Sampling-Based Approaches for Multimarginal Optimal Transport Problems with Coulomb Cost

The multimarginal optimal transport problem with Coulomb cost arises in quantum physics and is vital in understanding strongly correlated quantum systems. Its intrinsic curse of dimensionality can be overcome with a Monge-like ansatz. A nonconvex quadratic programmming then emerges after employing discretization and $\ell_1$ penalty. To globally solve this nonconvex problem, we adopt a grid refinements-based framework, in which a local solver is heavily invoked and hence significantly determines the overall efficiency. The block structure of this nonconvex problem suggests taking block coordinate descent-type methods as the local solvers, while the existing ones can get seriously afflicted with the poor scalability induced by the associated sparse-dense matrix multiplications. In this work, borrowing the tools from optimal transport, we develop novel methods that favor highly scalable schemes for subproblems and are completely free of the full matrix multiplications after introducing entrywise sampling. Convergence and asymptotic properties are built on the theory of random matrices. The numerical results on several typical physical systems corroborate the effectiveness and better scalability of our approach, which also allows the first visualization for the approximate optimal transport maps between electrons in three-dimensional contexts.Comment: 31 pages, 6 figures, 3 table

A force-based gradient descent method for ab initio\mathit{\text{ab initio}} atomic structure relaxation

Force-based algorithms for $\mathit{\text{ab initio}}$ atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive $\mathit{\text{ab initio}}$ calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial stepsize capturing the local curvature of the energy surface. The exit is controlled by an unrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only two parameters are present without tuning.Comment: 8 pages, 9 figure

The Exactness of the ℓ1\ell_1 Penalty Function for a Class of Mathematical Programs with Generalized Complementarity Constraints

In a Mathematical Program with Generalized Complementarity Constraints (MPGCC), complementarity relationships are imposed between each pair of variable blocks. MPGCC includes the traditional Mathematical Program with Complementarity Constraints (MPCC) as a special case. On account of the disjunctive feasible region, MPCC and MPGCC are generally difficult to handle. The $\ell_1$ penalty method, often adopted in computation, opens a way of circumventing the difficulty. Yet it remains unclear about the exactness of the $\ell_1$ penalty function, namely, whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original one. In this paper, we consider a class of MPGCCs that are of multi-affine objective functions. This problem class finds applications in various fields, e.g., the multi-marginal optimal transport problems in many-body quantum physics and the pricing problem in network transportation. We first provide an instance from this class, the exactness of whose $\ell_1$ penalty function cannot be derived by existing tools. We then establish the exactness results under rather mild conditions. Our results cover those existing ones for MPCC and apply to multi-block contexts.Comment: 11 pages, 3 figure

How to Identify Future Priority Areas for Urban Development: An Approach of Urban Construction Land Suitability in Ecological Sensitive Areas

The suitability of urban construction land (SUCL) is key to the appropriate utilization of land resources and represents an important foundation for regional exploration and land management. This study explores the SUCL conceptual framework by considering the theory of human-land relationships. The upper reaches of the Yangtze River were studied, a typical ecologically-sensitive area of China. The spatial pattern and control of the SUCL were determined using the improved entropy method. The results show that an area of 91 × 104 km2 was categorized as prohibited or restricted, and these categories account for 28.61% and 50.66% of the total area, respectively. Priority areas and suitable areas are mainly located in the Chengdu Plain, the urban agglomeration of southern Sichuan Province, Chongqing, and the economic corridor in the west, and the surrounding cities of Guiyang and Kunming. SUCL hotspots feature obvious spatial heterogeneity and are concentrated in Sichuan Basin and Guizhou Plateau. The SUCL is obviously constrained by the physical geography of this region. In addition, towns affected by the pole–axis effect have stronger suitability for development and construction. These findings will be very useful for land managers as they provide relevant information about urban development in mountainous areas

Research on Ground Calibration Technology for Geomagnetism Sensors

The measurements of geomagnetism sensors are often affected by self-factors, install-factors and environment factors, therefore they often exist error and cause measurement accuracy reduction. Focus on these problems, this paper analyse existing ground calibration algorithms and their merits and demerits respectively. Besides, a comprehensive geomagnetism sensor error model is presented. Based on this model, a least square method based ellipsoid fitting calibration and compensation algorithm is presented. The experiment results show that this novel calibration algorithm can effectively restrain and compensate geomagnetism signal measurement error

