State Key Laboratory of Scientific and Engineering Computing

In a cellular wireless system, users located at cell edges often suffer significant out-of-cell interference. Assuming each base station is equipped with multiple antennas, we can model this scenario as a multiple-input single-output (MISO) interference channel. In this paper we consider a coordinated beamforming approach whereby multiple base stations jointly optimize their downlink beamforming vectors in order to simultaneously improve the data rates of a given group of cell edge users. Assuming perfect channel knowledge, we formulate this problem as the maximization of a system utility (which balances user fairness and average user rates), subject to individual power constraints at each base station. We show that, for the single-carrier case and when the number of antennas at each base station is at least two, the optimal coordinated beamforming problem is NP-hard for both the harmonic mean utility and the proportional fairness utility. For general utilities, we propose a cyclic coordinate descent algorithm, which enables each transmitter to update its beamformer locally with limited information exchange and establish its global convergence to a stationary point. We illustrate its effectiveness in computer simulations by using the space matched beamformer as the benchmark.

Abstract Conjugate gradient methods are a class of important methods for solving linear equations and for solving nonlinear optimization. In this article, a review on conjugate gradient methods for unconstrained optimization is given. They are divided into early conjugate gradient methods, descent conjugate gradient methods, and sufficient descent conjugate gradient methods. Two general convergence theorems are provided for the conjugate gradient method assuming the descent property of each search direction. Some research issues on conjugate gradient methods are mentioned.

This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the convergence of the FR method. Several examples are constructed to show that, if the search conditions are relaxed, the FR method may produce an ascent search direction, which implies that our result cannot be improved.

An elastic model for double-stranded polymers is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural parameter (the folding angle $\ensuremath{\phi}$), bending deformations of sugar-phosphate backbones, steric effects of nucleotide base pairs, and base-stacking interactions are considered. The comprehensive agreements between theory and experiments both on torsionally relaxed DNA and on negatively supercoiled DNA strongly indicate that base-stacking interactions, although short-ranged in nature, dominate the elasticity of DNA and, hence, are of vital biological significance.

This paper aims at a comprehensive understanding of the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for double-stranded biopolymers is proposed, and a structural parameter called the folding angle straight phi is introduced to characterize their deformations. The mechanical property of long dsDNA molecules is then studied based on this model, where the base-stacking interactions between DNA adjacent nucleotide base pairs, the steric effects of base pairs, and the electrostatic interactions along DNA backbones are taken into account. Quantitative results are obtained by using a path integral method, and excellent agreement between theory and the observations reported by five major experimental groups are attained. The strong intensity of the base stacking interactions ensures the structural stability of DNA, while the short-ranged nature of such interactions makes externally stimulated large structural fluctuations possible. The entropic elasticity, highly extensibility, and supercoiling property of DNA are all closely related to this account. The present work also suggests the possibility that negative torque can induce structural transitions in highly extended DNA from the right-handed B form to left-handed configurations similar to the Z-form configuration. Some formulas concerned with the application of path integral methods to polymeric systems are listed in the Appendixes.

In this paper, we investigate the design of energy-efficient beamforming for an ISAC system, where the transmitted waveform is optimized for joint multi-user communication and target estimation simultaneously. We aim to maximize the system energy efficiency (EE), taking into account the constraints of a maximum transmit power budget, a minimum required signal-to-interference-plus-noise ratio (SINR) for communication, and a maximum tolerable Cramér-Rao bound (CRB) for target estimation. We first consider communication-centric EE maximization. To handle the non-convex fractional objective function, we propose an iterative quadratic-transform-Dinkelbach method, where Schur complement and semi-definite relaxation (SDR) techniques are leveraged to solve the subproblem in each iteration. For the scenarios where sensing is critical, we propose a novel performance metric for characterizing the sensing-centric EE and optimize the metric adopted in the scenario of sensing a point-like target and an extended target. To handle the nonconvexity, we employ the successive convex approximation (SCA) technique to develop an efficient algorithm for approximating the nonconvex problem as a sequence of convex ones. Furthermore, we adopt a Pareto optimization mechanism to articulate the tradeoff between the communication-centric EE and sensing-centric EE. We formulate the search of the Pareto boundary as a constrained optimization problem and propose a computationally efficient algorithm to handle it. Numerical results validate the effectiveness of our proposed algorithms compared with the baseline schemes and the obtained approximate Pareto boundary shows that there is a non-trivial tradeoff between communication-centric EE and sensing-centric EE, where the number of communication users and EE requirements have serious effects on the achievable tradeoff.

