of the Poisson and Binomial approximations yields a good approximation if both α and λ are small.