The increasing scale of alternating current and direct current (AC/DC) hybrid systems necessitates a faster power flow analysis tool than ever. This letter thus proposes a specific physics-guided graph neural network (PG-GNN). The tailored graph modelling of AC and DC grids is firstly advanced to enhance the topology adaptability of the PG-GNN. To eschew unreliable experience emulation from data, AC/DC physics are embedded in the PG-GNN using duality. Augmented Lagrangian method-based learning scheme is then presented to help the PG-GNN better learn nonconvex patterns in an unsupervised label-free manner. Multi-PG-GNN is finally conducted to master varied DC control modes. Case study shows that, relative to the other 7 data-driven rivals, only the proposed method matches the performance of the model-based benchmark, also beats it in computational efficiency beyond 10 times.

Optimization problems aim to find the optimal solution, which is becoming increasingly complex and difficult to solve. Traditional evolutionary optimization methods always overlook the granular characteristics of solution space. In the real scenario of numerous optimizations, the solution space is typically partitioned into sub-regions characterized by varying degree distributions. These sub-regions present different granularity characteristics at search potential and difficulty. Considering the granular characteristics of the solution space, the number of coarse-grained regions is smaller than the number of points, so the calculation is more efficient. On the other hand, coarse-grained characteristics are not easily affected by fine-grained sample points, so the calculation is more robust. To this end, this paper proposes a new multi-granularity evolutionary optimization method, namely the Granular-ball Optimization (GBO) algorithm, which characterizes and searches the solution space from coarse to fine. Specifically, using granular-balls instead of traditional points for optimization increases the diversity and robustness of the random search process. At the same time, the search range in different iteration processes is limited by the radius of granular-balls, covering the solution space from large to small. The mechanism of granular-ball splitting is applied to continuously split and evolve the large granular-balls into smaller ones for refining the solution space. Extensive experiments on commonly used benchmarks have shown that GBO outperforms popular and advanced evolutionary algorithms. The code can be found in the supporting materials.

The large Nernst effect is advantageous for developing transverse Nernst thermoelectric generators or Ettingshausen coolers within a single component, avoiding the complexity of electron- and hole-modules in longitudinal Seebeck thermoelectric devices. We report a large Nernst signal reaching 130 uV/K at 8 K and 13 T in the layered metallic antiferromagnet EuAl$_2$Si$_2$. Notably, this large transverse Nernst thermopower is two orders of magnitude greater than its longitudinal counterpart. The Nernst coefficient peaks around 4 K and 8 K at 3 T and 13 T, respectively. At similar temperatures, both the Hall coefficient and the Seebeck signal change sign. Additionally, nearly compensated electron- and hole-like carriers with high mobility ($\sim$ 4000 cm$^2$/Vs at 4 K) are revealed from the magnetoconductivity. These findings suggest that the large Nernst effect and vanishing Seebeck thermopower in EuAl$_2$Si$_2$ are due to the compensated electron- and hole-like bands, along with the high mobility of the Weyl band near the Fermi level. Our results underscore the importance of band compensation and topological fermiology in achieving large Nernst thermopower and exploring potential Nernst thermoelectric applications at low temperatures.

Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical operators in harmonic analysis, such as the Hardy--Littlewood maximal operator, the Calderón--Zygmund operator, the Riesz potential, singular integral operators with the rough kernel, the Marcinkiewicz integral, the Bochner-Riesz operator, the Littlewood-Paley $g$ function and the intrinsic square function, are considered. Our main method is extrapolation. We obtain some new weak results for these operators on weighted amalgam spaces.