Distributed Optimization of Clique-Wise Coupled Problems via Three-Operator Splitting

In this study, we explore distributed optimization problems with clique-wise coupling through the lens of operator splitting. This framework of clique-wise coupling extends beyond conventional pairwise coupled problems, encompassing consensus optimization and formation control, and is applicable to a wide array of examples. We first introduce a matrix, called the clique-wise duplication (CD) matrix, which enables decoupled reformulations for operator splitting methods and distributed computation. Leveraging this matrix, we propose a new distributed optimization algorithm via Davis-Yin splitting (DYS), a versatile three-operator splitting method. We then delve into the properties of this method and demonstrate how existing consensus optimization methods (NIDS, Exact Diffusion, and Diffusion) can be derived from our proposed method. Furthermore, being inspired by this observation, we derive a Diffusion-like method, the clique-based projected gradient descent (CPGD), and present Nesterov's acceleration and in-depth convergence analysis for various step sizes. The paper concludes with numerical examples that underscore the efficacy of our proposed method.Comment: 16page

Distributed Optimization of Clique-wise Coupled Problems

This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled optimization problems (e.g., consensus optimization) and allows us to handle coupling of variables consisting of more than two agents systematically. To solve this problem, we propose a clique-based linearized ADMM algorithm, which is proved to be distributed. Additionally, we consider objective functions given as a sum of nonsmooth and smooth convex functions and present a more flexible algorithm based on the FLiP-ADMM algorithm. Moreover, we provide convergence theorems of these algorithms. Notably, all the algorithmic parameters and the derived condition in the theorems depend only on local information, which means that each agent can choose the parameters in a distributed manner. Finally, we apply the proposed methods to a consensus optimization problem and demonstrate their effectiveness via numerical experiments

Gradient-Based Distributed Controller Design Over Directed Networks

In this study, we propose a design methodology of distributed controllers for multi-agent systems on a class of directed interaction networks by extending the gradient-flow method. Although the gradient-flow method is a common design tool for distributed controllers, it is inapplicable to directed networks. First, we demonstrate how to construct a distributed controller for systems over a class of time-invariant directed graphs. Subsequently, we achieve better convergence properties and performance enhancement than the conventional gradient-flow method. To illustrate its application in time-varying networks, we address the dynamic matching problem of two distinct groups of agents with different sensing ranges. This problem is a novel coordination task that involves pairing agents from two distinct groups to achieve a convergence of the paired agents' states to the same value. Accordingly, we apply the proposed method to this problem and provide sufficient conditions for successful matching. Lastly, numerical examples for systems on both time-invariant and time-varying networks demonstrate the effectiveness of the proposed method

Sign change in c-axis thermal expansion and lattice collapse by Ni substitution in Co1-xNixZr2 superconductors

We investigated the structural, electronic, and superconducting properties of Co1-xNixZr2, in which c-axis thermal expansion is systematically controlled. At x (smaller than) 0.3, c-axis negative thermal expansion (NTE) was observed, and the thermal expansion constant {\alpha}c approached zero with increasing x. At x = 0.4-0.6, zero thermal expansion was observed, and positive thermal expansion (PTE) appeared for x (greater than) 0.7. By analyzing the c/a ratio, we observed a possible collapsed transition in the tetragonal lattice at around x = 0.6-0.8. The lattice collapse results in c-axis PTE and the suppression of bulk superconductivity.Comment: 16 pages, 5 figures, 1 table, Supporting material

Alteration Reaction and Mass Transfer via Fluids with Progress of Fracturing along the Median Tectonic Line, Mie Prefecture, Southwest Japan

We have analyzed mass transfer in the cataclasite samples collected from the Median Tectonic Line, southwest Japan, in which the degree of fracturing is well correlated with the bulk rock chemical compositions determined by the X-ray fluorescence (XRF) analysis. The results of “isocon” analysis indicate not only a large volume increase up to 110% but also the two-stage mass transfer during cataclasis. At the first stage from the very weakly to weakly fractured rocks, the weight percents of SiO2, Na2O, and K2O increase, while those of TiO2, FeO, MnO, MgO, and CaO decrease. At the second stage from the weakly to moderately and strongly fractured rocks, the trend of mass transfer is reversed. The principal component analysis reveals that the variation of chemical compositions in the cataclasite samples can be mostly interpreted by the mass transfer via fluids and by the difference in chemical composition in the protolith rocks to lesser degree. Finally, the changes in the modal composition of minerals with increasing cataclasis analyzed by the X-ray diffraction (XRD) with the aid of “RockJock” software clearly elucidate that the mass transfer of chemical elements was caused by dissolution and precipitation of minerals via fluids in the cataclasite samples

knn-seq: Efficient, Extensible kNN-MT Framework

k-nearest-neighbor machine translation (kNN-MT) boosts the translation quality of a pre-trained neural machine translation (NMT) model by utilizing translation examples during decoding. Translation examples are stored in a vector database, called a datastore, which contains one entry for each target token from the parallel data it is made from. Due to its size, it is computationally expensive both to construct and to retrieve examples from the datastore. In this paper, we present an efficient and extensible kNN-MT framework, knn-seq, for researchers and developers that is carefully designed to run efficiently, even with a billion-scale large datastore. knn-seq is developed as a plug-in on fairseq and easy to switch models and kNN indexes. Experimental results show that our implemented kNN-MT achieves a comparable gain to the original kNN-MT, and the billion-scale datastore construction took 2.21 hours in the WMT'19 German-to-English translation task. We publish our knn-seq as an MIT-licensed open-source project and the code is available on https://github.com/naist-nlp/knn-seq . The demo video is available on https://youtu.be/zTDzEOq80m0