Signature invariants of covering links

We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.

     

Zeros Distribution of the Jones Polynomial for Pretzel Links

In this paper, we deal with basic properties of some pretzel links and properties of the Jones polynomials of some pretzel links. By using these properties, the zero distribution of pretzel links is st...     

Alternating link and its generalization

The alternating links give a classical class of links. They play an important role in Knot Theory. Ozsváth and Szabó introduced a quasi-alternating link which is a generalization of an alternating link. In this paper we review some results of alternating links and quasi-alternating links on the Jones polynomial and the Khovanov homology. Moreover, we introduce a long pass link. Several problems worthy of further study are provided.     

Linking polynomials of virtual string links

In this paper, we define two polynomial invariants for virtual string links. One can be defined only on 2-component virtual string links. The other is defined on virtual string links with arbitrary components.Both invariants can distinguish virtual string links from their mirror images. In addition, we also show that these two invariants are link homotopic invariants. In the end, we give some interesting examples to show that the two invariants are different.     

On 2-Adjacency Between Links

The author discusses 2-adjacency of two-component links and study the relations between the signs of the crossings to realize 2-adjacency and the coefficients of the Conway polynomial of two related links. By discussing the coefficient of the lowest $m$ power in the Homfly polynomial, the author obtains some results and conditions on whether the trivial link is 2-adjacent to a nontrivial link, whether there are two links 2-adjacent to each other, etc. Finally, this paper shows that the Whitehead link is not 2-adjacent to the trivial link, and gives some examples to explain that for any given two-component link, there are infinitely many links 2-adjacent to it. In particular, there are infinitely many links 2-adjacent to it with the same Conway polynomial.     

Covering Sato-Levine invariants

Two covering versions of the Sato-Levine invariant are constructed which provide obstructions to certain two-component oriented links in the 3-sphere being link concordant to boundary links. These covering invariants are rational functions one of which detects both nonamphicheirality and noninvertibility of oriented links.

     

Emergence of epidemics in rapidly varying networks

We describe a simple model mimicking disease spreading on a network with dynamically varying connections, and investigate the dynamical consequences of switching links in the network. Our central observation is that the disease cycles get more synchronized, indicating the onset of epidemics, as the underlying network changes more rapidly. This behavior is found for periodically switched links, as well as links that switch randomly in time. We find that the influence of changing links is more pronounced in networks where the nodes have lower degree, and the disease cycle has a longer infective stage. Further, when the switching of links is periodic we observe finer dynamical features, such as beating patterns in the emergent oscillations and resonant enhancement of synchronization, arising from the interplay between the time-scales of the connectivity changes and that of the epidemic outbreaks.     

Efficient automatic simulation of parallel computation on networks of workstations

Andrews et al. [Automatic method for hiding latency in high bandwidth networks, in: Proceedings of the ACM Symposium on Theory of Computing, 1996, pp. 257-265; Improved methods for hiding latency in high bandwidth networks, in: Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, 1996, pp. 52-61] introduced a number of techniques for automatically hiding latency when performing simulations of networks with unit delay links on networks with arbitrary unequal delay links. In their work, they assume that processors of the host network are identical in computational power to those of the guest network being simulated. They further assume that the links of the host are able to pipeline messages, i.e., they are able to deliver P packets in time O(P+d) where d is the delay on the link.In this paper we examine the effect of eliminating one or both of these assumptions. In particular, we provide an efficient simulation of a linear array of homogeneous processors connected by unit-delay links on a linear array of heterogeneous processors connected by links with arbitrary delay. We show that the slowdown achieved by our simulation is optimal. We then consider the case of simulating cliques by cliques; i.e., a clique of heterogeneous processors with arbitrary delay links is used to simulate a clique of homogeneous processors with unit delay links. We reduce the slowdown from the obvious bound of the maximum delay link to the average of the link delays. In the case of the linear array we consider both links with and without pipelining. For the clique simulation the links are not assumed to support pipelining.The main motivation of our results (as was the case with Andrews et al.) is to mitigate the degradation of performance when executing parallel programs designed for different architectures on a network of workstations (NOW). In such a setting it is unlikely that the links provided by the NOW will support pipelining and it is quite probable the processors will be heterogeneous. Combining our result on clique simulation with well-known techniques for simulating shared memory PRAMs on distributed memory machines provides an effective automatic compilation of a PRAM algorithm on a NOW.     

