A 3d-3d appetizer

We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d ${\cal N}=2$ "Lens space theory" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition function of Chern-Simons theory arises from the index of a free theory. For large $p$, we find that the index of $T[L(p,1)]$ becomes a constant independent of $p$. In addition, we study $T[L(p,1)]$ on the squashed three-sphere $S^3_b$. This enables us to see clearly, at the level of partition function, to what extent $G_\mathbb{C}$ complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group $G$.Comment: 27 pages. v2: misprints corrected, references added. v3: misprints corrected, a clarification adde

A linear method to extract diode model parameters of solar panels from a single I–V curve

The I-V characteristic curve is very important for solar cells/modules being a direct indicator of performance. But the reverse derivation of the diode model parameters from the I-V curve is a big challenge due to the strong nonlinear relationship between the model parameters. It seems impossible to solve such a nonlinear problem accurately using linear identification methods, which is proved wrong in this paper. By changing the viewpoint from conventional static curve fitting to dynamic system identification, the integral-based linear least square identification method is proposed to extract all diode model parameters simultaneously from a single I-V curve. No iterative searching or approximation is required in the proposed method. Examples illustrating the accuracy and effectiveness of the proposed method, as compared to the existing approaches, are presented in this paper. The possibility of real-time monitoring of model parameters versus environmental factors (irradiance and/or temperatures) is also discussed

Exact Single-Source SimRank Computation on Large Graphs

SimRank is a popular measurement for evaluating the node-to-node similarities based on the graph topology. In recent years, single-source and top-$k$ SimRank queries have received increasing attention due to their applications in web mining, social network analysis, and spam detection. However, a fundamental obstacle in studying SimRank has been the lack of ground truths. The only exact algorithm, Power Method, is computationally infeasible on graphs with more than $10^6$ nodes. Consequently, no existing work has evaluated the actual trade-offs between query time and accuracy on large real-world graphs. In this paper, we present ExactSim, the first algorithm that computes the exact single-source and top-$k$ SimRank results on large graphs. With high probability, this algorithm produces ground truths with a rigorous theoretical guarantee. We conduct extensive experiments on real-world datasets to demonstrate the efficiency of ExactSim. The results show that ExactSim provides the ground truth for any single-source SimRank query with a precision up to 7 decimal places within a reasonable query time.Comment: ACM SIGMOD 202