A key task in analyzing social networks and other complex networks is role analysis: describing and categorizing nodes by how they interact with other nodes. Two nodes have the same role if they interact with equivalent sets of neighbors. The most fundamental role equivalence is automorphic equivalence. Unfortunately, the fastest algorithm known for graph automorphism is nonpolynomial. Moreover, since exact equivalence is rare, a more meaningful task is measuring the role similarity between any two nodes. This task is closely related to the link-based similarity problem that SimRank addresses. However, SimRank and other existing simliarity measures are not sufficient because they do not guarantee to recognize automorphically or structurally equivalent nodes. This paper makes two contributions. First, we present and justify several axiomatic properties necessary for a role similarity measure or metric. Second, we present RoleSim, a role similarity metric which satisfies these axioms and which can be computed with a simple iterative algorithm. We rigorously prove that RoleSim satisfies all the axiomatic properties and demonstrate its superior interpretative power on both synthetic and real datasets.

Understanding the pathophysiology of white matter hyperintensity (WMH) is necessary to reduce its harmfulness. Dilated perivascular space (PVS) had been found related to WMH. In the present study, we aimed to examine the topological connections between WMH and PVS, and to investigate whether increased interstitial fluid mediates the correlation between PVS and WMH volumes. One hundred and thirty-six healthy elder subjects were retrospectively included from a prospectively collected community cohort. Sub-millimeter T2 weighted and FLAIR images were acquired for assessing the association between PVS and WMH. Diffusion tensor imaging and free-water (FW) analytical methods were used to quantify white matter free water content, and to explore whether it mediates the PVS-WMH association. We found that most (89%) of the deep WMH lesions were spatially connected with PVS, exhibiting several interesting topological types. PVS and WMH volumes were also significantly correlated (r = 0.222, p < 0.001). FW mediated this association in the whole sample (β = 0.069, p = 0.037) and in subjects with relatively high WMH load (β = 0.118, p = 0.006). These findings suggest a tight association between PVS dilation and WMH formation, which might be linked by the impaired glymphatic drainage function and accumulated local interstitial fluid.

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The spurious eigenvalues of an annular domain have been veri ed for the singular and hypersingular boundary-element methods (BEMs) and circumvented by using the Burton{Miller approach. Do they also occur in other formulations: continuous formulations such as the singular and hypersingular boundary integral equations (BIEs), the null-eld BIEs and the ctitious BIEs, or such discrete formulations as the null-eld BEMs and the ctitious BEMs? For the ten formulations of the multiply connected problem the study of otherwise the same issues is continued in the present paper. By using the degenerate kernels and the Fourier series, it is demonstrated analytically for the six continuous formulations of BIEs that spurious eigensolutions depend on the geometry of the inner boundary but not on that of the outer boundary. This conclusion can be extended to the six discrete formulations of BEMs. To lter out the spurious eigenvalues, the CHIEF (combined Helmholtz integral equation formulation) method is used here instead of the Burton{Miller approach. The optimum number and appropriate positions of the CHIEF points are also addressed. It is then shown that, in the null-eld and ctitious BEMs, the spurious and true eigenvalues can be detected and distinguished by using the singular-value-decompositionupdating techniques in conjunction with the Fredholm alternative theorem. Illustrative examples show the validity of the proposed methodologies.

Assessing glymphatic function using in-vivo imaging method is of great value for understanding its contribution to major brain diseases. In the present study, we aim to validate the association between a variety of risk factors and a potential index of glymphatic function—Diffusion Tensor Image Analysis Along the Perivascular Space (ALPS index). We enrolled 142 subjects from communities and performed multi-modality magnetic resonance imaging scans. The ALPS index was calculated from diffusion tensor imaging data, and its associations with demographic factors, vascular factors were investigated using regression analyses. We found that the ALPS index was negatively associated with age (β = −0.284, p &lt; 0.001). Compared to males, females had significantly higher ALPS index (β = −0.243, p = 0.001). Hypertensive subjects had significantly lower ALPS index compared to non-hypertensive subjects (β = −0.189, p = 0.013). Furthermore, venous disruption could decrease ALPS index (β = −0.215, p = 0.003). In general, our results are in consistent with previous conceptions and results from animal studies about the pathophysiology of glymphatic dysfunction. Future studies utilizing this method should consider introducing the above-mentioned factors as important covariates.

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