38,079 research outputs found

    The principle of least action and the geometric basis of D-branes

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    We analyze thoroughly the boundary conditions allowed in classical non-linear sigma models and derive from first principle the corresponding geometric objects, i.e. D-branes. In addition to giving classical D-branes an intrinsic and geometric foundation, D-branes in nontrivial H flux and D-branes embedded within D-branes are precisely defined. A well known topological condition on D-branes is replaced

    Capacity of Compound MIMO Gaussian Channels with Additive Uncertainty

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    This paper considers reliable communications over a multiple-input multiple-output (MIMO) Gaussian channel, where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix, i.e., an instance of the compound MIMO Gaussian channel. We study the optimal transmit covariance matrix design to achieve the capacity of compound MIMO Gaussian channels, where the channel uncertainty region is characterized by the spectral norm. This design problem is a challenging non-convex optimization problem. However, in this paper, we reveal that this problem has a hidden convexity property, which can be exploited to map the problem into a convex optimization problem. We first prove that the optimal transmit design is to diagonalize the nominal channel, and then show that the duality gap between the capacity of the compound MIMO Gaussian channel and the min-max channel capacity is zero, which proves the conjecture of Loyka and Charalambous (IEEE Trans. Inf. Theory, vol. 58, no. 4, pp. 2048-2063, 2012). The key tools for showing these results are a new matrix determinant inequality and some unitarily invariant properties.Comment: 8 pages, submitted to IEEE Transactions on Information Theor

    Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes

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    Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications

    Characterizing Human Mobility Patterns in a Large Street Network

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    Previous studies demonstrated empirically that human mobility exhibits Levy flight behaviour. However, our knowledge of the mechanisms governing this Levy flight behaviour remains limited. Here we analyze over 72 000 people's moving trajectories, obtained from 50 taxicabs during a six-month period in a large street network, and illustrate that the human mobility pattern, or the Levy flight behaviour, is mainly attributed to the underlying street network. In other words, the goal-directed nature of human movement has little effect on the overall traffic distribution. We further simulate the mobility of a large number of random walkers, and find that (1) the simulated random walkers can reproduce the same human mobility pattern, and (2) the simulated mobility rate of the random walkers correlates pretty well (an R square up to 0.87) with the observed human mobility rate.Comment: 13 figures, 17 page

    Update or Wait: How to Keep Your Data Fresh

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    In this work, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information, or simply age, which is defined as how old the freshest received update is since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered and the channel becomes free, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semi-Markov decision problem (SMDP) with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies, and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if (i) the age penalty function grows quickly with respect to the age, (ii) the packet transmission times over the channel are positively correlated over time, or (iii) the packet transmission times are highly random (e.g., following a heavy-tail distribution)

    Incentivizing High Quality Crowdwork

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    We study the causal effects of financial incentives on the quality of crowdwork. We focus on performance-based payments (PBPs), bonus payments awarded to workers for producing high quality work. We design and run randomized behavioral experiments on the popular crowdsourcing platform Amazon Mechanical Turk with the goal of understanding when, where, and why PBPs help, identifying properties of the payment, payment structure, and the task itself that make them most effective. We provide examples of tasks for which PBPs do improve quality. For such tasks, the effectiveness of PBPs is not too sensitive to the threshold for quality required to receive the bonus, while the magnitude of the bonus must be large enough to make the reward salient. We also present examples of tasks for which PBPs do not improve quality. Our results suggest that for PBPs to improve quality, the task must be effort-responsive: the task must allow workers to produce higher quality work by exerting more effort. We also give a simple method to determine if a task is effort-responsive a priori. Furthermore, our experiments suggest that all payments on Mechanical Turk are, to some degree, implicitly performance-based in that workers believe their work may be rejected if their performance is sufficiently poor. Finally, we propose a new model of worker behavior that extends the standard principal-agent model from economics to include a worker's subjective beliefs about his likelihood of being paid, and show that the predictions of this model are in line with our experimental findings. This model may be useful as a foundation for theoretical studies of incentives in crowdsourcing markets.Comment: This is a preprint of an Article accepted for publication in WWW \c{opyright} 2015 International World Wide Web Conference Committe

    Determination of Wave Function Functionals: The Constrained-Search--Variational Method

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    In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function ψ\psi to be a functional of functions χ:ψ=ψ[χ] \chi: \psi = \psi[\chi] rather than a function. The space of variations is expanded because a search over the functions χ\chi can in principle lead to the true wave function. As the space of such variations is large, we proposed the constrained-search-- variational method whereby a constrained search is first performed over all functions χ\chi such that the wave function functional ψ[χ]\psi[\chi] satisfies a physical constraint such as normalization or the Fermi-Coulomb hole sum rule, or leads to the known value of an observable such as the diamagnetic susceptibility, nuclear magnetic constant or Fermi contact term. A rigorous upper bound to the energy is then obtained by application of the variational principle. A key attribute of the method is that the wave function functional is accurate throughout space, in contrast to the standard variational method for which the wave function is accurate only in those regions of space contributing principally to the energy. In this paper we generalize the equations of the method to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. The description is general and applicable to both ground and excited states. A discussion on excited states in conjunction with the theorem of Theophilou is provided.Comment: 26 pages, 4 figures, 5 table
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