Related papers: A specious unlinking strategy
In this Letter, we proposed a mixing navigation mechanism, which interpolates between random-walk and shortest-path protocol. The navigation efficiency can be remarkably enhanced via a few routers. Some advanced strategies are also…
We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal…
The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…
While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly…
The Gauss self-linking integral of an unframed knot is not a knot invariant, but it can be turned into an invariant by adding a correction term which requires adding extra structure to the knot. We collect the different…
Optimal percolation concerns the identification of the minimum-cost strategy for the destruction of any extensive connected components in a network. Solutions of such a dismantling problem are important for the design of optimal strategies…
We give a brief survey of some known results on intrinsically linked or knotted graphs.
We prove that if an alternating knot has unknotting number one, then there exists an unknotting crossing in any alternating diagram. This is done by showing that the obstruction to unknotting number one developed by Greene in his work on…
In this paper, we proposed the \textit{link injection}, a novel method that helps any differentiable graph machine learning models to go beyond observed connections from the input data in an end-to-end learning fashion. It finds out (weak)…
We investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant…
Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…
In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks.…
Future communication scenarios for NASA spacecraft may involve multiple communication links and relay nodes, so that there is essentially a network in which there may be multiple paths from a sender to a destination. The availability of…
Network optimization strategies for the process of synchronization have generally focused on the re-wiring or re-weighting of links in order to: (1) expand the range of coupling strengths that achieve synchronization, (2) expand the basin…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a…
Any knot diagram can be transformed into the unknot by a series of unknotting operations. This paper introduces the diagonal move, a novel unknotting operation that generalizes and unifies several existing moves. We prove that the diagonal…
We explore the application of automated reasoning techniques to unknot detection, a classical problem of computational topology. We adopt a two-pronged experimental approach, using a theorem prover to try to establish a positive result…
In this paper we close the gap between end-to-end diversity coding and intra-session network coding for unicast connections resilient against single link failures. In particular, we show that coding operations are sufficient to perform at…
In this paper, we present algorithms for designing networks that are robust to node failures with minimal or limited number of links. We present algorithms for both the static network setting and the dynamic network setting; setting where…