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 consider the Cauchy problem for the Helmholtz equation with a domain in R^d, d>2 with N cylindrical outlets to infinity with bounded inclusions in R^{d-1}. Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Maz'ya proposed an alternating iterative method for solving Cauchy problems associated with elliptic,self-adjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Mpinganzima et al. for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R^2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters, the Robin-Dirichlet alternating iterative procedure is convergent.

In the coming years, quantum networks will allow quantum applications to thrive thanks to the new opportunities offered by end-to-end entanglement of qubits on remote hosts via quantum repeaters. On a geographical scale, this will lead to the dawn of the Quantum Internet. While a full-blown deployment is yet to come, the research community is already working on a variety of individual enabling technologies and solutions. In this paper, with the guidance of extensive simulations, we take a broader view and investigate the problems of Quality of Service (QoS) and provisioning in the context of quantum networks, which are very different from their counterparts in classical data networks due to some of their fundamental properties. Our work leads the way towards a new class of studies that will allow the research community to better understand the challenges of quantum networks and their potential commercial exploitation.

Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.

Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being dedicated by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the QCN performance. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite quantum states' lifetime. In this paper, we introduce a novel framework, dubbed physics-informed QCNs, for designing and analyzing the performance of QCNs, by relying on the quantum physics principles that underly the different QCN components. The need of the proposed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-the-art advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of future communication networks (6G and beyond, and the quantum Internet).

Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices, which use different gate sets, and can miss optimizations that are hard to find manually. We propose Quartz, a quantum circuit superoptimizer that automatically generates and verifies circuit transformations for arbitrary quantum gate sets. For a given gate set, Quartz generates candidate circuit transformations by systematically exploring small circuits and verifies the discovered transformations using an automated theorem prover. To optimize a quantum circuit, Quartz uses a cost-based backtracking search that applies the verified transformations to the circuit. Our evaluation on three popular gate sets shows that Quartz can effectively generate and verify transformations for different gate sets. The generated transformations cover manually designed transformations used by existing optimizers and also include new transformations. Quartz is therefore able to optimize a broad range of circuits for diverse gate sets, outperforming or matching the performance of hand-tuned circuit optimizers.

In this work a quantum analogue of Bayesian statistical inference is considered. Based on the notion of instrument, we propose a sequential measurement scheme from which observations needed for statistical inference are obtained. We further put forward a quantum analogue of Bayes rule, which states how the prior normal state of a quantum system updates under those observations. We next generalize the fundamental notions and results of Bayesian statistics according to the quantum Bayes rule. It is also note that our theory retains the classical one as its special case. Finally, we investigate the limit of posterior normal state as the number of observations tends to infinity.

We present a data-efficient framework for solving sequential decision-making problems which exploits the combination of reinforcement learning (RL) and latent variable generative models. The framework, called GenRL, trains deep policies by introducing an action latent variable such that the feed-forward policy search can be divided into two parts: (i) training a sub-policy that outputs a distribution over the action latent variable given a state of the system, and (ii) unsupervised training of a generative model that outputs a sequence of motor actions conditioned on the latent action variable. GenRL enables safe exploration and alleviates the data-inefficiency problem as it exploits prior knowledge about valid sequences of motor actions. Moreover, we provide a set of measures for evaluation of generative models such that we are able to predict the performance of the RL policy training prior to the actual training on a physical robot. We experimentally determine the characteristics of generative models that have most influence on the performance of the final policy training on two robotics tasks: shooting a hockey puck and throwing a basketball. Furthermore, we empirically demonstrate that GenRL is the only method which can safely and efficiently solve the robotics tasks compared to two state-of-the-art RL methods.

We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be even worse than purely using ML predictions. In order to address the "how to learn" challenge, we propose EC-L2O (expert-calibrated learning to optimize), which trains an ML-based optimizer by explicitly taking into account the downstream expert calibrator. To accomplish this, we propose a new differentiable expert calibrator that generalizes regularized online balanced descent and offers a provably better competitive ratio than pure ML predictions when the prediction error is large. For training, our loss function is a weighted sum of two different losses -- one minimizing the average ML prediction error for better robustness, and the other one minimizing the post-calibration average cost. We also provide theoretical analysis for EC-L2O, highlighting that expert calibration can be even beneficial for the average cost performance and that the high-percentile tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle (i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running simulations for sustainable datacenter demand response. Our results demonstrate that EC-L2O can empirically achieve a lower average cost as well as a lower competitive ratio than the existing baseline algorithms.

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as "quantum combs"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate many of these algorithms by using a variational approach with parameterized quantum circuits. We find that the simulations converge well in both the noiseless and noisy scenarios, for all examples considered. Furthermore, the noisy simulations exhibit a parameter noise resilience.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.