搜索结果：link

We study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, disoriented link cobordism, which tracks the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a disoriented link cobordism. Furthermore, we give a comparison with Oszváth-Stipsicz-Szabó's and Manolescu's constructions of link cobordism maps for an unoriented band move.

With the development of temporal networks such as E-commerce networks and social networks, the issue of temporal link prediction has attracted increasing attention in recent years. The Temporal Link Prediction task of WSDM Cup 2022 expects a single model that can work well on two kinds of temporal graphs simultaneously, which have quite different characteristics and data properties, to predict whether a link of a given type will occur between two given nodes within a given time span. Our team, named as nothing here, regards this task as a link prediction task in heterogeneous temporal networks and proposes a generic model, i.e., Heterogeneous Temporal Graph Network (HTGN), to solve such temporal link prediction task with the unfixed time intervals and the diverse link types. That is, HTGN can adapt to the heterogeneity of links and the prediction with unfixed time intervals within an arbitrary given time period. To train the model, we design a Bi-Time-Window training strategy (BTW) which has two kinds of mini-batches from two kinds of time windows. As a result, for the final test, we achieved an AUC of 0.662482 on dataset A, an AUC of 0.906923 on dataset B, and won 2nd place with a

Although beneficial information abounds on social media, the dissemination of harmful information such as so-called ``fake news'' has become a serious issue. Therefore, many researchers have devoted considerable effort to limiting the diffusion of harmful information. A promising approach to limiting diffusion of such information is link deletion methods in social networks. Link deletion methods have been shown to be effective in reducing the size of information diffusion cascades generated by synthetic models on a given social network. In this study, we evaluate the effectiveness of link deletion methods by using actual logs of retweet cascades, rather than by using synthetic diffusion models. Our results show that even after deleting 10\%--50\% of links from a social network, the size of cascades after link deletion is estimated to be only 50\% the original size under the optimistic estimation, which suggests that the effectiveness of the link deletion strategy for suppressing information diffusion is limited. Moreover, our results also show that there is a considerable number of cascades with many seed users, which renders link deletion methods inefficient.

Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize explicit counting of even and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction, QLP, using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction.

There is a question asking whether a handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link. This question for the case of a trivial surface-link is affirmatively answered. That is, a handle-irreducible summand of every stably trivial surface-link is only a trivial 2-link. By combining this result with an old result of F. Hosowaka and the author that every surface-knot with infinite cyclic fundamental group is a stably trivial surface-knot, it is concluded that every surface-knot with infinite cyclic fundamental group is a trivial (i.e., an unknotted) surface-knot.

In the first part of this paper, we constructed a filtered U(r)-equivariant stable homotopy type called the spectrum of strict broken symmetries sB(L) of links L given by closing a braid with r strands. Evaluating this filtered spectrum on suitable U(r)-equivariant cohomology theories gives rise to a spectral sequence of link invariants that converges to the cohomology of the limiting spectrum. In this paper, we evaluate our construction on Borel equivariant singular cohomology HU(r). We show that the E_2-term of the spectral sequence is isomorphic to an unreduced verision of triply-graded link homology. More precisely, we show that the E_1-term of the spectral sequence is isomorphic to the Hochschild-homology of Soergel bimodules that was shown by M. Khovanov in to compute triply-graded link homology. We also set up the theory that allows for evaluating our construction on equivariant cohomologies that are twisted by adjoint-equivariant local systems on U(r). This allows us to apply Borel equivariant cohomology twisted by a universal power series p(x) with coefficients given by formal variables, and no constant term. The specialization of p(x) to x^n gives rise to a link homology

In the first part of this paper, we constructed a filtered U(r)-equivariant stable homotopy type called the spectrum of strict broken symmetries sB(L) of links L given by closing a braid with r strands. We further showed that evaluating this spectrum on suitable U(r)-equivariant cohomology theories gives rise to a spectral sequence of link invariants, converging to the homology of the limiting spectrum. In this followup, we fix a positive integer n and apply a version of an equivariant K-theory known as Dominant K-theory, which is built from level n representations of the loop group of U(r). The E_2-term of the spectral sequence appears to be a deformation of sl(n)-link homology, and has the property that its value on the unlink is the Grothendieck group of level n-representations of the loop group of U(1). Seen in contrast to the standard interpretation of sl(n)-link homology using the fundamental representation of the quantum group U_q(sl(n)), suggests a level-rank duality at play.