We report on our code, in which the moving puncture method is applied and an adaptive/fixed mesh refinement is implemented, and on its preliminary performance on black hole simulations. Based on the Baumgarte-Sharpiro-Shibata-Nakamura (BSSN) formulation, up-to-date gauge conditions and the modifications of the formulation are also implemented and tested. In this work, we present our primary results about the simulation of a single static black hole, of a moving single black hole, and of the head-on collision of a binary black hole system. For the static punctured black hole simulations, different modifications of the BSSN formulation are applied. It is demonstrated that both the currently used sets of modifications lead to a stable evolution. For cases of a moving punctured black hole with or without spin, we search for viable gauge conditions and study the effect of spin on the black hole evolution. Our results confirm previous results obtained by other research groups. In addition, we find a new gauge condition, which has not yet been adopted by any other researchers, which can also give stable and accurate black hole evolution calculations. We examine the performance of the code for the head-on collision of a binary black hole system, and the agreement of the gravitational waveform it produces with that obtained in other works. In order to understand qualitatively the influence of matter on the binary black hole collisions, we also investigate the same head-on collision scenarios but perturbed by a scalar field. The numerical simulations performed with this code not only give stable and accurate results that are consistent with the works by other numerical relativity groups, but also lead to the discovery of a new viable gauge condition, as well as clarify some ambiguities in the modification of the BSSN formulation. These results demonstrate that this code is reliable and ready to be used in the study of more realistic astrophysical scenarios and of numerical relativity.

Image scene classification aiming to assign specific semantic labels for each image is vital important for the applications of remote sensing (RS) data. In real world, since the observation environment is open and dynamic, RS images are collected sequentially and the numbers of images and classes grow rapidly over time. Most existing scene classification methods are offline learning algorithms which are inefficient and unscalable for this scenario. In this paper, an incremental learning with open set recognition framework is proposed for RS image scene classification in the open and dynamic environment, called ILOSR, which can identify the unknown classes from a stream of data and learn these new classes incrementally. Specifically, a controllable convex hull-based exemplar selection strategy is designed to address the catastrophic forgetting issue in incremental learning, which can reduce training time and memory footprint effectively. In addition, a new loss function based on prototype learning and uncertainty measurement is proposed for open set recognition to enhance the inter-class discrimination and intra-class compactness of the learned deep features. Experimental results on real remote sensing datasets demonstrate that the proposed method can not only outperform the state-of-the-art approaches on offline classification, incremental learning and OSR problem separately, but also achieve better and more stable performance in the experiments for incremental learning with OSR.

Consider the max-min fairness linear transceiver design for a multi-user MIMO interference channel. Assuming perfect channel knowledge, this problem can be formulated as the maximization of minimum SINR utility, subject to individual power constraints at each transmitter. In this paper, it is shown that when the number of antennas at each transmitter (receiver) is at least two and at each receiver (transmitter) is at least three, the problem of checking whether the given target SINR is feasible is strongly NP-hard. A cyclic coordinate ascent algorithm is also proposed for this design problem. Monotonicity and global convergence to KKT solution of the proposed algorithm are proved.

