On the Shapley-like Payoff Mechanisms in Peer-Assisted Services with Multiple Content Providers

This paper studies an incentive structure for cooperation and its stability in peer-assisted services when there exist multiple content providers, using a coalition game theoretic approach. We first consider a generalized coalition structure consisting of multiple providers with many assisting peers, where peers assist providers to reduce the operational cost in content distribution. To distribute the profit from cost reduction to players (i.e., providers and peers), we then establish a generalized formula for individual payoffs when a "Shapley-like" payoff mechanism is adopted. We show that the grand coalition is unstable, even when the operational cost functions are concave, which is in sharp contrast to the recently studied case of a single provider where the grand coalition is stable. We also show that irrespective of stability of the grand coalition, there always exist coalition structures which are not convergent to the grand coalition. Our results give us an important insight that a provider does not tend to cooperate with other providers in peer-assisted services, and be separated from them. To further study the case of the separated providers, three examples are presented; (i) underpaid peers, (ii) service monopoly, and (iii) oscillatory coalition structure. Our study opens many new questions such as realistic and efficient incentive structures and the tradeoffs between fairness and individual providers' competition in peer-assisted services.Comment: 13 pages, 4 figures, an extended version of the paper to be presented in ICST GameNets 2011, Shanghai, China, April 201

Dynamics of Learning with Restricted Training Sets I: General Theory

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

A multi-layer market for vehicle-to-grid energy trading in the smart grid

In this paper, we propose a novel multi-layer market for analyzing the energy exchange process between electric vehicles and the smart grid. The proposed market consists essentially of two layers: a macro layer and a micro layer. At the macro layer, we propose a double auction mechanism using which the aggregators, acting as sellers, and the smart grid elements, acting as buyers, interact so as to trade energy. We show that this double auction mechanism is strategy-proof and converges asymptotically. At the micro layer, the aggregators, which are the sellers in the macro layer, are given monetary incentives so as to sell the energy of associated plug-in hybrid electric vehicles (PHEVs) and to maximize their revenues. We analyze the interaction between the macro and micro layers and study some representative cases. Depending on the elasticity of the supply and demand, the utility functions are analyzed under different scenarios. Simulation results show that the proposed approach can significantly increase the utility of PHEVs, compared to a classical greedy approach.postprin

Komparasi USAhatani Padi Sawah Sistem Tapin dan Sistem Tabela di Kecamatan Geragai Kebupaten Tanjung Jabung Timur

Penelitian ini bertujuan untuk (1) mengetahui perbandingan keragaan USAhatani padi sawah sistem TAPIN dan sistem TABELA, (2) mengetahui perbandingan penggunaan waktu, tenaga kerja, dan biaya produksi USAhatani padi sawah sistem TAPIN dan sistem TABELA, dan (3) mengetahui faktor-faktor yang mempengaruhi petani padi sawah sistem TAPIN beralih ke sistem TABELA di Desa Lagan Ulu dan Desa Pandan Jaya Kecamatan Geragai Kabupaten Tanjung Jabung Timur. Metode analisis yang digunakan adalah analisis biaya dan penerimaan USAhatani, kelayakan USAhatani, efisiensi USAhatani dan analisis regresi logistik biner. Berdasarkan hasil penelitian diperoleh bahwa :(1) perbandingan keragaan USAhatani padi sawah sistem TAPIN dan sistem TABELA yaitu pada tahapan kegiatan penyiapan media persemaian benih, persemaian benih, pemeraman benih, penaburan benih, penanaman, penyisipan dan pengairan. (2) Penggunaan waktu dan tenaga kerja pada USAhatani padi sawah sistem TABELA adalah 38,59 HOK/Ha lebih efisien dibandingkan sistem TAPIN sebesar 64,05 HOK/Ha. Hasil perhitungan nilai R/C rasio menunjukkan dengan nilai R/C rasio sistem TABELA sebesar 1,99 per Ha lebih layak diterapkan dibandingkan sistem TAPIN dengan nilai R/C rasio sebesar 1,04 per Ha. Hasil perhitungan nilai B/C rasio menunjukkan bahwa sistem TABELA dengan nilai B/C rasio sebesar 1,00 lebih efisien dibandingkan sistem TAPIN dengan nilai B/C rasio sebesar 0,04. 3) Faktor-faktor yang mempengaruhi petani untuk beralih ke sistem TABELA secara signifikan melalui analisis regresi logistik biner adalah faktor luas lahan, penggunaan tenaga kerja dan penerimaan

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

Quantum Circulant Preconditioner for Linear System of Equations

We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017]. However, some modifications of SVE should be made to solve the preconditioned linear system $C^{-1} Ax = C^{-1} b$. Moreover, different from the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett., 2013], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1} A$, as well as the Frobenius norm $\|A\|_F$

Solvable Systems of Linear Differential Equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

Soft Tissue Reconstruction following Hemipelvectomy: Eight-Year Experience and Literature Review

Background and Objectives. Hemipelvectomy is a major surgical procedure that associates with significant morbidity, functional impairment, and psychological and body image problem. Reconstruction of the defect is a challenged since a large amount of composite tissues are needed. We would like to share our eight-year experience with massive pelvic resection and reconstruction. Methods. A retrospective analysis of all cases of hemipelvectomy was conducted in our institution over eight-year period with particular attention given to the reconstruction choices and associated complications. Results. Thirteen patients were included with median age of 39 years (range 13–78) of which all had advanced tumour with stage IIb (54%) and Stage III (46%). External hemipelvectomy was performed in all cases, and resultant defects were reconstructed with variety type of flaps. These include fillet thigh flaps, regional pedicle flaps of different designs, and free flap. Conclusions. Massive pelvic tumour is rarely encountered in our population but can be seen across all age groups and usually due to late presentation. The defects should be reconstructed using local or regional flaps, incorporating the muscle component to enhance flap perfusion. The tissue should be harvested from the amputated limb, as it can limit the donor site morbidity