arXiv subjects
Publications and source records attributed to Xiaodong Wang.
In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$ keys. Then the algorithm is improved to some $O(\log n)$ time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of $r(n)$.
Self-organized V-N co-doped TiO2 nanotube arrays (TNAs) with various doping amount were synthesized by anodizing in association with hydrothermal treatment. Impacts of V-N co-doping on the morphologies, phase structures, and photoelectrochemical properties of the TNAs films were thoroughly investigated. The co-doped TiO2 photocatalysts show remarkably enhanced photocatalytic activity for the CO2 photoreduction to methane under ultraviolet illumination. The mechanism of the enhanced photocatalytic activity is discussed in detail.
We study the massive multiple-input multiple-output (MIMO) multicast transmission in cellular networks where each base station (BS) is equipped with a large-scale antenna array and transmits a common message using a single beamformer to multiple mobile users. We first show that when each BS knows the perfect channel state information (CSI) of its own served users, the asymptotically optimal beamformer at each BS is a linear combination of the channel vectors of its multicast users. Moreover, the optimal combining coefficients are obtained in closed form. Then we consider the imperfect CSI scenario where the CSI is obtained through uplink channel estimation in timedivision duplex systems. We propose a new pilot scheme that estimates the composite channel which is a linear combination of the individual channels of multicast users in each cell. This scheme is able to completely eliminate pilot contamination. The pilot power control for optimizing the multicast beamformer at each BS is also derived. Numerical results show that the asymptotic performance of the proposed scheme is close to the ideal case with perfect CSI. Simulation also verifies the effectiveness of the proposed scheme with finite number of antennas at each BS.
In this work, we deal with resource allocation in the downlink of spatial multiplexing MIMO-OFDMA systems. In particular, we concentrate on the problem of jointly optimizing the transmit and receive processing matrices, the channel assignment and the power allocation with the objective of minimizing the total power consumption while satisfying different quality-of-service requirements. A layered architecture is used in which users are first partitioned in different groups on the basis of their channel quality and then channel assignment and transceiver design are sequentially addressed starting from the group of users with most adverse channel conditions. The multi-user interference among users belonging to different groups is removed at the base station using a Tomlinson-Harashima pre-coder operating at user level. Numerical results are used to highlight the effectiveness of the proposed solution and to make comparisons with existing alternatives.
Recommendation systems for online dating have recently attracted much attention from the research community. In this paper we proposed a two-side matching framework for online dating recommendations and design an LDA model to learn the user preferences from the observed user messaging behavior and user profile features. Experimental results using data from a large online dating website shows that two-sided matching improves significantly the rate of successful matches by as much as 45%. Finally, using simulated matchings we show that the the LDA model can correctly capture user preferences.
Online dating sites have become popular platforms for people to look for potential romantic partners. It is important to understand users' dating preferences in order to make better recommendations on potential dates. The message sending and replying actions of a user are strong indicators for what he/she is looking for in a potential date and reflect the user's actual dating preferences. We study how users' online dating behaviors correlate with various user attributes using a large real-world dateset from a major online dating site in China. Many of our results on user messaging behavior align with notions in social and evolutionary psychology: males tend to look for younger females while females put more emphasis on the socioeconomic status (e.g., income, education level) of a potential date. In addition, we observe that the geographic distance between two users and the photo count of users play an important role in their dating behaviors. Our results show that it is important to differentiate between users' true preferences and random selection. Some user behaviors in choosing attributes in a potential date may largely be a result of random selection. We also find that both males and females are more likely to reply to users whose attributes come closest to the stated preferences of the receivers, and there is significant discrepancy between a user's stated dating preference and his/her actual online dating behavior. These results can provide valuable guidelines to the design of a recommendation engine for potential dates.
