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In this article we present a new method for performing Bayesian parameter inference and model choice for low-count time series models with intractable likelihoods. The method involves incorporating an alive particle filter within a sequential Monte Carlo (SMC) algorithm to create a novel exact-approximate algorithm, which we refer to as alive SMC2. The advantages of this approach over competing methods are that it is naturally adaptive, it does not involve between-model proposals required in reversible jump Markov chain Monte Carlo, and does not rely on potentially rough approximations. The algorithm is demonstrated on Markov process and integer autoregressive moving average models applied to real biological datasets of hospital-acquired pathogen incidence, animal health time series, and the cumulative number of prion disease cases in mule deer.

The purpose of this paper is to develop an approximate method for the evaluation of the normal force acting on a flexible plate normal to the wind flow and the deformation of the plate. A theoretical modelling is firstly proposed to predict the relationship between the normal drag coefficient of a rigid curved-plate and the configuration of the plate with the aid of a series of numerical analyses of structure and fluid dynamics. Then, based on the theoretical modelling, an approximate method for the evaluation of the normal force acting on the plate and the deformation of the plate is constructed using only the iteration of structure mechanics analysis, instead of conventional complex iterations of fluid-structure coupling analysis. Simulation tests for 3D flexible plates with different lengths and different material moduli are conducted. Also a comparative simulation test of a 3D flexible plate used in a previous experiment is performed to further confirm the validity and accuracy of the approximate method. Numerical results obtained from the approximate method agree well with those obtained from the fluid dynamics analysis as well as the results of the previous wind tunnel experiment.

K-nearest neighbors searching (KNNS) is to find K -nearest neighbors for query points. It is a primary problem in clustering analysis, classification, outlier detection and pattern recognition, and has been widely used in various applications. The exact searching algorithms, like KD-tree, M-tree, are not suitable for high-dimensional data. Approximate KNNS algorithms for high-dimensional data based on locality sensitive hashing (LSH) is becoming popular. However, the existing searching strategies are sensitive to the parameters of constructing LSH index. To solve this problem, a robust strategy for KNNS, called Robust-LSH, is proposed. It makes full use of points that frequently appear together with the query points to improve the diversity of candidates, so that it can use fewer hash tables to obtain more valuable candidates for KNNS. We do experiments on synthetic and real data. The results show that in terms of searching accuracy and running time, Robust-LSH has better performance than the p-stable LSH, RLSH and KD-tree algorithms.

In response to the longstanding concerns regarding the impracticality of ACI318 prestressed concrete (PC) one-way shear provisions, rational improvements to the approximate method were discussed. This study addresses new limit conditions reflecting prestress effects and corresponding updates on upper-limit shear strength (Vc). Also, a consistent and straightforward definition of effective depth (dv) and coefficient accounting for longitudinal reinforcement effect (K) were newly introduced. The proposed approximate method was verified through use of an extensive PC shear database to have analytical accuracy and conservatism statistically comparable to the ACI 318-19 approximate provision. In addition, applicability was confirmed through analysis of four design examples. The proposed modifications are an advisable alternative to the current approximate method. They provide for simple, economical, and safe PC member design while resolving underlying issues in the current approximate method.

We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted ‘onion-shell’ geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.

Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields. In this paper, a new approach called the Hussein–Jassim (HJ) method is presented for solving nonlinear fractional ordinary differential equations. The new method is based on a power series of fractional order. The proposed approach is employed to obtain an approximate solution for the fractional differential equations. The results of this study show that the solutions obtained from solving the fractional differential equations are highly consistent with those obtained by exact solutions.

The paper work presents two practical methods to draw the development of a surface unable to be developed applying classical methods of Descriptive Geometry, the toroidal surface, frequently met in technical practice. The described methods are approximate ones; the development is obtained with the help of points. The accuracy of the methods is given by the number of points used when drawing. As for any other approximate method, when practically manufactured the development may need to be adjusted on site.

The paper work presents two practical methods to draw the development of a surface unable to be developed applying classical methods of Descriptive Geometry, the toroidal surface, frequently met in technical practice. The described methods are approximate ones; the development is obtained with the help of points. The accuracy of the methods is given by the number of points used when drawing. As for any other approximate method, when practically manufactured the development may need to be adjusted on site.

In this study, we discuss the application of an analytical technique namely modified homotopy analysis transform method (MHATM) for solving coupled one- dimensional time-fractional Keller-Segel (K-S) equations. The MHATM is a new analytical technique based on homotopy polynomial. We provide a convergence analysis of MHATM and the solution obtained by the proposed method is verified through different graphical representations. The results demonstrate that the proposed methodology is very useful and simple in the determination of the solution of the K-S equations of fractional order.

In this paper, a new technique is proposed to deal with strongly nonlinear stochastic systems with fractional derivative damping and random harmonic excitation. Combining the advantages of Linstedt–Poincaré (L–P) method and multiple scales method, introducing a different frequency expansion form and a time transformation, a series of perturbation equations is obtained according to the powers of parameter. Then, we eliminate the secular producing terms to solve the perturbation equations to derive the second-order approximate solution. Furthermore, the steady-state frequency–amplitude function in deterministic case is analyzed, and the first-order and second-order steady-state moments of the amplitude are also discussed in the presence of random harmonic excitation. In order to explore the effectiveness of the proposed approximate method, two classical examples were proposed to verify the theoretical results through numerical simulations. Especially, the method can be used to investigate some types of extremely strong odd nonlinear terms via the discussions of each example.