This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and state process
es are present in the cost functional. Based on a Hilbert space method, necessary and sufficient conditions are derived for the solvability of the problem, and a general approach for constructing optimal controls is developed. The crucial step in this construction is to establish the solvability of a Riccati-type equation, which is accomplished under a fairly weak condition by investigating the connection with forward stochastic LQ optimal control problems.
The magnon-magnon coupling in synthetic antiferromagnets advances it as hybrid magnonic systems to explore the quantum information technologies. To induce the magnon-magnon coupling, the parity symmetry between two magnetization needs to be broken. H
ere we experimentally demonstrate a convenient method to break the parity symmetry by the asymmetric thickness of two magnetic layers and thus introduce a magnon-magnon coupling in Ir-based synthetic antiferromagnets CoFeB(10 nm)/Ir(tIr=0.6 nm, 1.2 nm)/CoFeB(13 nm). Remarkably, we find that the weakly uniaxial anisotropy field (~ 20 Oe) makes the magnon-magnon coupling anisotropic. The coupling strength presented by a characteristic anticrossing gap varies in the range between 0.54 GHz and 0.90 GHz for tIr =0.6 nm, and between nearly zero to 1.4 GHz for tIr = 1.2 nm, respectively. Our results demonstrate a feasible way to induce the magnon-magnon coupling by an asymmetric structure and tune the coupling strength by varying the direction of in-plane magnetic field. The magnon-magnon coupling in this highly tunable material system could open exciting perspectives for exploring quantum-mechanical coupling phenomena.
Millimeter-wave (mmWave) communication systems rely on large-scale antenna arrays to combat large path-loss at mmWave band. Due to hardware characteristics and deployment environments, mmWave large-scale antenna systems are vulnerable to antenna elem
ent blockages and failures, which necessitate diagnostic techniques to locate faulty antenna elements for calibration purposes. Current diagnostic techniques require full or partial knowledge of channel state information (CSI), which can be challenging to acquire in the presence of antenna failures. In this letter, we propose a blind diagnostic technique to identify faulty antenna elements in mmWave large-scale antenna systems, which does not require any CSI knowledge. By jointly exploiting the sparsity of mmWave channel and failure pattern, we first formulate the diagnosis problem as a joint sparse recovery problem. Then, the atomic norm is introduced to induce the sparsity of mmWave channel over continuous Fourier dictionary. An efficient algorithm based on alternating direction method of multipliers (ADMM) is proposed to solve the formulated problem. Finally, the performance of the proposed technique is evaluated through numerical simulations.
Intelligent reflecting surface (IRS) is a promising technology for enhancing wireless communication systems. It adaptively configures massive passive reflecting elements to control wireless channel in a desirable way. Due to hardware characteristics
and deploying environments, an IRS may be subject to reflecting element blockages and failures, and hence developing diagnostic techniques is of great significance to system monitoring and maintenance. In this paper, we develop diagnostic techniques for IRS systems to locate faulty reflecting elements and retrieve failure parameters. Three cases of channel state information (CSI) availability are considered. In the first case where full CSI is available, a compressed sensing based diagnostic technique is proposed, which significantly reduces the required number of measurements. In the second case where only partial CSI is available, we jointly exploit the sparsity of the millimeter-wave channel and the failure, and adopt compressed sparse and low-rank matrix recovery algorithm to decouple channel and failure. In the third case where no CSI is available, a novel atomic norm is introduced as the sparsity-inducing norm of the cascaded channel, and the diagnosis problem is formulated as a joint sparse recovery problem. Finally, the proposed diagnostic techniques are validated through numerical simulations.
While deep learning demonstrates its strong ability to handle independent and identically distributed (IID) data, it often suffers from out-of-distribution (OoD) generalization, where the test data come from another distribution (w.r.t. the training
one). Designing a general OoD generalization framework to a wide range of applications is challenging, mainly due to possible correlation shift and diversity shift in the real world. Most of the previous approaches can only solve one specific distribution shift, such as shift across domains or the extrapolation of correlation. To address that, we propose DecAug, a novel decomposed feature representation and semantic augmentation approach for OoD generalization. DecAug disentangles the category-related and context-related features. Category-related features contain causal information of the target object, while context-related features describe the attributes, styles, backgrounds, or scenes, causing distribution shifts between training and test data. The decomposition is achieved by orthogonalizing the two gradients (w.r.t. intermediate features) of losses for predicting category and context labels. Furthermore, we perform gradient-based augmentation on context-related features to improve the robustness of the learned representations. Experimental results show that DecAug outperforms other state-of-the-art methods on various OoD datasets, which is among the very few methods that can deal with different types of OoD generalization challenges.
