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

In this paper, I present three closed-form approximations of the two-sample Pearson Bayes factor. The techniques rely on some classical asymptotic results about gamma functions. These approximations permit simple closed-form calculation of the Pearson Bayes factor in cases where only the summary statistics are available (i.e., the t-score and degrees of freedom).

In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to approximate within a factor of $n^{1-\varepsilon}$ for any $\varepsilon > 0$. Due to this, investigating the complexity of Maximum Independent Set in various graph classes in hope of finding better tractability results is an active research direction. In $H$-free graphs, that is, graphs not containing a fixed graph $H$ as an induced subgraph, the problem is known to remain NP-hard and APX-hard whenever $H$ contains a cycle, a vertex of degree at least four, or two vertices of degree at least three in one connected component. For the remaining cases, where every component of $H$ is a path or a subdivided claw, the complexity of Maximum Independent Set remains widely open, with only a handful of polynomial-time solvability results for small graphs $H$ such as $P_5$, $P_6$, the claw, or the fork. We show that for every graph $H$ for which Maximum Independent Set is not known to be APX-hard and SUBEXP-hard in $H$-free graphs, the problem admits a quasi-polynomial time approximation scheme and a subexponential-time exact algorithm in this graph class. Our algorithm works also in the more general weighted setting, where the input graph is supplied with a weight function on vertices and we are maximizing the total weight of an independent set.

We investigate the algebra and geometry of general interventions in discrete DAG models. To this end, we introduce a theory for modeling soft interventions in the more general family of staged tree models and develop the formalism to study these models as parametrized subvarieties of a product of probability simplices. We then consider the problem of finding their defining equations, and we derive a combinatorial criterion for identifying interventional staged tree models for which the defining ideal is toric. We apply these results to the class of discrete interventional DAG models and establish a criteria to determine when these models are toric varieties.

The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism problem only asks to find a single non-scalar endomorphism. We prove that these two problems are equivalent, under probabilistic polynomial time reductions. We prove a number of consequences. First, assuming the hardness of the endomorphism ring problem, the Charles--Goren--Lauter hash function is collision resistant, and the SQIsign identification protocol is sound. Second, the endomorphism ring problem is equivalent to the problem of computing arbitrary isogenies between supersingular elliptic curves, a result previously known only for isogenies of smooth degree. Third, there exists an unconditional probabilistic algorithm to solve the endomorphism ring problem in time O~(sqrt(p)), a result that previously required to assume the generalized Riemann hypothesis. To prove our main result, we introduce a flexible framework for the study of isogeny graphs with additional information. We prove a general and easy-to-use rapid mixing theorem. The proof of this result goes via an augmented Deuring correspondence and the Jacquet-Langlands correspondence.

We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of circulant or block circulant matrices, which commonly arise in the discretization of differential equations using finite element or finite difference methods. We prove the convergence of the new iteration without making any assumptions regarding the symmetry or diagonal-dominance of the matrix. To illustrate the efficacy of the new iteration we present various applications. These include extensions of the new iteration to block matrices that arise in certain saddle point problems as well as two-dimensional finite difference discretizations. The new method exhibits fast convergence in all of the test cases we used. It has minimal storage requirements, straightforward implementation and compatibility with nearly circulant matrices via the Fast Fourier Transform. For this reasons it can be a valuable tool for the solution of various finite element and finite difference discretizations of differential equations.

The categorical Gini correlation, $\rho_g$, was proposed by Dang et al. to measure the dependence between a categorical variable, $Y$ , and a numerical variable, $X$. It has been shown that $\rho_g$ has more appealing properties than current existing dependence measurements. In this paper, we develop the jackknife empirical likelihood (JEL) method for $\rho_g$. Confidence intervals for the Gini correlation are constructed without estimating the asymptotic variance. Adjusted and weighted JEL are explored to improve the performance of the standard JEL. Simulation studies show that our methods are competitive to existing methods in terms of coverage accuracy and shortness of confidence intervals. The proposed methods are illustrated in an application on two real datasets.

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method. In particular, we consider the framework of multi-level Monte Carlo for parametric expectations and propose modifications of the MLMC estimator, error estimation procedure, and adaptive MLMC parameter selection to ensure the estimation of the CVaR and sensitivities for a given design with a prescribed accuracy. We then propose combining the MLMC framework with an alternating inexact minimisation-gradient descent algorithm, for which we prove exponential convergence in the optimisation iterations under the assumptions of strong convexity and Lipschitz continuity of the gradient of the objective function. We demonstrate the performance of our approach on two numerical examples of practical relevance, which evidence the same optimal asymptotic cost-tolerance behaviour as standard MLMC methods for fixed design computations of output expectations.

Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs for a large class of problems throughout the so-called uniqueness regime, including, for example, the problems of sampling independent sets, matchings, and Ising-model configurations. Our main contribution is to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. Previous methods for avoiding degree bounds rely on using $L^p$-norms to analyse contraction on graphs with bounded connective constant (Sinclair, Srivastava, Yin; FOCS'13). The non-linearity of $L^p$-norms is an obstacle to applying these results to bound spectral independence. Our solution is to capture the $L^p$-analysis recursively by amortising over the subtrees of the recurrence used to analyse contraction. Our method generalises previous analyses that applied only to bounded-degree graphs. As a main application of our techniques, we consider the random graph $G(n,d/n)$, where the previously known algorithms run in time $n^{O(\log d)}$ or applied only to large $d$. We refine these algorithmic bounds significantly, and develop fast $n^{1+o(1)}$ algorithms based on Glauber dynamics that apply to all $d$, throughout the uniqueness regime.

In this paper, by using methods of $D$-companion matrix, we reprove a generalization of the Guass-Lucas theorem and get the majorization relationship between the zeros of convex combinations of incomplete polynomials and an origin polynomial. Moreover, we prove that the set of all zeros of all convex combinations of incomplete polynomials coincides with the closed convex hull of zeros of the original polynomial. The location of zeros of convex combinations of incomplete polynomials is determined.

This paper proposes a general optimization framework for rate splitting multiple access (RSMA) in beyond diagonal (BD) reconfigurable intelligent surface (RIS) assisted ultra-reliable low-latency communications (URLLC) systems. This framework can provide a suboptimal solution for a large family of optimization problems in which the objective and/or constraints are linear functions of the rates and/or energy efficiency (EE) of users. Using this framework, we show that RSMA and RIS can be mutually beneficial tools when the system is overloaded, i.e., when the number of users per cell is higher than the number of base station (BS) antennas. Additionally, we show that the benefits of RSMA increase when the packets are shorter and/or the reliability constraint is more stringent. Furthermore, we show that the RSMA benefits increase with the number of users per cell and decrease with the number of BS antennas. Finally, we show that RIS (either diagonal or BD) can highly improve the system performance, and BD-RIS outperforms regular RIS.