Dynamic spectrum access under channel uncertainties is considered. With the goal of maximizing the secondary user (SU) throughput subject to constraints on the primary user (PU) outage probability we formulate a joint problem of spectrum sensing and channel state estimation. The problem is cast into a sequential framework since sensing time minimization is crucial for throughput maximization. In the optimum solution, the sensing decision rule is coupled with the channel estimator, making the separate treatment of the sensing and channel estimation strictly suboptimal. Using such a joint structure for spectrum sensing and channel estimation we propose a distributed (cooperative) dynamic spectrum access scheme under statistical channel state information (CSI). In the proposed scheme, the SUs report their sufficient statistics to a fusion center (FC) via level-triggered sampling, a nonuniform sampling technique that is known to be bandwidth-and-energy efficient. Then, the FC makes a sequential spectrum sensing decision using local statistics and channel estimates, and selects the SU with the best transmission opportunity. The selected SU, using the sensing decision and its channel estimates, computes the transmit power and starts data transmission. Simulation results demonstrate that the proposed scheme significantly outperforms its conventional counterparts, under the same PU outage constraints, in terms of the achievable SU throughput.
The recently proposed sequential distributed detector based on level-triggered sampling operates as simple as the decision fusion techniques and at the same time performs as well as the data fusion techniques. Hence, it is well suited for resource-constrained wireless sensor networks. However, in practical cases where sensors observe discrete-time signals, the random overshoot above or below the sampling thresholds considerably degrades the performance of the considered detector. We propose, for systems with stringent energy constraints, a novel approach to tackle this problem by encoding the overshoot into the time delay between the sampling time and the transmission time. Specifically, each sensor computes the local log-likelihood ratio (LLR) and samples it using level-triggered sampling. Then, it transmits a single pulse to the fusion center (FC) after a transmission delay that is proportional to the overshoot, as in pulse position modulation (PPM). The FC, upon receiving a bit decodes the corresponding overshoot and recovers the transmitted LLR value. It then updates the approximate global LLR and compares it with two threshold to either make a decision or to continue the sequential process. We analyze the asymptotic average detection delay performance of the proposed scheme. We then apply the proposed sequential scheme to target detection in wireless sensor networks under the four Swerling fluctuating target models. It is seen that the proposed sequential distributed detector offers significant performance advantage over conventional decision fusion techniques.
In this paper, we develop optimal energy scheduling algorithms for $N$-user fading multiple-access channels with energy harvesting to maximize the channel sum-rate, assuming that the side information of both the channel states and energy harvesting states for $K$ time slots is known {\em a priori}, and the battery capacity and the maximum energy consumption in each time slot are bounded. The problem is formulated as a convex optimization problem with ${\cal O}(NK)$ constraints making it hard to solve using a general convex solver since the computational complexity of a generic convex solver is exponential in the number of constraints. This paper gives an efficient energy scheduling algorithm, called the iterative dynamic water-filling algorithm, that has a computational complexity of ${\cal O}(NK^2)$ per iteration. For the single-user case, a dynamic water-filling method is shown to be optimal. Unlike the traditional water-filling algorithm, in dynamic water-filling, the water level is not constant but changes when the battery overflows or depletes. An iterative version of the dynamic water-filling algorithm is shown to be optimal for the case of multiple users. Even though in principle the optimality is achieved under large number of iterations, in practice convergence is reached in only a few iterations. Moreover, a single iteration of the dynamic water-filling algorithm achieves a sum-rate that is within $(N-1)K/2$ nats of the optimal sum-rate.
We consider power allocation for an access-controlled transmitter with energy harvesting capability based on causal observations of the channel fading state. We assume that the system operates in a time-slotted fashion and the channel gain in each slot is a random variable which is independent across slots. Further, we assume that the transmitter is solely powered by a renewable energy source and the energy harvesting process can practically be predicted. With the additional access control for the transmitter and the maximum power constraint, we formulate the stochastic optimization problem of maximizing the achievable rate as a Markov decision process (MDP) with continuous state. To efficiently solve the problem, we define an approximate value function based on a piecewise linear fit in terms of the battery state. We show that with the approximate value function, the update in each iteration consists of a group of convex problems with a continuous parameter. Moreover, we derive the optimal solution to these convex problems in closed-form. Further, we propose power allocation algorithms for both the finite- and infinite-horizon cases, whose computational complexity is significantly lower than that of the standard discrete MDP method but with improved performance. Extension to the case of a general payoff function and imperfect energy prediction is also considered. Finally, simulation results demonstrate that the proposed algorithms closely approach the optimal performance.
