Mechanism Design with Limited Information: The Case of Nonlinear Pricing

We analyze the canonical nonlinear pricing model with limited information. A seller offers a menu with a finite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal finite menu for the socially efficient and the revenue-maximizing mechanism. In both cases, we provide an estimate of the loss resulting from the usage of a finite n-class menu. We show that the losses converge to zero at a rate proportional to 1/n^2 as n becomes large.Mechanism design, Limited information, Nonlinear pricing, Quantization, Lloyd-max optimality

Driving positron beam acceleration with coherent transition radiation

Positron acceleration in plasma wakefield faces significant challenges since the positron beam must be pre-generated and precisely coupled into the wakefield, and most critically, suffers from defocusing issues. Here we propose a scheme that utilizes laser-driven electrons to produce, inject and accelerate positrons in a single set-up. The high-charge electron beam from wakefield acceleration creates copious electron-positron pairs via the Bethe-Heitler process, followed by enormous coherent transition radiation due to the electrons' exiting from the metallic foil. Simulation results show that the coherent transition radiation field reaches up to 10's GV m-1, which captures and accelerates the positrons to cut-off energy of 1.5 GeV with energy peak of 500 MeV and energy spread is about 24.3%. An external longitudinal magnetic field of 30 T is also applied to guide the electrons and positrons during the acceleration process. This proposed method offers a promising way to obtain GeV fast positron sources

Multicell Edge Coverage Enhancement Using Mobile UAV-Relay

Unmanned aerial vehicle (UAV)-assisted communication is a promising technology in future wireless communication networks. UAVs can not only help offload data traffic from ground base stations (GBSs) but also improve the Quality of Service (QoS) of cell-edge users (CEUs). In this article, we consider the enhancement of cell-edge communications through a mobile relay, i.e., UAV, in multicell networks. During each transmission period, GBSs first send data to the UAV, and then the UAV forwards its received data to CEUs according to a certain association strategy. In order to maximize the sum rate of all CEUs, we jointly optimize the UAV mobility management, including trajectory, velocity, and acceleration, and association strategy of CEUs to the UAV, subject to minimum rate requirements of CEUs, mobility constraints of the UAV, and causal buffer constraints in practice. To address the mixed-integer nonconvex problem, we transform it into two convex subproblems by applying tight bounds and relaxations. An iterative algorithm is proposed to solve the two subproblems in an alternating manner. Numerical results show that the proposed algorithm achieves higher rates of CEUs as compared with the existing benchmark schemes

Generation of Ultra-intense Gamma-ray Train by QED Harmonics

When laser intensity exceeds 10^22W/cm^2, photons with energy above MeV can be generated from high-order harmonics process in the laser-plasma interaction. We find that under such laser intensity, QED effect plays a dominating role in the radiation pattern. Contrast to the gas and relativistic HHG processes, both the occurrence and energy of gamma-ray emission produced by QED harmonics are random and QED harmonics are usually not coherent, while the property of high intensity and ultra-short duration is conserved. Our simulation shows that the period of gamma-ray train is half of the laser period and the peak intensity is 1.4e22W/cm^2. This new harmonic production with QED effects are crucial to light-matter interaction in strong field and can be verified in experiments by 10PW laser facilities in the near future.Comment: 12 pages, 4 figure

Mechanism Design with Limited Information: The Case of Nonlinear Pricing

We analyze the canonical nonlinear pricing model with limited information. A seller offers a menu with a finite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal finite menu for the socially efficient and the revenue-maximizing mechanism. In both cases, we provide an estimate of the loss resulting from the usage of a finite n-class menu. We show that the losses converge to zero at a rate proportional to 1/n2 asn becomes large

Nonlinear Pricing with Finite Information

We analyze nonlinear pricing with finite information. A seller offers a menu to a continuum of buyers with a continuum of possible valuations. The menu is limited to offering a finite number of choices representing a finite communication capacity between buyer and seller. We identify necessary conditions that the optimal finite menu must satisfy, either for the socially efficient or for the revenue-maximizing mechanism. These conditions require that information be bundled, or “quantized” optimally. We show that the loss resulting from using the n -item menu converges to zero at a rate proportional to 1 = n 2 . We extend our model to a multi-product environment where each buyer has preferences over a d dimensional variety of goods. The seller is limited to offering a finite number n of d -dimensional choices. By using repeated scalar quantization, we show that the losses resulting from using the d -dimensional n -class menu converge to zero at a rate proportional to d = n 2 / d . We introduce vector quantization and establish that the losses due to finite menus are significantly reduced by offering optimally chosen bundles

DETA: Denoised Task Adaptation for Few-Shot Learning

Test-time task adaptation in few-shot learning aims to adapt a pre-trained task-agnostic model for capturing taskspecific knowledge of the test task, rely only on few-labeled support samples. Previous approaches generally focus on developing advanced algorithms to achieve the goal, while neglecting the inherent problems of the given support samples. In fact, with only a handful of samples available, the adverse effect of either the image noise (a.k.a. X-noise) or the label noise (a.k.a. Y-noise) from support samples can be severely amplified. To address this challenge, in this work we propose DEnoised Task Adaptation (DETA), a first, unified image- and label-denoising framework orthogonal to existing task adaptation approaches. Without extra supervision, DETA filters out task-irrelevant, noisy representations by taking advantage of both global visual information and local region details of support samples. On the challenging Meta-Dataset, DETA consistently improves the performance of a broad spectrum of baseline methods applied on various pre-trained models. Notably, by tackling the overlooked image noise in Meta-Dataset, DETA establishes new state-of-the-art results. Code is released at https://github.com/nobody-1617/DETA.Comment: 10 pages, 5 figure