亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We present a numerical stability analysis of the immersed boundary(IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier transforms defined differently on the fluid grid and the boundary grid. This approach gives accurate theoretical results about the stability boundary since it takes the effects of the spreading kernel of the immersed boundary method on the numerical stability into account. In this paper, the spreading kernel is the standard 4-point IB delta function. A three-dimensional incompressible viscous flow and a no-slip planar boundary are considered. The case of a planar elastic membrane is also analyzed using the same analysis framework and it serves as an example of many possible generalizations of our theory. We present some numerical results and show that the observed stability behaviors are consistent with what are predicted by our theory.

Independent Component Analysis (ICA) is intended to recover the mutually independent sources from their linear mixtures, and F astICA is one of the most successful ICA algorithms. Although it seems reasonable to improve the performance of F astICA by introducing more nonlinear functions to the negentropy estimation, the original fixed-point method (approximate Newton method) in F astICA degenerates under this circumstance. To alleviate this problem, we propose a novel method based on the second-order approximation of minimum discrimination information (MDI). The joint maximization in our method is consisted of minimizing single weighted least squares and seeking unmixing matrix by the fixed-point method. Experimental results validate its efficiency compared with other popular ICA algorithms.

We show that the nonstandard limiting distribution of HAR test statistics under fixed-b asymptotics is not pivotal (even after studentization) when the data are nonstationarity. It takes the form of a complicated function of Gaussian processes and depends on the integrated local long-run variance and on on the second moments of the relevant series (e.g., of the regressors and errors for the case of the linear regression model). Hence, existing fixed-b inference methods based on stationarity are not theoretically valid in general. The nuisance parameters entering the fixed-b limiting distribution can be consistently estimated under small-b asymptotics but only with nonparametric rate of convergence. Hence, We show that the error in rejection probability (ERP) is an order of magnitude larger than that under stationarity and is also larger than that of HAR tests based on HAC estimators under conventional asymptotics. These theoretical results reconcile with recent finite-sample evidence in Casini (2021) and Casini, Deng and Perron (2021) who showing that fixed-b HAR tests can perform poorly when the data are nonstationary. They can be conservative under the null hypothesis and have non-monotonic power under the alternative hypothesis irrespective of how large the sample size is.

We study the Maximum Independent Set (MIS) problem under the notion of stability introduced by Bilu and Linial (2010): a weighted instance of MIS is $\gamma$-stable if it has a unique optimal solution that remains the unique optimum under multiplicative perturbations of the weights by a factor of at most $\gamma\geq 1$. The goal then is to efficiently recover the unique optimal solution. In this work, we solve stable instances of MIS on several graphs classes: we solve $\widetilde{O}(\Delta/\sqrt{\log \Delta})$-stable instances on graphs of maximum degree $\Delta$, $(k - 1)$-stable instances on $k$-colorable graphs and $(1 + \varepsilon)$-stable instances on planar graphs. For general graphs, we present a strong lower bound showing that there are no efficient algorithms for $O(n^{\frac{1}{2} - \varepsilon})$-stable instances of MIS, assuming the planted clique conjecture. We also give an algorithm for $(\varepsilon n)$-stable instances. As a by-product of our techniques, we give algorithms and lower bounds for stable instances of Node Multiway Cut. Furthermore, we prove a general result showing that the integrality gap of convex relaxations of several maximization problems reduces dramatically on stable instances. Moreover, we initiate the study of certified algorithms, a notion recently introduced by Makarychev and Makarychev (2018), which is a class of $\gamma$-approximation algorithms that satisfy one crucial property: the solution returned is optimal for a perturbation of the original instance. We obtain $\Delta$-certified algorithms for MIS on graphs of maximum degree $\Delta$, and $(1+\varepsilon)$-certified algorithms on planar graphs. Finally, we analyze the algorithm of Berman and Furer (1994) and prove that it is a $\left(\frac{\Delta + 1}{3} + \varepsilon\right)$-certified algorithm for MIS on graphs of maximum degree $\Delta$ where all weights are equal to 1.

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies suitable conditions, expectations can be estimated by averaging over subsets of transformations, and these estimators are strongly consistent. We show that, if a mixing condition holds, the averages also satisfy a central limit theorem, a Berry-Esseen bound, and concentration. These are extended further to apply to triangular arrays, to randomly subsampled averages, and to a generalization of U-statistics. As applications, we obtain new results on exchangeability, random fields, network models, and a class of marked point processes. We also establish asymptotic normality of the empirical entropy for a large class of processes. Some known results are recovered as special cases, and can hence be interpreted as an outcome of symmetry. The proofs adapt Stein's method.

