An efficient method for calculating resonant modes in biperiodic photonic structures

Many photonic devices, such as photonic crystal slabs, cross gratings, and periodic metasurfaces, are biperiodic structures with two independent periodic directions, and are sandwiched between two homogeneous media. Many applications of these devices are closely related to resonance phenomena. Therefore, efficient computation of resonant modes is crucial in device design and structure analysis. Since resonant modes satisfy outgoing radiation conditions, perfectly matched layers (PMLs) are usually used to truncate the unbounded spatial variable perpendicular to the periodic directions. In this paper, we develop an efficient method without using PMLs to calculate resonant modes in biperiodic structures. We reduce the original eigenvalue problem to a small matrix nonlinear eigenvalue problem which is solved by the contour integral method. Numerical examples show that our method is efficient with respect to memory usage and CPU time, free of spurious solutions, and determines degenerate resonant modes without any difficulty

Compressing MIMO Channel Submatrices with Tucker Decomposition: Enabling Efficient Storage and Reducing SINR Computation Overhead

Massive multiple-input multiple-output (MIMO) systems employ a large number of antennas to achieve gains in capacity, spectral efficiency, and energy efficiency. However, the large antenna array also incurs substantial storage and computational costs. This paper proposes a novel data compression framework for massive MIMO channel matrices based on tensor Tucker decomposition. To address the substantial storage and computational burdens of massive MIMO systems, we formulate the high-dimensional channel matrices as tensors and propose a novel groupwise Tucker decomposition model. This model efficiently compresses the tensorial channel representations while reducing SINR estimation overhead. We develop an alternating update algorithm and HOSVD-based initialization to compute the core tensors and factor matrices. Extensive simulations demonstrate significant channel storage savings with minimal SINR approximation errors. By exploiting tensor techniques, our approach balances channel compression against SINR computation complexity, providing an efficient means to simultaneously address the storage and computational challenges of massive MIMO

The LqL_q-weighted dual programming of the linear Chebyshev approximation and an interior-point method

Given samples of a real or complex-valued function on a set of distinct nodes, the traditional linear Chebyshev approximation is to compute the best minimax approximation on a prescribed linear functional space. Lawson's iteration is a classical and well-known method for that task. However, Lawson's iteration converges linearly and in many cases, the convergence is very slow. In this paper, by the duality theory of linear programming, we first provide an elementary and self-contained proof for the well-known Alternation Theorem in the real case. Also, relying upon the Lagrange duality, we further establish an $L_q$-weighted dual programming for the linear Chebyshev approximation. In this framework, we revisit the convergence of Lawson's iteration, and moreover, propose a Newton type iteration, the interior-point method, to solve the $L_2$-weighted dual programming. Numerical experiments are reported to demonstrate its fast convergence and its capability in finding the reference points that characterize the unique minimax approximation.Comment: 29 pages, 8 figure

Lifshitz Scaling Effects on Holographic Superconductors

Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent $z$ on holographic superconductors are studied in some detail, including $s$ wave and $p$ wave models. Working in the probe limit, we find that the behaviors of holographic models indeed depend on concrete value of $z$. We obtain the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with general $z$. For both $s$ wave and $p$ wave models in the black hole backgrounds, as $z$ increases, the phase transition becomes more difficult and the growth of conductivity is suppressed. For the Lifshitz soliton backgrounds, when $z$ increases ($z=1,~2,~3$), the critical chemical potential decreases in the $s$ wave cases but increases in the $p$ wave cases. For $p$ wave models in both Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when $z$ increases. The analytical results uphold the numerical results.Comment: Typos corrected; Footnote added; References added; To be published in Nuclear Physics

Federated Primal Dual Fixed Point Algorithm

Federated learning (FL) is a distributed learning paradigm that allows several clients to learn a global model without sharing their private data. In this paper, we generalize a primal dual fixed point (PDFP) \cite{PDFP} method to federated learning setting and propose an algorithm called Federated PDFP (FPDFP) for solving composite optimization problems. In addition, a quantization scheme is applied to reduce the communication overhead during the learning process. An $O(\frac{1}{k})$ convergence rate (where $k$ is the communication round) of the proposed FPDFP is provided. Numerical experiments, including graph-guided logistic regression, 3D Computed Tomography (CT) reconstruction are considered to evaluate the proposed algorithm.Comment: 29 pages and 8 figure

Lifshitz effects on holographic pp-wave superfluid

In the probe limit, we numerically build a holographic $p$-wave superfluid model in the four-dimensional Lifshitz black hole coupled to a Maxwell-complex vector field. We observe the rich phase structure and find that the Lifshitz dynamical exponent $z$ contributes evidently to the effective mass of the matter field and dimension of the gravitational background. Concretely, we obtain the Cave of Winds appeared only in the five-dimensional anti-de Sitter~(AdS) spacetime, and the increasing $z$ hinders not only the condensate but also the appearance of the first-order phase transition. Furthermore, our results agree with the Ginzburg-Landau results near the critical temperature. In addition, the previous AdS superfluid model is generalized to the Lifshitz spacetime.Comment: 14 pages,5 figures, and 1 table, accepted by Phys. Lett.