In the manuscript, we present several numerical schemes to approximate the coupled nonlinear Schrödinger equations. Three of them are high‐order compact and conservative, and the other two are noncompact but conservative. After some numerical analysis, we can find that the schemes are uniquely solvable and convergent. All of them are conservative and stable. By calculating the complexity, we can find that the compact schemes have the same computational cost with the noncompact ones. Numerical illustrations support our analysis. They verify that compact schemes are more efficient than noncompact ones from computation cost and accuracy. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1814–1843, 2015

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. This paper proposes a three-parameter family of hybrid conjugate gradient methods. Two important features of the family are that (i) it can avoid the propensity of small steps, namely, if a small step is generated away from the solution point, the next search direction will be close to the negative gradient direction; and (ii) its descent property and global convergence are likely to be achieved provided that the line search satisfies the Wolfe conditions. Some numerical results with the family are also presented.

In this paper, five 2+1 dimensional lattices considered by several authors are revisited again. First of all we will show that two lattices proposed by Blaszak and Szum [J. Math. Phys. 42, 225 (2001)] become the so-called differential-difference KP equation due to Date, Jimbo, and Miwa [J. Phys. Soc. Jpn. 51, 4116 (1982); 51, 4125 (1982); 52, 388 (1983); 52, 761 (1983); 52, 766 (1983)] by simple variable transformations, while another lattice found by Blaszak and Szum can be viewed as a higher-dimensional generalization of a lattice given by Wu and Hu [J. Phys. A 32, 1515 (1999)]. Some integrable properties on these three lattices are derived. Second, it is shown that a 2+1 dimensional Toda-like lattice studied by Cao, Geng, and Wu [J. Phys. A 32, 8059 (1999)] can be transformed into the bilinear equation given by Hu, Clarkson, and Bullough [J. Phys. A 30, L669 (1997)]. For this bilinear version we also present some rational solutions and Lie symmetries. Finally, a lattice due to Levi, Ragnisco, and Shabat [Can. J. Phys. 72, 439 (1994)] is transformed into coupled bilinear equations. It is shown that these coupled bilinear equations do not have two-soliton solutions. This further confirms that the lattice under consideration is not completely integrable.

In this paper, we consider the joint multicast and unicast beamforming design problem in the multi-input single-output downlink wireless network, where all base stations (BSs) potentially can cooperate (as a single virtual BS) to transmit a common multicast and multiple dedicated unicast data streams at the same time on the same frequency band. To reduce cooperation overhead (among different BSs), we prefer partial cooperation transmission such that each user's data stream (either multicast or unicast) is served by only a small subset of BSs. We formulate the problem from a (group) sparse optimization perspective and propose a branch-and-bound (BB) algorithm for solving the problem. Our proposed BB algorithm is guaranteed to find the globally optimal solution of the problem. We also propose an efficient successive linear approximation (SLA) algorithm for solving the problem. Numerical results show that the SLA algorithm can perform very close to the BB algorithm but with significantly less computational complexity. It is also shown that the proposed mixed ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> /ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> regularizer in the sparse formulation provides a flexible and effective tradeoff between the total transmission power cost and the cooperation cost.

The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2+1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal's direct method but also a great diversity of classical and nonclassical conditional similarity reductions.

Satellites are currently being used to track the positions of trains. Positioning systems using satellites can help reduce the cost of installing and maintaining trackside equipment. This paper develops a nonlinear combinatorial data reduction model for a large amount of railway Global Positioning System (GPS) data to decrease the memory space and, thus, speed up train positioning. Three algorithms are proposed by employing the concept of looking ahead, using the dichotomy idea, or adopting the breadth-first strategy after changing the problem into a shortest path problem to obtain an optimal solution. Two techniques are developed to substantially cut down the computing time for the optimal algorithm. The surveyed GPS data of the Qinghai–Tibet railway (QTR) are used to compare the performance of the algorithms. Results show that the algorithms can extract a few data points from the large amount of GPS data points, thus enabling a simpler representation of the train tracks. Furthermore, these proposed algorithms show a tradeoff between the solution quality and computation time of the algorithms.