This work establishes a direct operational connection between the entanglement structures of specific three-qubit states (i.e. multipartite entanglement) and their corresponding topological links. We investigate the symmetric $\wwbar$ state and the asymmetric $\starstate$ state through local projective measurements on individual qubits. The post measurement states are analyzed via their Schmidt rank to characterize residual bipartite entanglement. For the symmetric $\wwbar$ state, measurement of any qubit consistently results in a non-maximally entangled post-measurement state (Schmidt rank 2), analogous to the behavior of a \textit{3-Hopf link} structure, where cutting any ring leaves the remaining two nontrivially linked. On the other hand, the $\starstate$ state exhibits a context-dependent fragility. Its behavior predominantly mirrors that of a \textit{3-link chain}, where severing the central qubit decouples the system, while cutting an outer qubit often preserves a residual link. Crucially, for specific measurement outcomes, the $\starstate$ state also exhibits the defining property of the \textit{Borromean rings}, where the loss of one qubit completely disentangles the remai

Link prediction methods use patterns in known network data to infer which connections may be missing. Previous work has shown that continuous-time quantum walks can be used to represent path-based link prediction, which we further study here to develop a more optimized quantum algorithm. Using a sampling framework for link prediction, we analyze the query access to the input network required to produce a certain number of prediction samples. Considering both well-known classical path-based algorithms using powers of the adjacency matrix as well as our proposed quantum algorithm for path-based link prediction, we argue that there is a polynomial quantum advantage on the dependence on $N$, the number of nodes in the network. We further argue that the complexity of our algorithm, although sub-linear in $N$, is limited by the complexity of performing a quantum simulation of the network's adjacency matrix, which may prove to be an important problem in the development of quantum algorithms for network science in general.

We study configuration space integral formulas for Milnor's homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of trivalent "homotopy link diagrams" which corresponds to all finite type homotopy link invariants via configuration space integrals. An important ingredient is the fact that configuration space integrals take the shuffle product of diagrams to the product of invariants. We ultimately deduce a partial recipe for writing explicit integral formulas for products of Milnor invariants from trivalent forests. We also obtain cohomology classes in spaces of link maps from the same data.

We study throughput-optimum localized link scheduling in wireless networks. The majority of results on link scheduling assume binary interference models that simplify interference constraints in actual wireless communication. While the physical interference model reflects the physical reality more precisely, the problem becomes notoriously harder under the physical interference model. There have been just a few existing results on link scheduling under the physical interference model, and even fewer on more practical distributed or localized scheduling. In this paper, we tackle the challenges of localized link scheduling posed by the complex physical interference constraints. By cooperating the partition and shifting strategies into the pick-and-compare scheme, we present a class of localized scheduling algorithms with provable throughput guarantee subject to physical interference constraints. The algorithm in the linear power setting is the first localized algorithm that achieves at least a constant fraction of the optimal capacity region subject to physical interference constraints. The algorithm in the uniform power setting is the first localized algorithm with a logarithmic app

We enumerate all the principal congruence link complements in $S^3$, there by answering a question of W. Thurston. Related articles: "Technical Report: All Principal Congruence Link Groups" (arXiv:1902.04722), "All Known Principal Congruence Links" (arXiv:1902.04426).

