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

Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how "well-linearizable" the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary.

Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian term number, comparing unfavorably to algorithms using more advanced techniques. We develop methods to perform faster Trotter steps with complexity sublinear in the number of terms. We achieve this for a class of Hamiltonians whose interaction strength decays with distance according to power law. Our methods include one based on a recursive block encoding and one based on an average-cost simulation, overcoming the normalization-factor barrier of these advanced quantum simulation techniques. We also realize faster Trotter steps when certain blocks of Hamiltonian coefficients have low rank. Combining with a tighter error analysis, we show that it suffices to use $\left(\eta^{1/3}n^{1/3}+\frac{n^{2/3}}{\eta^{2/3}}\right)n^{1+o(1)}$ gates to simulate uniform electron gas with $n$ spin orbitals and $\eta$ electrons in second quantization in real space, asymptotically improving over the best previous work. We obtain an analogous result when the external potential of nuclei is introduced under the Born-Oppenheimer approximation. We prove a circuit lower bound when the Hamiltonian coefficients take a continuum range of values, showing that generic $n$-qubit $2$-local Hamiltonians with commuting terms require at least $\Omega(n^2)$ gates to evolve with accuracy $\epsilon=\Omega(1/poly(n))$ for time $t=\Omega(\epsilon)$. Our proof is based on a gate-efficient reduction from the approximate synthesis of diagonal unitaries within the Hamming weight-$2$ subspace, which may be of independent interest. Our result thus suggests the use of Hamiltonian structural properties as both necessary and sufficient to implement Trotter steps with lower gate complexity.

At STOC 2002, Eiter, Gottlob, and Makino presented a technique called ordered generation that yields an $n^{O(d)}$-delay algorithm listing all minimal transversals of an $n$-vertex hypergraph of degeneracy $d$, for an appropriate definition of degeneracy. Recently at IWOCA 2019, Conte, Kant\'e, Marino, and Uno asked whether, even for a more restrictive notion of degeneracy, this XP-delay algorithm parameterized by $d$ could be made FPT-delay parameterized by $d$ and the maximum degree $\Delta$, i.e., an algorithm with delay $f(d,\Delta)\cdot n^{O(1)}$ for some computable function $f$. We answer this question in the affirmative whenever the hypergraph corresponds to the closed neighborhoods of a graph, i.e., we show that the intimately related problem of enumerating minimal dominating sets in graphs admits an FPT-delay algorithm parameterized by the degeneracy and the maximum degree.

Not everybody can be equipped with professional photography skills and sufficient shooting time, and there can be some tilts in the captured images occasionally. In this paper, we propose a new and practical task, named Rotation Correction, to automatically correct the tilt with high content fidelity in the condition that the rotated angle is unknown. This task can be easily integrated into image editing applications, allowing users to correct the rotated images without any manual operations. To this end, we leverage a neural network to predict the optical flows that can warp the tilted images to be perceptually horizontal. Nevertheless, the pixel-wise optical flow estimation from a single image is severely unstable, especially in large-angle tilted images. To enhance its robustness, we propose a simple but effective prediction strategy to form a robust elastic warp. Particularly, we first regress the mesh deformation that can be transformed into robust initial optical flows. Then we estimate residual optical flows to facilitate our network the flexibility of pixel-wise deformation, further correcting the details of the tilted images. To establish an evaluation benchmark and train the learning framework, a comprehensive rotation correction dataset is presented with a large diversity in scenes and rotated angles. Extensive experiments demonstrate that even in the absence of the angle prior, our algorithm can outperform other state-of-the-art solutions requiring this prior. The code and dataset are available at //github.com/nie-lang/RotationCorrection.

Nearly thirty years ago, it was shown that $\Omega(\sqrt{n})$ registers are needed to solve obstruction-free consensus among $n$ processes. This lower bound was improved to $n$ registers in 2018, which exactly matches the best upper bound. The $\Omega(\sqrt{n})$ space complexity lower bound actually applies to a class of objects called historyless objects, which includes registers, test-and-set objects, and readable swap objects. However, every known $n$-process obstruction-free consensus algorithm from historyless objects uses $\Omega (n)$ objects. We give the first $\Omega (n)$ space complexity lower bounds on consensus algorithms for two kinds of historyless objects. First, we show that any obstruction-free consensus algorithm from swap objects uses at least $n-1$ objects. More generally, we prove that any obstruction-free $k$-set agreement algorithm from swap objects uses at least $\lceil \frac{n}{k}\rceil - 1$ objects. This is the first non-constant lower bound on the space complexity of solving $k$-set agreement with swap objects when $k > 1$. We also present an obstruction-free $k$-set agreement algorithm from $n-k$ swap objects, exactly matching our lower bound when $k=1$. Second, we show that any obstruction-free binary consensus algorithm from readable swap objects with domain size $b$ uses at least $\frac{n-2}{3b+1}$ objects. Since any historyless object can be simulated by a readable swap object with the same domain, our results imply that any obstruction-free consensus algorithm from historyless objects with domain size $b$ uses at least $\frac{n-2}{3b+1}$ objects. For $b = 2$, we show a slightly better lower bound of $n-2$. The best known obstruction-free binary consensus algorithm from readable swap objects with domain size $2$ uses $2n-1$ objects, asymptotically matching our lower bound.