Beta regression model is useful in the analysis of bounded continuous outcomes such as proportions. It is well known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood estimators. The ridge type estimators have been proposed to alleviate the adverse effects of the multicollinearity. Furthermore, when some of the predictors have insignificant or weak effects on the outcomes, it is desired to recover as much information as possible from these predictors instead of discarding them all together. In this paper we proposed ridge type shrinkage estimators for the low and high dimensional beta regression model, which address the above two issues simultaneously. We compute the biases and variances of the proposed estimators in closed forms and use Monte Carlo simulations to evaluate their performances. The results show that, both in low and high dimensional data, the performance of the proposed estimators are superior to ridge estimators that discard weak or insignificant predictors. We conclude this paper by applying the proposed methods for two real data from econometric and medicine.

We consider Broyden's method and some accelerated schemes for nonlinear equations having a strongly regular singularity of first order with a one-dimensional nullspace. Our two main results are as follows. First, we show that the use of a preceding Newton-like step ensures convergence for starting points in a starlike domain with density 1. This extends the domain of convergence of these methods significantly. Second, we establish that the matrix updates of Broyden's method converge q-linearly with the same asymptotic factor as the iterates. This contributes to the long-standing question whether the Broyden matrices converge by showing that this is indeed the case for the setting at hand. Furthermore, we prove that the Broyden directions violate uniform linear independence, which implies that existing results for convergence of the Broyden matrices cannot be applied. Numerical experiments of high precision confirm the enlarged domain of convergence, the q-linear convergence of the matrix updates, and the lack of uniform linear independence. In addition, they suggest that these results can be extended to singularities of higher order and that Broyden's method can converge r-linearly without converging q-linearly. The underlying code is freely available.

A common approach to tackle a combinatorial optimization problem is to first solve a continuous relaxation and then round the obtained fractional solution. For the latter, the framework of contention resolution schemes (or CR schemes), introduced by Chekuri, Vondrak, and Zenklusen, is a general and successful tool. A CR scheme takes a fractional point $x$ in a relaxation polytope, rounds each coordinate $x_i$ independently to get a possibly non-feasible set, and then drops some elements in order to satisfy the independence constraints. Intuitively, a CR scheme is $c$-balanced if every element $i$ is selected with probability at least $c \cdot x_i$. It is known that general matroids admit a $(1-1/e)$-balanced CR scheme, and that this is (asymptotically) optimal. This is in particular true for the special case of uniform matroids of rank one. In this work, we provide a simple and explicit monotone CR scheme with a balancedness of $1 - \binom{n}{k}\:\left(1-\frac{k}{n}\right)^{n+1-k}\:\left(\frac{k}{n}\right)^k$, and show that this is optimal. As $n$ grows, this expression converges from above to $1 - e^{-k}k^k/k!$. While this asymptotic bound can be obtained by combining previously known results, these require defining an exponential-sized linear program, as well as using random sampling and the ellipsoid algorithm. Our procedure, on the other hand, has the advantage of being simple and explicit. Moreover, this scheme generalizes into an optimal CR scheme for partition matroids.

In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove that the method is of second order accuracy and obtain an estimate for the total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent work has shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al.~\cite{AroraGeLiMaZh17} suggests a dilemma about GANs' statistical properties: powerful discriminators cause overfitting, whereas weak discriminators cannot detect mode collapse. In contrast, we show in this paper that GANs can in principle learn distributions in Wasserstein distance (or KL-divergence in many cases) with polynomial sample complexity, if the discriminator class has strong distinguishing power against the particular generator class (instead of against all possible generators). For various generator classes such as mixture of Gaussians, exponential families, and invertible neural networks generators, we design corresponding discriminators (which are often neural nets of specific architectures) such that the Integral Probability Metric (IPM) induced by the discriminators can provably approximate the Wasserstein distance and/or KL-divergence. This implies that if the training is successful, then the learned distribution is close to the true distribution in Wasserstein distance or KL divergence, and thus cannot drop modes. Our preliminary experiments show that on synthetic datasets the test IPM is well correlated with KL divergence, indicating that the lack of diversity may be caused by the sub-optimality in optimization instead of statistical inefficiency.