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Related Articles from SNS
Detecting Large Quasi-cliques on Dynamic Networks
arXiv:2606.05809v1 Announce Type: new Abstract: Motivated by the problem of detecting large and cohesive groups of vertices in real networks, the task of finding large \emph{quasi-cliques} has attracted considerable attention across different research areas. From a computational complexity perspective, strong inapproximability results are known for this problem, yet several heuristics have been proposed to identify large quasi-cliques in real-world networks. Recently, [Pang \emph{et al.},...
Beyond Outerplanarity
Announce Type: replace Abstract: We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., \emph{convex drawings}. We consider two families of graph classes with convex drawings: \emph{outer $k$-planar} graphs, where each edge is crossed by at most $k$ other edges; and \emph{outer $k$-quasi-planar} graphs, where no $k$ edges can mutually cross. We show that the outer $k$-planar graphs are $\lfloor3.5\sqrt{k}\rfloor$-degenerate, and...
Backward Coherence and Hidden-State Stability in Recurrent Neural Networks: A Quasi-Reverse-Martingale Theory
Announce Type: new Abstract: Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear. We study hidden-state stability through \emph{backward coherence}: the extent to which $h_t$ can be reconstructed from $h_{t+1}$ by a learned backward projector $g_\phi$. Under contraction and summable backward drift, the hidden-state sequence forms a quasi-reverse-martingale. This yields almost-sure convergence, rates under mixing, an interpretable limiting...
Topological Edge States from Molecular Chirality: A General Framework for Dimerized Dipolar Arrays
arXiv:2606.00877v1 Announce Type: cross Abstract: We establish a general theoretical framework for realizing topological edge states in dimerized arrays of chiral dipolar molecules and demonstrate that molecular handedness provides a natural and tunable route to SSH-like topology in an interacting one-dimensional setting. Starting from an effective spin-$\tfrac{1}{2}$ model generated by Stark-dressed chiral molecules, we introduce bond dimerization and show that the chirality-induced...