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...     

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.

     

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.     

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.     

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.     

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.     

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.     

Strict achirality of prime links up to 11-crossing

In this paper we determine all strictly achiral prime links up to 11 crossings. There are exactly four strictly achiral non-trivial prime links up to 11 crossings.     

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.     

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。     

Link Homology in 4-Manifolds

We define link homology in 4-manifolds, and show that it hasa close connection to linking numbers and intersection matricesof 4-manifolds. We also define null-homologous links in 4-manifolds.We give a necessary and sufficient condition for links to benull-homologous in 4-manifolds. This condition implies thatfor any 4-manifold with second Betti number n, there are (n+ 2)-component links which are not nullhomologous in the 4-manifold.     

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.     

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.     

Three geometric applications of quandle homology

In this paper we describe three geometric applications of quandle homology. We show that it gives obstructions to tangle embeddings, provides the lower bound for the 4-move distance between links, and can be used in determining periodicity of links.     

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.     

Power and reversal power links for binary regressions: An application for motor insurance policyholders

In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Self-synchronization of coupled chaotic FitzHugh–Nagumo systems with unreliable communication links

The problem for self-synchronization of coupled chaotic FitzHugh–Nagumo (FHN) systems with unreliable communication links is investigated in this paper. Different from ordinary coupled chaotic systems, the links between two neurons are long-distance and unreliable. Some special network characteristics, such as nonuniform sampling, transmission-induced delays and data packet dropouts, are analyzed in detail. The sufficient condition in terms of linear matrix inequality (LMI) is obtained to guarantee the asymptotical self-synchronization of coupled chaotic FHN systems with unreliable communication links. Lastly, an illustrative example is provided to show the validity of the proposed sufficient condition.