Research on Ground Calibration Technology for Geomagnetism Sensors

The measurements of geomagnetism sensors are often affected by self-factors, install-factors and environment factors, therefore they often exist error and cause measurement accuracy reduction. Focus on these problems, this paper analyse existing ground calibration algorithms and their merits and demerits respectively. Besides, a comprehensive geomagnetism sensor error model is presented. Based on this model, a least square method based ellipsoid fitting calibration and compensation algorithm is presented. The experiment results show that this novel calibration algorithm can effectively restrain and compensate geomagnetism signal measurement error

Study of the Forming Characteristics of Small-Caliber Ammunition with Circumferential MEFP

To study the influence of the structural parameters of the ammunition liner of small-caliber ammunition on the forming characteristics of the projectile, an integrated circumferential multiple explosively formed projectile (MEFP) warhead with an integrated shell and the liner was initially designed, and the wall thickness of the liner is variable. LS-DYNA finite-element software is used to simulate the integral circumferential MEFP of the preliminary design, based on the numerical simulation results, the influence of the thickness at the center of the liner, and the curvature radius of the liner on the shape and velocity of the formed projectile. The numerical simulation results show that when the thickness of the center of the liner is constant and the curvature radius increases gradually, the velocity of the formed projectile decreases and the length: Diameter ratio of formed projectile decreases gradually. When the curvature radius of the liner remains unchanged, the velocity of the formed projectile decreases with the increase of the thickness of the center of the liner, and the shape of the formed projectile does not change significantly. The results show that when the design of integrating the shell and the liner was adopted for the integral circumferential MEFP warhead, the shape of the formed projectile is greatly affected by the curvature radius of the liner (curvature radius of inner and outer walls of the liner), but less by the thickness of the center of the liner. The velocity of the formed projectile is affected by the curvature radius of the inner and outer walls of the liner and the thickness of the center of the liner. Moreover, the influence of the thickness of the center of the liner on the velocity of the formed projectile is greater than that of the curvature radius of the outer wall of the liner

Multimodal supply chains: iron ore from Australia to China

Purpose – This paper aims to analyse available multimodal transport route variations for iron ore shipments from northwest Australia to northeast China, focusing on a major iron and steel manufacturer. Design/methodology/approach – The research is focused on a case study and uses an established cost model as a framework, for the first time, in the context of heavy bulk cargo shipments. Field interviews and a questionnaire form the principal methods of primary data collection. The characteristics of bulk iron ore transport flow are analysed against traditional criteria and an appraisal of the transport infrastructure in north east China is made, considering both road and rail options, and various possible combinations for transport being evaluated. All factors affecting modal choice in the region are examined, including cargo volume, weight, and value, transport distance, transit time, transport costs and schedule reliability

NRT-YOLO: Improved YOLOv5 Based on Nested Residual Transformer for Tiny Remote Sensing Object Detection

To address the problems of tiny objects and high resolution of object detection in remote sensing imagery, the methods with coarse-grained image cropping have been widely studied. However, these methods are always inefficient and complex due to the two-stage architecture and the huge computation for split images. For these reasons, this article employs YOLO and presents an improved architecture, NRT-YOLO. Specifically, the improvements can be summarized as: extra prediction head and related feature fusion layers; novel nested residual Transformer module, C3NRT; nested residual attention module, C3NRA; and multi-scale testing. The C3NRT module presented in this paper could boost accuracy and reduce complexity of the network at the same time. Moreover, the effectiveness of the proposed method is demonstrated by three kinds of experiments. NRT-YOLO achieves 56.9% mAP0.5 with only 38.1 M parameters in the DOTA dataset, exceeding YOLOv5l by 4.5%. Also, the results of different classifications show its excellent ability to detect small sample objects. As for the C3NRT module, the ablation study and comparison experiment verified that it has the largest contribution to accuracy increment (2.7% in mAP0.5) among the improvements. In conclusion, NRT-YOLO has excellent performance in accuracy improvement and parameter reduction, which is suitable for tiny remote sensing object detection