Mathematics and Computers in Simulation最新文献

In this current paper, we consider the problem of estimating the stress–strength parameter $\psi =P(X<Y)$. This is done by using Bayesian and non-Bayesian approaches when $X$ and $Y$ are independent random variables from two exponential-Rayleigh distributions with different shape parameters but the same scale parameter. Maximum likelihood and Bayes estimators are used to estimate and construct the asymptotic confidence interval and credible interval of $\psi$. Finally, an intensive simulation study is performed to compare the proposed methods and analyze a real data set for illustrative purposes.

We present some efficient algorithms based on an exponential time differencing spectral deferred correction (ETDSDC) method for multidimensional second and fourth-order parabolic problems with non-periodic boundary conditions including Dirichlet, Neumann, Robin boundary conditions. Similar to the Fourier spectral method for periodic problems, the key to the efficiency of our algorithms is to construct diagonal discrete linear operators via Legendre–Galerkin methods with Fourier-like basis functions. In combination with the ETDSDC scheme, the proposed methods are spectrally accurate in space and up to 10th-order accurate in time (as shown in this work). We demonstrate the high-order of convergence and efficiency of our algorithms in solving parabolic equations through a series of two-dimensional and three-dimensional examples including Ginzburg–Landau and Allen–Cahn equations.

To avoid computing moments, this work adopts generalized quadrature method for Volterra integral equations with highly oscillatory Bessel kernel. At first, we study the influence of the interval length and frequency in detail after recalling the construction of the quadrature method. Then, the two-point quadrature method is employed for the equation. By estimating the weights, we could guarantee that the discretized equation is solvable. For its convergence, our analysis shows that the proposed method enjoys asymptotic order $5/2$ and as $h$ decreases it converges with order 2 as well. Some numerical illustrations are provided to test the method in the numerical part.

Targeted therapeutic interventions utilizing low-intensity ultrasound (LIUS) exhibit substantial potential for hindering the proliferation of cancer stem cells. This investigation introduces a multiscale model and computational framework to comprehensively explore the therapeutic LIUS on poroelastic tumor dynamics, thereby unraveling the intricacies of mechanotransduction mechanisms at play. Our model includes both macroscopic timescales encompassing days and rapid timescales spanning from microseconds to seconds, facilitating an in-depth comprehension of tumor behavior. We unveil the discerning suppression or reorientation of cancer cell proliferation and migration, enhancing a notable redistribution of cellular phases and stresses within the tumor microenvironment. Our findings defy existing paradigms by elucidating the impact of LIUS on cancer stem cell behavior. This endeavor advances our fundamental understanding of mechanotransduction phenomena in the context of LIUS therapy, thus underscoring its promising as a targeted therapeutic modality for cancer treatment. Furthermore, our results make a substantial contribution to the broader scientific community by shedding light on the intricate interplay between mechanical forces, cellular responses, and the spatiotemporal evolution of tumors. These insights hold the promising to promote a new perspective for the future development of pioneering and highly efficacious therapeutic strategies for combating cancer in a personalized manner.

In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the inconsistencies arising from the relationship between the different critical points as well as the indeterminacy caused by the square roots involved in their computation.

We analyse the suitability of this algorithm by drawing the parameter planes of different Newton-like methods with two and three critical points. We also present some results of the expressions of the Newton-like operators and their derivatives in terms of palindromic polynomials, and we show how to obtain the expression of the critical points of a Newton-like method with real coefficients.

Research in recognising and fitting simple geometric shapes has been ongoing since the 1970s, with various approaches proposed, including stochastic methods, parameter methods, primitive-based registration techniques, and more recently, deep learning. The Hough transform is a method of interest due to its demonstrated robustness to noise and outliers, ability to handle missing data, and support for multiple model instances. Unfortunately, one of the main limitations of the Hough transform is how to properly discretise its parameter space, as increasing their number or decreasing the sampling frequency can make it computationally expensive.

The relationship between the approximation accuracy and the parameter space’s discretisation is investigated to address this. We present two distinct discretisations to illustrate how the fitting and recognition quality can be improved by selecting an appropriate parameter discretisation. Our parameter-driven space discretisation is shown to significantly improve the parameter recognition quality over the classical method and reduce computational time and space by decreasing the discretisation’s dimension, as demonstrated by an extensive validation on a benchmark of geometric primitives. Preliminary experiments are also presented on segmenting datasets from urban buildings and CAD objects.

In the balls-into-bins setting, $n$ balls are thrown uniformly at random into $n$ bins. The naïve way to generate the final load vector takes $\Theta \left(n\right)$ time. However, it is well-known that this load vector has with high probability bin cardinalities of size $\Theta \left(\frac{logn}{loglogn}\right)$. Here, we present an algorithm in the RAM model that generates the bin cardinalities of the final load vector in the optimal $\Theta \left(\frac{logn}{loglogn}\right)$ time in expectation and with high probability.

Further, the algorithm that we present is still optimal for any $m\in [n,nlogn]$ balls and can also be used as a building block to efficiently simulate more involved load balancing algorithms. In particular, for the Two-Choice algorithm, which samples two bins in each step and allocates to the least-loaded of the two, we obtain roughly a quadratic speed-up over the naïve simulation.