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Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable. Depending on the coupling strength of the two equations, we explicitly quantify the needed number of inner iteration steps to guarantee first-order convergence. Within a number of numerical experiments, we confirm the theoretical results and study the dependence of inner iteration steps in terms of the coupling strength. Moreover, we compare our method to the well-known fixed-stress scheme.

In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.

In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called \emph{optimal error bounds}, which established some necessary and sufficient conditions for convergence and derived both the error estimates and bounds on the convergence rates for iterative schemes. Although a special interest here is devoted to the Ishikawa and modified Ishikawa iterative sequences, the theory of \emph{optimal error bounds} proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of non-expansive mappings.

In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require any modeling effort from the user. A novel catalog-based contractor (or filtering operator) guarantees consistency between the categorical properties and the existing catalog items. This results in an intuitive and generic approach that is exact, rigorous (robust to roundoff errors) and can be easily implemented in an off-the-shelf interval-based continuous solver that interleaves branching and constraint propagation. We demonstrate the validity of the approach on a numerical problem in which a categorical variable is described by a two-dimensional property space. A Julia prototype is available as open-source software under the MIT license at //github.com/cvanaret/CateGOrical.jl

Minimizing data storage poses a significant challenge in large-scale metagenomic projects. In this paper, we present a new method for improving the encoding of FASTQ files generated by metagenomic sequencing. This method incorporates metagenomic classification followed by a recursive filter for clustering reads by DNA sequence similarity to improve the overall reference-free compression. In the results, we show an overall improvement in the compression of several datasets. As hypothesized, we show a progressive compression gain for higher coverage depth and number of identified species. Additionally, we provide an implementation that is freely available at //github.com/cobilab/mizar and can be customized to work with other FASTQ compression tools.

In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM.

In this paper, our objective is to present a constraining principle governing the spectral properties of the sample covariance matrix. This principle exhibits harmonious behavior across diverse limiting frameworks, eliminating the need for constraints on the rates of dimension $p$ and sample size $n$, as long as they both tend to infinity. We accomplish this by employing a suitable normalization technique on the original sample covariance matrix. Following this, we establish a harmonic central limit theorem for linear spectral statistics within this expansive framework. This achievement effectively eliminates the necessity for a bounded spectral norm on the population covariance matrix and relaxes constraints on the rates of dimension $p$ and sample size $n$, thereby significantly broadening the applicability of these results in the field of high-dimensional statistics. We illustrate the power of the established results by considering the test for covariance structure under high dimensionality, freeing both $p$ and $n$.

In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators.

In this paper, to the best of our knowledge, we make the first attempt at studying the parametric semilinear elliptic eigenvalue problems with the parametric coefficient and some power-type nonlinearities. The parametric coefficient is assumed to have an affine dependence on the countably many parameters with an appropriate class of sequences of functions. In this paper, we obtain the upper bound estimation for the mixed derivatives of the ground eigenpairs that has the same form obtained recently for the linear eigenvalue problem. The three most essential ingredients for this estimation are the parametric analyticity of the ground eigenpairs, the uniform boundedness of the ground eigenpairs, and the uniform positive differences between ground eigenvalues of linear operators. All these three ingredients need new techniques and a careful investigation of the nonlinear eigenvalue problem that will be presented in this paper. As an application, considering each parameter as a uniformly distributed random variable, we estimate the expectation of the eigenpairs using a randomly shifted quasi-Monte Carlo lattice rule and show the dimension-independent error bound.

In this paper, we tackle the following problem: compute the gcd for several univariate polynomials with parametric coefficients. It amounts to partitioning the parameter space into ``cells'' so that the gcd has a uniform expression over each cell and constructing a uniform expression of gcd in each cell. We tackle the problem as follows. We begin by making a natural and obvious extension of subresultant polynomials of two polynomials to several polynomials. Then we develop the following structural theories about them. 1. We generalize Sylvester's theory to several polynomials, in order to obtain an elegant relationship between generalized subresultant polynomials and the gcd of several polynomials, yielding an elegant algorithm. 2. We generalize Habicht's theory to several polynomials, in order to obtain a systematic relationship between generalized subresultant polynomials and pseudo-remainders, yielding an efficient algorithm. Using the generalized theories, we present a simple (structurally elegant) algorithm which is significantly more efficient (both in the output size and computing time) than algorithms based on previous approaches.