An autonomous airborne network (AN) consists of multiple unmanned aerial vehicles (UAVs), which can self-configure to provide seamless, low-cost and secure connectivity. AN is preferred for applications in civilian and military sectors because it can improve the network reliability and fault tolerance, reduce mission completion time through collaboration, and adapt to dynamic mission requirements. However, facilitating seamless communication in such ANs is a challenging task due to their fast node mobility, which results in frequent link disruptions. Many existing AN-specific mobility-aware schemes restrictively assume that UAVs fly in straight lines, to reduce the high uncertainty in the mobility pattern and simplify the calculation of link lifetime (LLT). Here, LLT represents the duration after which the link between a node pair terminates. However, the application of such schemes is severely limited, which makes them unsuitable for practical autonomous ANs. In this report, a mathematical framework is described to accurately compute the \textit{LLT} value for a UAV node pair, where each node flies independently in a randomly selected smooth trajectory. In addition, the impact of

We report on a model built to predict links in a complex network of scientific concepts, in the context of the Science4Cast 2021 competition. We show that the network heavily favours linking nodes of high degree, indicating that new scientific connections are primarily made between popular concepts, which constitutes the main feature of our model. Besides this notion of popularity, we use a measure of similarity between nodes quantified by a normalized count of their common neighbours to improve the model. Finally, we show that the model can be further improved by considering a time-weighted adjacency matrix with both older and newer links having higher impact in the predictions, representing rooted concepts and state of the art research, respectively.

Real-world knowledge graphs are often characterized by low-frequency relations - a challenge that has prompted an increasing interest in few-shot link prediction methods. These methods perform link prediction for a set of new relations, unseen during training, given only a few example facts of each relation at test time. In this work, we perform a systematic study on a spectrum of models derived by generalizing the current state of the art for few-shot link prediction, with the goal of probing the limits of learning in this few-shot setting. We find that a simple zero-shot baseline - which ignores any relation-specific information - achieves surprisingly strong performance. Moreover, experiments on carefully crafted synthetic datasets show that having only a few examples of a relation fundamentally limits models from using fine-grained structural information and only allows for exploiting the coarse-grained positional information of entities. Together, our findings challenge the implicit assumptions and inductive biases of prior work and highlight new directions for research in this area.

We consider quantum holonomy of some three-dimensional general covariant non-Abelian field theory in Landau gauge and confirm a previous result partially proven. We show that quantum holonomy retains metric independence after explicit gauge fixing and hence possesses the topological property of a link invariant. We examine the generalized quantum holonomy defined on a multi-component link and discuss its relation to a polynomial for the link.

The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce is the $n$-quandle. Hoste and Shanahan gave a complete list of the knots and links which have finite $n$-quandles for some $n$. We introduce a generalization of $n$-quandles, denoted $N$-quandles (for a quandle with $k$ algebraic components, $N$ is a $k$-tuple of positive integers). We conjecture a classification of the links with finite $N$-quandles for some $N$, and we prove one direction of the classification.

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato-Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link in the 3-sphere. Applications include computation of the grope filtration, and new geometric characterizations of Milnor's link invariants.

We propose a scalable temporal latent space model for link prediction in dynamic social networks, where the goal is to predict links over time based on a sequence of previous graph snapshots. The model assumes that each user lies in an unobserved latent space and interactions are more likely to form between similar users in the latent space representation. In addition, the model allows each user to gradually move its position in the latent space as the network structure evolves over time. We present a global optimization algorithm to effectively infer the temporal latent space, with a quadratic convergence rate. Two alternative optimization algorithms with local and incremental updates are also proposed, allowing the model to scale to larger networks without compromising prediction accuracy. Empirically, we demonstrate that our model, when evaluated on a number of real-world dynamic networks, significantly outperforms existing approaches for temporal link prediction in terms of both scalability and predictive power.

A group invariant for links in thickened closed orientable surfaces is studied. Associated polynomial invariants are defined. The group detects nontriviality of a virtual link and determines its virtual genus.