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We show how to translate a subset of RISC-V machine code compiled from a subset of C to quadratic unconstrained binary optimization (QUBO) models that may be solved by a quantum annealing machine: given a bound $n$, there is input $I$ to a program $P$ such that $P$ runs into a given program state $E$ executing no more than $n$ machine instructions if and only if the QUBO model of $P$ for $n$ evaluates to 0 on $I$. Thus, with more qubits on the machine than variables in the QUBO model, quantum annealing the model reaches 0 (ground) energy in constant time with high probability on some input $I$ that is part of the ground state if and only if $P$ runs into $E$ on $I$ executing no more than $n$ instructions. Translation takes $\mathcal{O}(n^2)$ time effectively turning a quantum annealer into a polynomial-time symbolic execution engine and bounded model checker, eliminating their path and state explosion problems. Here, we take advantage of the fact that any machine instruction may only increase the size of the program state by a constant amount of bits. Translation time comes down from $\mathcal{O}(n^2)$ to $\mathcal{O}(n\cdot|P|)$ if memory consumption of $P$ is bounded by a constant, establishing a linear (quadratic) upper bound on quantum space, in number of qubits on a quantum annealer, in terms of algorithmic time (space) in classical computing. The construction provides a non-relativizing argument for $NP\subseteq BQP$, without violating the optimality of Grover's algorithm, also on gate-model quantum machines, and motivates a temporal and spatial metric of quantum advantage. Our prototypical open-source toolchain translates machine code that runs on real RISC-V hardware to models that can be solved by real quantum annealing hardware, as shown in our experiments.

Prescriptive process monitoring methods seek to optimize a business process by recommending interventions at runtime to prevent negative outcomes or poorly performing cases. In recent years, various prescriptive process monitoring methods have been proposed. This paper studies existing methods in this field via a Systematic Literature Review (SLR). In order to structure the field, the paper proposes a framework for characterizing prescriptive process monitoring methods according to their performance objective, performance metrics, intervention types, modeling techniques, data inputs, and intervention policies. The SLR provides insights into challenges and areas for future research that could enhance the usefulness and applicability of prescriptive process monitoring methods. The paper highlights the need to validate existing and new methods in real-world settings, to extend the types of interventions beyond those related to the temporal and cost perspectives, and to design policies that take into account causality and second-order effects.

A mega-constellation of low-altitude earth orbit (LEO) satellites (SATs) are envisaged to provide a global coverage SAT network in beyond fifth-generation (5G) cellular systems. LEO SAT networks exhibit extremely long link distances of many users under time-varying SAT network topology. This makes existing multiple access protocols, such as random access channel (RACH) based cellular protocol designed for fixed terrestrial network topology, ill-suited. To overcome this issue, in this paper, we propose a novel grant-free random access solution for LEO SAT networks, dubbed emergent random access channel protocol (eRACH). In stark contrast to existing model-based and standardized protocols, eRACH is a model-free approach that emerges through interaction with the non-stationary network environment, using multi-agent deep reinforcement learning (MADRL). Furthermore, by exploiting known SAT orbiting patterns, eRACH does not require central coordination or additional communication across users, while training convergence is stabilized through the regular orbiting patterns. Compared to RACH, we show from various simulations that our proposed eRACH yields 54.6% higher average network throughput with around two times lower average access delay while achieving 0.989 Jain's fairness index.

A detection system, modeled in a graph, is composed of "detectors" positioned at a subset of vertices in order to uniquely locate an ``intruder" at any vertex. \emph{Identifying codes} use detectors that can sense the presence or absence of an intruder within distance one. We introduce a fault-tolerant identifying code called a \emph{redundant identifying code}, which allows at most one detector to go offline or be removed without disrupting the detection system. In real-world applications, this would be a necessary feature, as it would allow for maintenance on individual components without disabling the entire system. Specifically, we prove that the problem of determining the lowest cardinality of an identifying code for an arbitrary graph is NP-complete, we determine the bounds on the lowest cardinality for special classes of graphs, including trees, cylinders, and cubic graphs.

The guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on standard semi-definite programming techniques and therefore lead to approximated results. In contrast, our main result is an algorithm that, upon the input of any qubit ensemble over a discrete ring and with uniform probability distribution, after finitely many steps outputs the exact closed-form analytic expression of its guesswork. The complexity of our guesswork-computing algorithm is factorial in the number of states, with a more-than-quadratic speedup for symmetric ensembles. To find such symmetries, we provide an algorithm that, upon the input of any point set over a discrete ring, after finitely many steps outputs its exact symmetries. The complexity of our symmetries-finding algorithm is polynomial in the number of points. As examples, we compute the guesswork of regular and quasi-regular sets of qubit states.

Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated with a class of highly entangled many-body wavefunctions. It has been suggested that this approach can be certified with the Linear Cross-Entropy Benchmark (XEB). We critically examine this notion. First, in a "benign" setting where an honest implementation of noisy quantum circuits is assumed, we characterize the conditions under which the XEB approximates the fidelity. Second, in an "adversarial" setting where all possible classical algorithms are considered for comparison, we show that achieving relatively high XEB values does not imply faithful simulation of quantum dynamics. We present an efficient classical algorithm that, with 1 GPU within 2s, yields high XEB values, namely 2-12% of those obtained in experiments. By identifying and exploiting several vulnerabilities of the XEB, we achieve high XEB values without full simulation of quantum circuits. Remarkably, our algorithm features better scaling with the system size than noisy quantum devices for commonly studied random circuit ensembles. To quantitatively explain the success of our algorithm and the limitations of the XEB, we use a theoretical framework in which the average XEB and fidelity are mapped to statistical models. We illustrate the relation between the XEB and the fidelity for quantum circuits in various architectures, with different gate choices, and in the presence of noise. Our results show that XEB's utility as a proxy for fidelity hinges on several conditions, which must be checked in the benign setting but cannot be assumed in the adversarial setting. Thus, the XEB alone has limited utility as a benchmark for quantum advantage. We discuss ways to overcome these limitations.

A matrix formalism for the determination of the best estimator in certain simulation-based parameter estimation problems will be presented and discussed. The equations, termed as the Linear Template Fit, combine a linear regression with a least square method and its optimization. The Linear Template Fit employs only predictions that are calculated beforehand and which are provided for a few values of the parameter of interest. Therefore, the Linear Template Fit is particularly suited for parameter estimation with computationally intensive simulations that are otherwise often limited in their usability for statistical inference, or for performance critical applications. Equations for error propagation are discussed, and the analytic form provides comprehensive insights into the parameter estimation problem. Furthermore, the quickly-converging algorithm of the Quadratic Template Fit will be presented, which is suitable for a non-linear dependence on the parameters. As an example application, a determination of the strong coupling constant, $\alpha_s(m_Z)$, from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.

Unpaired image-to-image translation has been applied successfully to natural images but has received very little attention for manifold-valued data such as in diffusion tensor imaging (DTI). The non-Euclidean nature of DTI prevents current generative adversarial networks (GANs) from generating plausible images and has mainly limited their application to diffusion MRI scalar maps, such as fractional anisotropy (FA) or mean diffusivity (MD). Even if these scalar maps are clinically useful, they mostly ignore fiber orientations and therefore have limited applications for analyzing brain fibers. Here, we propose a manifold-aware CycleGAN that learns the generation of high-resolution DTI from unpaired T1w images. We formulate the objective as a Wasserstein distance minimization problem of data distributions on a Riemannian manifold of symmetric positive definite 3x3 matrices SPD(3), using adversarial and cycle-consistency losses. To ensure that the generated diffusion tensors lie on the SPD(3) manifold, we exploit the theoretical properties of the exponential and logarithm maps of the Log-Euclidean metric. We demonstrate that, unlike standard GANs, our method is able to generate realistic high-resolution DTI that can be used to compute diffusion-based metrics and potentially run fiber tractography algorithms. To evaluate our model's performance, we compute the cosine similarity between the generated tensors principal orientation and their ground-truth orientation, the mean squared error (MSE) of their derived FA values and the Log-Euclidean distance between the tensors. We demonstrate that our method produces 2.5 times better FA MSE than a standard CycleGAN and up to 30% better cosine similarity than a manifold-aware Wasserstein GAN while synthesizing sharp high-resolution DTI.

Model quantization is a widely used technique to compress and accelerate deep neural network (DNN) inference. Emergent DNN hardware accelerators begin to support flexible bitwidth (1-8 bits) to further improve the computation efficiency, which raises a great challenge to find the optimal bitwidth for each layer: it requires domain experts to explore the vast design space trading off among accuracy, latency, power, and model size, which is both time-consuming and sub-optimal. Conventional quantization algorithm ignores the different hardware architectures and quantizes all the layers in an uniform way. In this paper, we introduce the Hardware-Aware Automated Quantization (HAQ) framework which leverages the reinforcement learning to automatically determine the quantization policy, and we take the hardware accelerator's feedback in the design loop. Rather than relying on proxy signals such as FLOPs and model size, we employ a hardware simulator to generate direct feedback signals to the RL agent. Compared with conventional methods, our framework is fully automated and can specialize the quantization policy for different neural network architectures and hardware architectures. Our framework effectively reduced the latency by 1.4-1.95x and the energy consumption by 1.9x with negligible loss of accuracy compared with the fixed bitwidth (8 bits) quantization. Our framework reveals that the optimal policies on different hardware architectures (i.e., edge and cloud architectures) under different resource constraints (i.e., latency, power and model size) are drastically different. We interpreted the implication of different quantization policies, which offer insights for both neural network architecture design and hardware architecture design.

Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a separate generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients -- a key element in generative adversarial network training -- using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical experiment to demonstrate that quantum generative adversarial networks can be trained successfully.