Online Pricing with Offline Data: Phase Transition and Inverse Square Law

This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of $T$ periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that before the start of the selling horizon, the seller already has some pre-existing offline data. The offline data set contains $n$ samples, each of which is an input-output pair consisting of a historical price and an associated demand observation. The seller wants to utilize both the pre-existing offline data and the sequential online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning process. Specifically, the size, location and dispersion of the offline data are measured by the number of historical samples $n$, the distance between the average historical price and the optimal price $\delta$, and the standard deviation of the historical prices $\sigma$, respectively. We show that the optimal regret is $\widetilde \Theta\left(\sqrt{T}\wedge \frac{T}{(n\wedge T)\delta^2+n\sigma^2}\right)$, and design a learning algorithm based on the "optimism in the face of uncertainty" principle, whose regret is optimal up to a logarithmic factor. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law.Comment: Forthcoming in Management Scienc

Device-free Localization using Received Signal Strength Measurements in Radio Frequency Network

Device-free localization (DFL) based on the received signal strength (RSS) measurements of radio frequency (RF)links is the method using RSS variation due to the presence of the target to localize the target without attaching any device. The majority of DFL methods utilize the fact the link will experience great attenuation when obstructed. Thus that localization accuracy depends on the model which describes the relationship between RSS loss caused by obstruction and the position of the target. The existing models is too rough to explain some phenomenon observed in the experiment measurements. In this paper, we propose a new model based on diffraction theory in which the target is modeled as a cylinder instead of a point mass. The proposed model can will greatly fits the experiment measurements and well explain the cases like link crossing and walking along the link line. Because the measurement model is nonlinear, particle filtering tracing is used to recursively give the approximate Bayesian estimation of the position. The posterior Cramer-Rao lower bound (PCRLB) of proposed tracking method is also derived. The results of field experiments with 8 radio sensors and a monitored area of 3.5m 3.5m show that the tracking error of proposed model is improved by at least 36 percent in the single target case and 25 percent in the two targets case compared to other models.Comment: This paper has been withdrawn by the author due to some mistake

I. Toward the Quantum Limit in Gravitational Wave Detectors. II. Several Theoretical Problems in Condensed Matter Physics.

Part I. We analyze a gravity wave detector consisting of a Weber type resonant antenna, an inductive transducer and a dc SQUID coupling system. We derive the complete set of equations of motion for the system and discuss their implications and solutions in detail. The results obtained are applied to the LSU gravity wave detector, and the optimum system parameters are calculated. We show that it is possible to approach quantum limited sensitivity for the detector if these optimum system parameters and matching conditions are properly satisfied. In the final chapter we present our preliminary experimental results. We have built an electronic feedback system and operated a very sensitive and well coupled planar dc SQUID at liquid helium temperature. The parameters and characteristics of dc SQUID, the dynamic property of feedback loop, and the noise performance of the system have been carefully measured. Part II. We first present a critical comparison of the work of Ramana and Rajagopal (RR) with the work of McDonald (MD) on the spin polarized relativistic electron gas system. After correcting some errors in previous work of RR, a new analytical expression for exchange energy and exchange potential which are convenient for practical applications are then derived. We have therefore set up the correct relativistic generalization of spin density functional theory. We prove that, in general, the mapping V((\u27)r,t) (---\u3e) (\u27)J((\u27)r,t), is not invertible for a given initital condition, and a particle density func- tional theory comparable to the HK Theorem for stationary problems cannot be established for general time-dependent systems. We suggest a new current density functional theory for time-dependent systems. We emphasize that (\u27)J((\u27)r,t) instead of n((\u27)r,t) plays a central role in time-dependent problems. In chapter IV, we examine the effects of the underlying crystal structure and the surface/interface normal on spin waves at surfaces and interfaces for cubic crystals described by the Heisenberg Hamiltonian. Our detailed numerical results show that, with the same perturbations, there are pronounced differences in the results obtained for different faces of the same crystal, or in those for the same face of different crystals

Construction of Evaluation Indicator System for Rural Elderly Facilities Configuration in Datong City

China has entered a deeply aging society, and the aging problem in rural areas is particularly serious compared with that in cities and towns. In order to actively respond to the challenges of aging in rural areas, the Rural Revitalization Bureau of Datong City has issued the “Rural Nursing Care Project” Implementation Plan, exploring the establishment of a well-functioning, moderately scaled, and orderly functioning rural pension model. In this paper, through the field research of rural pension facilities and questionnaire interviews with the elderly, and using the SPSS factor analysis method for data statistics and analysis, we finally constructed the evaluation index system of rural pension facilities configuration in Datong City, and established the index basis for the construction of the evaluation system of rural pension facilities configuration, so as to make the sense of acquisition of the elderly in the countryside more adequate, the sense of well-being more sustainable, and the sense of security more secure, which is the most important task for the construction and improvement of the rural pension service system at the moment. It is an urgent task to improve the construction of rural pension service system