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 recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the system of differential equations with solution-dependent factors. These include the classes of modified Patankar--Runge--Kutta (MPRK) and Geometric Conservative (GeCo) methods. Compared to traditional RK methods, the analysis of accuracy and stability of these methods is more complicated. In this work, we provide a comprehensive and unifying theory of order conditions for such RK-like methods, which differ from original RK schemes in that their coefficients are solution-dependent. The resulting order conditions are themselves solution-dependent and obtained using the theory of NB-series, and thus, can easily be read off from labeled N-trees. We present for the first time order conditions for MPRK and GeCo schemes of arbitrary order; For MPRK schemes, the order conditions are given implicitly in terms of the stages. From these results, we recover as particular cases all known order conditions from the literature for first- and second-order GeCo as well as first-, second- and third-order MPRK methods. Additionally, we derive sufficient and necessary conditions in an explicit form for 3rd and 4th order GeCo schemes as well as 4th order MPRK methods.

Multi-signature aggregates signatures from multiple users on the same message into a joint signature, which is widely applied in blockchain to reduce the percentage of signatures in blocks and improve the throughput of transactions. The $k$-sum attacks are one of the major challenges to design secure multi-signature schemes. In this work, we address $k$-sum attacks from a novel angle by defining a Public Third Party (PTP), which is an automatic process that can be verifiable by the public and restricts the signing phase from continuing until receiving commitments from all signers. Further, a two-round multi-signature scheme MEMS with PTP is proposed, which is secure based on discrete logarithm assumption in the random oracle model. As each signer communicates directly with the PTP instead of other co-signers, the total amount of communications is significantly reduced. In addition, as PTP participates in the computation of the aggregation and signing algorithms, the computation cost left for each signer and verifier remains the same as the basis Schnorr signature. To the best of our knowledge, this is the maximum efficiency that a Schnorr-based multi-signature scheme can achieve. Further, MEMS is applied in blockchain platform, e.g., Fabric, to improve the transaction efficiency.

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the accuracy achieved in a specific iteration with the discretization accuracy of the same iteration. Apart from the computational advantage, the new modified methods allow to naturally perform p-adaptivity, stopping the iterations when appropriate conditions are met. Moreover, the modification is very easy to be included in an existing implementation of an arbitrary high order iterative scheme and it does not ruin the possibility of parallelization, if this was achievable by the original method. An application to the Arbitrary DERivative (ADER) method for hyperbolic Partial Differential Equations (PDEs) is presented here. We explain how such framework can be interpreted as an arbitrary high order iterative scheme, by recasting it as a Deferred Correction (DeC) method, and how to easily modify it to obtain a more efficient formulation, in which a local a posteriori limiter can be naturally integrated leading to p-adaptivity and structure preserving properties. Finally, the novel approach is extensively tested against classical benchmarks for compressible gas dynamics to show the robustness and the computational efficiency.

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE context, we investigate several strategies to improve this approach. Our initial emphasis is on the order of accuracy of the method in connection with the polynomial discretization of the weak formulation. We demonstrate that precise choices lead to higher-order convergences in comparison to the existing literature. Then, we put ADER methods into a Deferred Correction (DeC) formalism. This allows to determine the optimal number of iterations, which is equal to the formal order of accuracy of the method, and to introduce efficient $p$-adaptive modifications. These are defined by matching the order of accuracy achieved and the degree of the polynomial reconstruction at each iteration. We provide analytical and numerical results, including the stability analysis of the new modified methods, the investigation of the computational efficiency, an application to adaptivity and an application to hyperbolic PDEs with a Spectral Difference (SD) space discretization.

PDE solutions are numerically represented by basis functions. Classical methods employ pre-defined bases that encode minimum desired PDE properties, which naturally cause redundant computations. What are the best bases to numerically represent PDE solutions? From the analytical perspective, the Kolmogorov $n$-width is a popular criterion for selecting representative basis functions. From the Bayesian computation perspective, the concept of optimality selects the modes that, when known, minimize the variance of the conditional distribution of the rest of the solution. We show that these two definitions of optimality are equivalent. Numerically, both criteria reduce to solving a Singular Value Decomposition (SVD), a procedure that can be made numerically efficient through randomized sampling. We demonstrate computationally the effectiveness of the basis functions so obtained on several linear and nonlinear problems. In all cases, the optimal accuracy is achieved with a small set of basis functions.

Markov Switching models have had increasing success in time series analysis due to their ability to capture the existence of unobserved discrete states in the dynamics of the variables under study. This result is generally obtained thanks to the inference on states derived from the so--called Hamilton filter. One of the open problems in this framework is the identification of the number of states, generally fixed a priori; it is in fact impossible to apply classical tests due to the problem of the nuisance parameters present only under the alternative hypothesis. In this work we show, by Monte Carlo simulations, that fuzzy clustering is able to reproduce the parametric state inference derived from the Hamilton filter and that the typical indices used in clustering to determine the number of groups can be used to identify the number of states in this framework. The procedure is very simple to apply, considering that it is performed (in a nonparametric way) independently of the data generation process and that the indicators we use are present in most statistical packages. A final application on real data completes the analysis.

For solving linear inverse problems, particularly of the type that appear in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizers a regularized least squares objective function where the regularization is based on a compound Gaussian prior distribution. The Compound Gaussian prior subsumes many of the commonly used priors in image reconstruction, including those of sparsity-based approaches. The developed iterative algorithm gives rise to the paper's second new approach, which is a deep neural network that corresponds to an "unrolling" or "unfolding" of the iterative algorithm. Unrolled deep neural networks have interpretable layers and outperform standard deep learning methods. This paper includes a detailed computational theory that provides insight into the construction and performance of both algorithms. The conclusion is that both algorithms outperform other state-of-the-art approaches to tomographic image formation and compressive sensing, especially in the difficult regime of low training.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at //github.com/google-research/google-research/tree/master/cluster_gcn.

Retrieving object instances among cluttered scenes efficiently requires compact yet comprehensive regional image representations. Intuitively, object semantics can help build the index that focuses on the most relevant regions. However, due to the lack of bounding-box datasets for objects of interest among retrieval benchmarks, most recent work on regional representations has focused on either uniform or class-agnostic region selection. In this paper, we first fill the void by providing a new dataset of landmark bounding boxes, based on the Google Landmarks dataset, that includes $94k$ images with manually curated boxes from $15k$ unique landmarks. Then, we demonstrate how a trained landmark detector, using our new dataset, can be leveraged to index image regions and improve retrieval accuracy while being much more efficient than existing regional methods. In addition, we further introduce a novel regional aggregated selective match kernel (R-ASMK) to effectively combine information from detected regions into an improved holistic image representation. R-ASMK boosts image retrieval accuracy substantially at no additional memory cost, while even outperforming systems that index image regions independently. Our complete image retrieval system improves upon the previous state-of-the-art by significant margins on the Revisited Oxford and Paris datasets. Code and data will be released.