Chatterjee, Gmyr, and Pandurangan [PODC 2020] recently introduced the notion of awake complexity for distributed algorithms, which measures the number of rounds in which a node is awake. In the other rounds, the node is sleeping and performs no computation or communication. Measuring the number of awake rounds can be of significance in many settings of distributed computing, e.g., in sensor networks where energy consumption is of concern. In that paper, Chatterjee et al. provide an elegant randomized algorithm for the Maximal Independent Set (MIS) problem that achieves an $O(1)$ node-averaged awake complexity. That is, the average awake time among the nodes is $O(1)$ rounds. However, to achieve that, the algorithm sacrifices the more standard round complexity measure from the well-known $O(\log n)$ bound of MIS, due to Luby [STOC'85], to $O(\log^{3.41} n)$ rounds. Our first contribution is to present a simple randomized distributed MIS algorithm that, with high probability, has $O(1)$ node-averaged awake complexity and $O(\log n)$ worst-case round complexity. Our second, and more technical contribution, is to show algorithms with the same $O(1)$ node-averaged awake complexity and $O(\log n)$ worst-case round complexity for $(1+\varepsilon)$-approximation of maximum matching and $(2+\varepsilon)$-approximation of minimum vertex cover, where $\varepsilon$ denotes an arbitrary small positive constant.

Several precise and computationally efficient results for pointing errors models in two asymptotic cases are derived in this paper. The normalized mean-squared error (NMSE) performance metric is employed to quantify the accuracy of different models. For the case that the beam width is relatively larger than the detection aperture, we propose the three kinds of models that have the form of $c_1\exp(-c_2r^2) $.It is shown that the modified intensity uniform model not only achieves a comparable accuracy with the best linearized model, but also is expressed in an elegant mathematical way when compared to the traditional Farid model. This indicates that the modified intensity uniform model is preferable in the performance analysis of free space optical (FSO) systems considering the effects of the pointing errors. By analogizing the beam spot with a point in the case that beam width is smaller than the detection aperture, the solution of the pointing errors model is transformed to a smooth function approximation problem, and we find that a more accurate approximation can be achieved by the proposed point approximation model when compared to the model that is induced from the Vasylyev model in some scenarios.

Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for acyclic graphs, considering the \emph{width} of the graph (the minimum number of paths needed to cover all of its edges) yields advances in our understanding of its approximability. For the version of the problem that uses only non-negative weights, we identify and characterise a new class of \emph{width-stable} graphs, for which a popular heuristic is a \gwsimple-approximation ($|X|$ being the total flow of $X$), and strengthen its worst-case approximation ratio from $\Omega(\sqrt{m})$ to $\Omega(m / \log m)$ for sparse graphs, where $m$ is the number of edges in the graph. We also study a new problem on graphs with cycles, Minimum Cost Circulation Decomposition (MCCD), and show that it generalises MFD through a simple reduction. For the version allowing also negative weights, we give a $(\lceil \log \Vert X \Vert \rceil +1)$-approximation ($\Vert X \Vert$ being the maximum absolute value of $X$ on any edge) using a power-of-two approach, combined with parity fixing arguments and a decomposition of unitary circulations ($\Vert X \Vert \leq 1$), using a generalised notion of width for this problem. Finally, we disprove a conjecture about the linear independence of minimum (non-negative) flow decompositions posed by Kloster et al. [ALENEX 2018], but show that its useful implication (polynomial-time assignments of weights to a given set of paths to decompose a flow) holds for the negative version.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

In recent years, mobile devices have gained increasingly development with stronger computation capability and larger storage. Some of the computation-intensive machine learning and deep learning tasks can now be run on mobile devices. To take advantage of the resources available on mobile devices and preserve users' privacy, the idea of mobile distributed machine learning is proposed. It uses local hardware resources and local data to solve machine learning sub-problems on mobile devices, and only uploads computation results instead of original data to contribute to the optimization of the global model. This architecture can not only relieve computation and storage burden on servers, but also protect the users' sensitive information. Another benefit is the bandwidth reduction, as various kinds of local data can now participate in the training process without being uploaded to the server. In this paper, we provide a comprehensive survey on recent studies of mobile distributed machine learning. We survey a number of widely-used mobile distributed machine learning methods. We also present an in-depth discussion on the challenges and future directions in this area. We believe that this survey can demonstrate a clear overview of mobile distributed machine learning and provide guidelines on applying mobile distributed machine learning to real applications.