Projection Onto A Simplex

This mini-paper presents a fast and simple algorithm to compute the projection onto the canonical simplex $\triangle^n$. Utilizing the Moreau's identity, we show that the problem is essentially a univariate minimization and the objective function is strictly convex and continuously differentiable. Moreover, it is shown that there are at most n candidates which can be computed explicitly, and the minimizer is the only one that falls into the correct interval

Optimal Quality-of-Service Scheduling for Energy-Harvesting Powered Wireless Communications

XiaojingChen, Wei Ni, Xin Wang, YichuangSun, “Optimal Quality-of-Service Scheduling for Energy-Harvesting Powered Wireless Communications”, IEEE Transactions on Wireless Communications, Vol. 15 (5): 3269-3280, January 2016. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, a new dynamic string tautening algorithm is proposed to generate the most energy-efficient off-line schedule for delay-limited traffic of transmitters with non-negligible circuit power. The algorithm is based on two key findings that we derive through judicious convex formulation and resultant optimality conditions, specifies a set of simple but optimal rules, and generates the optimal schedule with a low complexity of O(N2) in the worst case. The proposed algorithm is also extended to on-line scenarios, where the transmit schedule is generated on-the-fly. Simulation shows that the proposed algorithm requires substantially lower average complexity by almost two orders of magnitude to retain optimality than general convex solvers. The effective transmit region, specified by the tradeoff of the data arrival rate and the energy harvesting rate, is substantially larger using our algorithm than using other existing alternatives. Significantly more data or less energy can be supported in the proposed algorithm.Peer reviewedFinal Accepted Versio

UV spectra of iron-doped carbon clusters FeC_n n = 3-6

Electronic transitions of jet-cooled FeC$_n$ clusters ($n = 3 - 6$) were measured between 230 and 300 nm by a mass-resolved 1+1 resonant two-photon ionization technique. Rotational profiles were simulated based on previous calculations of ground state geometries and compared to experimental observations. Reasonable agreement is found for the planar fan-like structure of FeC$_3$. The FeC$_4$ data indicate a shorter distance between the Fe atom and the bent C$_4$ unit of the fan. The transitions are suggested to be $^{3}$A$_{2} \leftarrow ^{3}$B$_{1}$ for FeC$_3$ and $^{5}$A$_{1} \leftarrow ^{5}$A$_{1}$ for FeC$_4$. In contrast to the predicted C$_{\infty \text{v}}$ geometry, non-linear FeC$_5$ is apparently observed. Line width broadening prevents analysis of the FeC$_6$ spectrum.Comment: 6 pages, 5 figure