A unifying model of strategic network formation

We provide a model that merges two basic models of strategic network formation and incorporates them as extreme cases: Jackson and Wolinsky’s connections model based on bilateral formation of links, and Bala and Goyal’s two-way flow model, where links can be unilaterally formed. In our model a link can be created unilaterally, but when it is only supported by one of the two players the flow through it suffers some friction or decay, but more than when it is supported by both players. When the friction in singly-supported links is maximal (i.e. there is no flow) we have Jackson and Wolinsky’s connections model, while when flow in singly-supported links is as good as in doubly-supported links we have Bala and Goyal’s two-way flow model. In this setting, a joint generalization of the results relative to efficiency and stability in both seminal papers is achieved, and the robustness in both models is tested with positive results.     

Polynomial invariants and quandles of twisted links

Bourgoin defined the notion of a twisted link which corresponds to a stable equivalence class of links in oriented thickenings. It is a generalization of a virtual link. Some invariants of virtual links are extended for twisted links including the knot group and the Jones polynomial. In this paper, we generalize a multivariable polynomial invariant of a virtual link to a twisted link. We also introduce a quandle of a twisted link.     

A geometric proof that boundary links are homotopically trivial

The goal of this paper is to give an elementary geometric proof that boundary links are homotopic to trivial links.     

基于计划行为理论的用户链接分享研究

基于计划行为理论梳理分析了移动互联网用户链接分享行为的影响因素,构建了各影响因素与网络用户链接行为关系的概念模型,并基于428条现实世界数据进行了实证分析。结果表明感知行为控制、自我实现需要、沉浸需要、主观规范等四大因素对移动互联网用户持链接分享链接意愿和链接行为具有显著的正向影响。该结论有利于指导信息门户网站开展网络链接技术优化以及社会商业信息的推广活动。     

Knots and the Bracket Calculus

In this paper, we introduce a way of encoding links (long links). This ways leads to a combinatorial representation of links by words in a given finite alphabet. We prove that the link semigroup is isomorphic to some algebraically defined semigroup with a simple system of relations. Thus, knot theory is represented as a bracket calculus: the link recognition problem is reduced to a recognition problem in this semigroup.     

On medial links and hyperbolic 3-manifolds with large isometry groups

Starting from the regular Platonic solids we construct links, generalizing the Borromean rings, with few components but large finite symmetry groups. We consider the 3-manifolds obtained by equivariant surgeries on these links, most of them hyperbolic, and the quotient orbifolds obtained from these group actions, among them various of the smallest known hyperbolic 3-orbifolds. Also, various of the manifolds obtained by equivariant surgery on these links are maximally symmetric hyperbolic 3-manifolds.     

An Analog of the Milnor Group of a Link in the Higher-Dimensional Link Theory

Singular links consisting of several k-spheres and a p-sphere in the (2k+1)-sphere are studied. For k>1, a theory of such singular links is constructed, which is parallel to J. Milnor's theory of one-dimensional links. Bibliography: 14 titles.     

On the fibration of augmented link complements

We study the fibration of augmented link complements. Given the diagram of an augmented link we associate a spanning surface and a graph. We then show that this surface is a fiber for the link complement if and only if the associated graph is a tree. We further show that fibration is preserved under Dehn filling on certain components of these links. This last result is then used to prove that within a very large class of links, called locally alternating augmented links, every link is fibered.     

Closed incompressible surfaces of genus two in 3-bridge knot complements

In this paper, we characterize closed incompressible surfaces of genus two in the complements of 3-bridge knots and links. This characterization includes that of essential 2-string tangle decompositions for 3-bridge knots and links.     

Mayberry-Murasugi's formula for links in homology 3-spheres

We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

     

Chord Diagrams, d-Diagrams, and Knots

A method of representing knots, links, and singular knots and links by words in a finite alphabet and so-called d-diagrams is given. A representation of the chord diagram algebra by words in a finite alphabet is considered. This method, unlike coding by Gauss diagrams, allows one to consider knots and links simultaneously. An algorithm for recognition of diagrams of classical knots in terms of d-diagrams is given. Bibliography: 9 titles.