In the era of big data, variable selection is a key technology for handling high-dimensional problems with a small sample size but a large number of covariables. Different variable selection methods were proposed for different models, such as linear
model, logistic model and generalized linear model. However, fewer works focused on variable selection for single index models, especially, for single index logistic model, due to the difficulty arose from the unknown link function and the slow mixing rate of MCMC algorithm for traditional logistic model. In this paper, we proposed a Bayesian variable selection procedure for single index logistic model by taking the advantage of Gaussian process and data augmentation. Numerical results from simulations and real data analysis show the advantage of our method over the state of arts.
We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources. The exact
solution to the problem by dynamic programming is computationally intractable due to the well-known curse of dimensionality. Existing works in the literature make use of the solution to the deterministic linear program (DLP) to design asymptotically optimal algorithms. Those algorithms rely on repeatedly solving DLPs to achieve near-optimal regret bounds. It is, however, time-consuming to repeatedly compute the DLP solutions in real time, especially in large-scale problems that may involve hundreds of millions of demand units. In this paper, we propose innovative algorithms for the NRM problem that are easy to implement and do not require solving any DLPs. Our algorithm achieves a regret bound of $O(log k)$, where $k$ is the system size. To the best of our knowledge, this is the first NRM algorithm that (i) has an $o(sqrt{k})$ asymptotic regret bound, and (ii) does not require solving any DLPs.
The paper studies the open-loop saddle point and the open-loop lower and upper values, as well as their relationship for two-person zero-sum stochastic linear-quadratic (LQ, for short) differential games with deterministic coefficients. It derives a
necessary condition for the finiteness of the open-loop lower and upper values and a sufficient condition for the existence of an open-loop saddle point. It turns out that under the sufficient condition, a strongly regular solution to the associated Riccati equation uniquely exists, in terms of which a closed-loop representation is further established for the open-loop saddle point. Examples are presented to show that the finiteness of the open-loop lower and upper values does not ensure the existence of an open-loop saddle point in general. But for the classical deterministic LQ game, these two issues are equivalent and both imply the solvability of the Riccati equation, for which an explicit representation of the solution is obtained.
We study in this paper a revenue management problem with add-on discounts. The problem is motivated by the practice in the video game industry, where a retailer offers discounts on selected supportive products (e.g. video games) to customers who have
also purchased the core products (e.g. video game consoles). We formulate this problem as an optimization problem to determine the prices of different products and the selection of products with add-on discounts. To overcome the computational challenge of this optimization problem, we propose an efficient FPTAS algorithm that can solve the problem approximately to any desired accuracy. Moreover, we consider the revenue management problem in the setting where the retailer has no prior knowledge of the demand functions of different products. To resolve this problem, we propose a UCB-based learning algorithm that uses the FPTAS optimization algorithm as a subroutine. We show that our learning algorithm can converge to the optimal algorithm that has access to the true demand functions, and we prove that the convergence rate is tight up to a certain logarithmic term. In addition, we conduct numerical experiments with the real-world transaction data we collect from a popular video gaming brands online store on Tmall.com. The experiment results illustrate our learning algorithms robust performance and fast convergence in various scenarios. We also compare our algorithm with the optimal policy that does not use any add-on discount, and the results show the advantages of using the add-on discount strategy in practice.
Using the symmetry of the near-horizon geometry and applying quantum field theory of a complex scalar field, we study the spontaneous pair production of charged scalars from near-extremal rotating, electrically and/or magnetically charged black holes
. Analytical expressions for pair production, vacuum persistence and absorption cross section are found, and the spectral distribution is given a thermal interpretation. The pair production in near-extremal black holes has a factorization into the Schwinger effect in AdS and Schwinger effect in Rindler space, measuring the deviational from extremality. The associated holographical correspondence is confirmed at the 2-point function level by comparing the absorption cross section ratio as well as the pair production rate both from the gravity and the conformal field theories. The production of monopoles is discussed.