In networked control systems (NCS), sensing and control signals between the plant and controllers are typically transmitted wirelessly. Thus, the time delay plays an important role for the stability of NCS, especially with distributed controllers. In this paper, the optimal control strategy is derived for distributed control networks with time delays. In particular, we form the optimal control problem as a non-cooperative linear quadratic game (LQG). Then, the optimal control strategy of each controller is obtained that is based on the current state and the last control strategies. The proposed optimal distributed controller reduces to some known controllers under certain conditions. Moreover, we illustrate the application of the proposed distributed controller to load frequency control in power grid systems.
We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As an application we prove a uniqueness result that generalizes the theorem of Jerison and Lee.
Motivated by a sharp eigenvalue estimate for the Kohn Laplacian, we prove a theorem that characterizes the CR sphere in terms of the existence of a non-trivial complex-valued function satisfying a certain overdetermined system.
We consider the problem of decentralized estimation using wireless sensor networks. Specifically, we propose a novel framework based on level-triggered sampling, a non-uniform sampling strategy, and sequential estimation. The proposed estimator can be used as an asymptotically optimal fixed-sample-size decentralized estimator under non-fading listening channels (through which sensors collect their observations), as an alternative to the one-shot estimators commonly found in the literature. It can also be used as an asymptotically optimal sequential decentralized estimator under fading listening channels. We show that the optimal centralized estimator under Gaussian noise is characterized by two processes, namely the observed Fisher information U_t, and the observed correlation V_t. It is noted that under non-fading listening channels only V_t is random, whereas under fading listening channels both U_t and V_t are random. In the proposed scheme, each sensor computes its local random process(es), and sends a single bit to the fusion center (FC) whenever the local random process(es) pass(es) certain predefined levels. The FC, upon receiving a bit from a sensor, updates its approximation to the corresponding global random process, and accordingly its estimate. The sequential estimation process terminates when the observed Fisher information (or the approximation to it) reaches a target value. We provide an asymptotic analysis for the proposed estimator and also the one based on conventional uniform-in-time sampling under both non-fading and fading channels; and determine the conditions under which they are asymptotically optimal, consistent, and asymptotically unbiased. Analytical results, together with simulation results, demonstrate the superiority of the proposed estimator based on level-triggered sampling over the traditional decentralized estimator based on uniform sampling.
We consider the problem of simultaneous detection and estimation under a sequential framework. In particular we are interested in sequential tests that distinguish between the null and the alternative hypothesis and every time the decision is in favor of the alternative they provide an estimate of a random parameter. As we demonstrate with our analysis treating the two subproblems separately with the corresponding optimal strategies does not result in the best possible performance. To enjoy optimality one needs to take into account the optimum estimator during the hypothesis testing phase.
In this paper, we study the effect of feedback on two-user MIMO interference channels. The capacity region of MIMO interference channels with feedback is characterized within a constant number of bits, where this constant is independent of the channel matrices. Further, it is shown that the capacity region of a MIMO interference channel with feedback and its reciprocal interference channel are within a constant number of bits. Finally, the generalized degrees of freedom region for the MIMO interference channel with feedback is characterized.
We prove that the isoperimetric constant is positive for all symmetric spaces of noncompact type and compute it explicitly.
This paper gives the approximate capacity region of a two-user MIMO interference channel with limited receiver cooperation, where the gap between the inner and outer bounds is in terms of the total number of receive antennas at the two receivers and is independent of the actual channel values. The approximate capacity region is then used to find the degrees of freedom region. For the special case of symmetric interference channels, we also find the amount of receiver cooperation in terms of the backhaul capacity beyond which the degrees of freedom do not improve. Further, the generalized degrees of freedom are found for MIMO interference channels with equal number of antennas at all nodes. It is shown that the generalized degrees of freedom improve gradually from a "W" curve to a "V" curve with increase in cooperation in terms of the backhaul capacity.