Sign problem free quantum Monte-Carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets

The microscopic mechanism of itinerant ferromagnetism is a long-standing problem due to the lack of non-perturbative methods to handle strong magnetic fluctuations of itinerant electrons. We have non-pertubatively studied thermodynamic properties and magnetic phase transitions of a two-dimensional multi-orbital Hubbard model exhibiting ferromagnetic ground states. Quantum Monte-Carlo simulations are employed, which are proved in a wide density region free of the sign problem usually suffered by simulations for fermions. Both Hund's coupling and electron itinerancy are essential for establishing the ferromagnetic coherence. No local magnetic moments exist in the system as a priori, nevertheless, the spin channel remains incoherent showing the Curie-Weiss type spin magnetic susceptibility down to very low temperatures at which the charge channel is already coherent exhibiting a weakly temperature-dependent compressibility. For the SU(2) invariant systems, the spin susceptibility further grows exponentially as approaching zero temperature in two dimensions. In the paramagnetic phase close to the Curie temperature, the momentum space Fermi distributions exhibit strong resemblance to those in the fully polarized state. The long-range ferromagnetic ordering appears when the symmetry is reduced to the Ising class, and the Curie temperature is accurately determined. These simulations provide helpful guidance to searching for novel ferromagnetic materials in both strongly correlated $d$-orbital transition metal oxide layers and the $p$-orbital ultra-cold atom optical lattice systems.Comment: 17 pages, 17 figure

A Tensor Analogy of Yuan's Theorem of the Alternative and Polynomial Optimization with Sign structure

Yuan's theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving two homogeneous quadratic functions. In this paper, we provide a tractable extension of Yuan's theorem of the alternative to the symmetric tensor setting. As an application, we establish that the optimal value of a class of nonconvex polynomial optimization problems with suitable sign structure (or more explicitly, with essentially non-positive coefficients) can be computed by a related convex conic programming problem, and the optimal solution of these nonconvex polynomial optimization problems can be recovered from the corresponding solution of the convex conic programming problem. Moreover, we obtain that this class of nonconvex polynomial optimization problems enjoy exact sum-of-squares relaxation, and so, can be solved via a single semidefinite programming problem.Comment: acceted by Journal of Optimization Theory and its application, UNSW preprint, 22 page

FedGiA: An Efficient Hybrid Algorithm for Federated Learning

Federated learning has shown its advances recently but is still facing many challenges, such as how algorithms save communication resources and reduce computational costs, and whether they converge. To address these critical issues, we propose a hybrid federated learning algorithm (FedGiA) that combines the gradient descent and the inexact alternating direction method of multipliers. The proposed algorithm is more communication- and computation-efficient than several state-of-the-art algorithms theoretically and numerically. Moreover, it also converges globally under mild conditions.Comment: arXiv admin note: substantial text overlap with arXiv:2110.15318; text overlap with arXiv:2204.1060

New Environment Adaptation with Few Shots for OFDM Receiver and mmWave Beamforming

Few-shot learning (FSL) enables adaptation to new tasks with only limited training data. In wireless communications, channel environments can vary drastically; therefore, FSL techniques can quickly adjust transceiver accordingly. In this paper, we develop two FSL frameworks that fit in wireless transceiver design. Both frameworks are base on optimization programs that can be solved by well-known algorithms like the inexact alternating direction method of multipliers (iADMM) and the inexact alternating direction method (iADM). As examples, we demonstrate how the proposed two FSL frameworks are used for the OFDM receiver and beamforming (BF) for the millimeter wave (mmWave) system. The numerical experiments confirm their desirable performance in both applications compared to other popular approaches, such as transfer learning (TL) and model-agnostic meta-learning

Communication-Efficient Decentralized Federated Learning via One-Bit Compressive Sensing

Decentralized federated learning (DFL) has gained popularity due to its practicality across various applications. Compared to the centralized version, training a shared model among a large number of nodes in DFL is more challenging, as there is no central server to coordinate the training process. Especially when distributed nodes suffer from limitations in communication or computational resources, DFL will experience extremely inefficient and unstable training. Motivated by these challenges, in this paper, we develop a novel algorithm based on the framework of the inexact alternating direction method (iADM). On one hand, our goal is to train a shared model with a sparsity constraint. This constraint enables us to leverage one-bit compressive sensing (1BCS), allowing transmission of one-bit information among neighbour nodes. On the other hand, communication between neighbour nodes occurs only at certain steps, reducing the number of communication rounds. Therefore, the algorithm exhibits notable communication efficiency. Additionally, as each node selects only a subset of neighbours to participate in the training, the algorithm is robust against stragglers. Additionally, complex items are computed only once for several consecutive steps and subproblems are solved inexactly using closed-form solutions, resulting in high computational efficiency. Finally, numerical experiments showcase the algorithm's effectiveness in both communication and computation

0/1 Deep Neural Networks via Block Coordinate Descent

The step function is one of the simplest and most natural activation functions for deep neural networks (DNNs). As it counts 1 for positive variables and 0 for others, its intrinsic characteristics (e.g., discontinuity and no viable information of subgradients) impede its development for several decades. Even if there is an impressive body of work on designing DNNs with continuous activation functions that can be deemed as surrogates of the step function, it is still in the possession of some advantageous properties, such as complete robustness to outliers and being capable of attaining the best learning-theoretic guarantee of predictive accuracy. Hence, in this paper, we aim to train DNNs with the step function used as an activation function (dubbed as 0/1 DNNs). We first reformulate 0/1 DNNs as an unconstrained optimization problem and then solve it by a block coordinate descend (BCD) method. Moreover, we acquire closed-form solutions for sub-problems of BCD as well as its convergence properties. Furthermore, we also integrate $\ell_{2,0}$-regularization into 0/1 DNN to accelerate the training process and compress the network scale. As a result, the proposed algorithm has a high performance on classifying MNIST and Fashion-MNIST datasets. As a result, the proposed algorithm has a desirable performance on classifying MNIST, FashionMNIST, Cifar10, and Cifar100 datasets

Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations

Chemical synthesis and characterization of zinc borohydride

AbstractMetal borohydrides have received increasing research interests on account of their high hydrogen storage capacities. In this paper, zinc borohydride Zn(BH4)2 was synthesized using NaBH4 and ZnCl2 in THF under room temperature for 72h, and the crystallographic constitution of the synthesized products were analyzed by XRD. The results showed that the major phase of the products was NaCl, alternatively, NaBH4 or ZnCl2 disappeared. This concluded the formation of Zn(BH4)2. Moreover, both experiment phenomena and fired products further confirmed the synthesis of Zn(BH4)2, which a XRD pattern of Zinc borohydride was obtained