This letter proposes a novel multiview feature extraction method for supervised polarimetric synthetic aperture radar (PolSAR) image classification. PolSAR images can be characterized by multiview feature sets, such as polarimetric features and textural features. Canonical correlation analysis (CCA) is a well-known dimensionality reduction (DR) method to extract valuable information from multiview feature sets. However, it cannot exploit the discriminative information, which influences its performance of classification. Local discriminant embedding (LDE) is a supervised DR method, which can preserve the discriminative information and the local structure of the data well. However, it is a single-view learning method, which does not consider the relation between multiple view feature sets. Therefore, we propose local discriminant CCA by incorporating the idea of LDE into CCA. Specific to PolSAR images, a symmetric version of revised Wishart distance is used to construct the between-class and within-class neighboring graphs. Then, by maximizing the correlation of neighboring samples from the same class and minimizing the correlation of neighboring samples from different classes, we find two projection matrices to achieve feature extraction. Experimental results on the real PolSAR data sets demonstrate the effectiveness of the proposed method.

In this paper the work on implementing two mesh partitioning algorithms, the refinement-tree based partitioning algorithm and the space-filling curve partitioning algorithm, in the parallel adaptive finite element toolbox PHG (parallel hierarchical grid) is presented. These algorithms are used for both initial mesh partitioning and mesh repartitioning for dynamical load balancing in adaptive finite element computations. In the implementations improved algorithms are designed. Partitioning time and quality of our code are compared with existing publicly available mesh or graph partitioners, including ParMETIS and Zoltan, through some numerical examples.

In this paper, we consider the one-bit precoding problem for the multiuser downlink massive multiple-input multiple-output (MIMO) system with phase shift keying (PSK) modulation. We focus on the celebrated constructive interference (CI)-based problem formulation. We first establish the NP-hardness of the problem (even in the single-user case), which reveals the intrinsic difficulty of globally solving the problem. Then, we propose a novel negative ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> penalty model for the considered problem, which penalizes the one-bit constraint into the objective by a negative ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm term, and show the equivalence between (global and local) solutions of the original problem and the penalty problem when the penalty parameter is sufficiently large. We further transform the penalty model into an equivalent min-max problem and propose an efficient alternating proximal/projection gradient descent ascent (APGDA) algorithm for solving it, which performs a proximal gradient decent over one block of variables and a projection gradient ascent over the other block of variables alternately. The APGDA algorithm enjoys a low per-iteration complexity and is guaranteed to converge to a stationary point of the min-max problem and a local minimizer of the penalty problem. To further reduce the computational cost, we also propose a low-complexity implementation of the APGDA algorithm, where the values of the variables will be fixed in later iterations once they satisfy the one-bit constraint. Numerical results show that, compared to the state-of-the-art CI-based algorithms, both of the proposed algorithms generally achieve better bit-error-rate (BER) performance with lower computational cost.

In this paper, we propose a family of symplectic structure-preserving numerical methods for the coupled Klein–Gordon–Schrodinger (KGS) system. The Hamiltonian formulation is constructed for the KGS. We discretize the Hamiltonian system in space first with a family of canonical difference methods which convert an infinite-dimensional Hamiltonian system into a finite-dimensional one. Next, we discretize the finite-dimensional system in time by a midpoint rule which preserves the symplectic structure of the original system. The conservation laws of the schemes are analyzed in succession, including the charge conservation law and the residual of energy conservation law, etc. We analyze the truncation errors and global errors of the numerical solutions for the schemes to end the theoretical analysis. Extensive numerical tests show the accordance between the theoretical and numerical results.

By introducing a 4 ×4 matrix spectral problem with three potentials, A hierarchy of nonlinear evolution equations are derived. An interesting equation in the hierarchy is a coupled KdV equation. It is shown that the hierarchy possesses the generalized bi-Hamiltonian structures with the aid of the trace identity. Through the nonlinearization of eigenvalue problems, a new infinite-dimensional Hamiltonian system is presented, which is completely integrable in Liouville sense.