LL-space surgeries on links

An $L$-space link is a link in $S^3$ on which all large surgeries are $L$-spaces. In this paper, we initiate a general study of the definitions, properties, and examples of $L$-space links. In particular, we find many hyperbolic $L$-space links, including some chain links and two-bridge links; from them, we obtain many hyperbolic $L$-spaces by integral surgeries, including the Weeks manifold. We give bounds on the ranks of the link Floer homology of $L$-space links and on the coefficients in the multi-variable Alexander polynomials. We also describe the Floer homology of surgeries on any $L$-space link using the link surgery formula of Ozsv\'{a}th and Manolescu. As applications, we compute the graded Heegaard Floer homology of surgeries on 2-component $L$-space links in terms of only the Alexander polynomial and the surgery framing, and give a fast algorithm to classify $L$-space surgeries among them.Comment: Section 2.4 deleted, proofs of Lemma 2.5, Theorem 3.8, and Theorem 1.15 adapted (which include the proof of Lemma 2.4, Lemma 3.9, and Theorem 3.10), and other various revision

Heegaard Floer homology of surgeries on two-bridge links

We give an $O(p^{2})$ time algorithm to compute the generalized Heegaard Floer complexes $A_{s_{1},s_{2}}^{-}(\overrightarrow{L})$'s for a two-bridge link $\overrightarrow{L}=b(p,q)$ by using nice diagrams. Using the link surgery formula of Manolescu-Ozsv\'{a}th, we also show that ${\bf HF}^{-}$ and their $d$-invariants of all integer surgeries on two-bridge links are determined by $A_{s_{1},s_{2}}^{-}(\overrightarrow{L})$'s. We obtain a polynomial time algorithm to compute ${\bf HF}^{-}$ of all the surgeries on two-bridge links, with $\mathbb{Z}/2\mathbb{Z}$ coefficients. In addition, we calculate some examples explicitly: ${\bf HF}^{-}$ and the $d$-invariants of all integer surgeries on a family of hyperbolic two-bridge links including the Whitehead link.Comment: 58 pages, 14 figures. Abstract and introduction revised; Theorem 1.1, Theorem 5.12 (now 5.13) adapted; Section 5.1 adapted; Section 5.6 and Example 5.16 added; sign errors fixed; typos in statement of Proposition 6.8 (now 6.9) corrected and computations simplified; Definition 2.2 (now 2.3) corrected. arXiv admin note: text overlap with arXiv:1011.1317 by other author

Numerical simulations on megathrust rupture stabilized under strong dilatancy strengthening in slow slip region

Author Posting. © American Geophysical Union, 2013. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 40 (2013): 1311–1316, doi:10.1002/grl.50298.Episodic slow slip events (SSEs) typically involve a few millimeters to centimeters of slip over several days to months at depths near or further downdip of megathrust seismogenic zones. Despite its widespread presence in subduction margins, it remains unknown how SSEs interact with the seismogenic zone and affect megathrust ruptures. Here, I construct a 2-D thrust fault model governed by rate-state friction to investigate how fault dilatancy influences the amplitude and spatial distribution of‘ coseismic slip, afterslip, and SSEs. Model results illustrate that, under strong dilatancy and high pore pressure around the friction stability transition, coseismic rupture stops at the onset of SSEs. Modeled SSEs have lower velocities, longer recurrence intervals and durations, and larger slip amounts as dilatancy becomes stronger, demonstrating a transition from short-term to long-term type of SSE behavior. These results qualitatively explain the range of spatial distributions of SSEs and megathrust ruptures observed or inferred in natural subduction zones. Furthermore, the relative depths of SSEs and megathrust afterslip may serve as an indicator of dilatancy effectiveness.This work was supported by NSF-EAR award 1015221 to Liu at WHOI and a NSERC Discovery Grant to Liu at McGill.2013-10-1

Performance bounds for greedy strategies in submodular optimization problems

2018 Summer.Includes bibliographical references.To view the abstract, please see the full text of the document

Seismicity relocation and fault structure near the Leech River Fault Zone, southern Vancouver Island

Relatively low rates of seismicity and fault loading have made it challenging to correlate microseismicity to mapped surface faults on the forearc of southern Vancouver Island. Here we use precise relocations of microsciesmicity integrated with existing geologic data, to present the first identification of subsurface seismogenic structures associated with the Leech River fault zone (LRFZ) on southern Vancouver Island. We used HypoDD double difference relocation method to relocate 1253 earthquakes reported by the Canadian National Seismograph Network (CNSN) catalog from 1985 to 2015. Our results reveal an ~8-10 km wide, NNE-dipping zone of seismicity representing a subsurface structure along the eastern 30 km of the terrestrial LRFZ and extending 20 km farther eastward offshore, where the fault bifurcates beneath the Juan de Fuca Strait. Using a clustering analysis we identify secondary structures within the NNE-dipping fault zone, many of which are sub-vertical and exhibit right-lateral strike-slip focal mechanisms. We suggest that the arrangement of these near-vertical dextral secondary structures within a more general NE-dipping fault zone, located well beneath (10-15 km) the Leech River fault (LRF) as imaged by LITHOPROBE, may be a consequence of the reactivation of this fault system as a right-lateral structure in the crust with pre-existing NNE-dipping foliations. Our results provide the first confirmation of active terrestrial crustal faults on Vancouver Island using a relocation method. We suggest that slowly slipping active crustal faults, especially in regions with pre-existing foliations, may result in microseismicity along fracture arrays rather than along single planar structures

Bounding the Greedy Strategy in Finite-Horizon String Optimization

We consider an optimization problem where the decision variable is a string of bounded length. For some time there has been an interest in bounding the performance of the greedy strategy for this problem. Here, we provide weakened sufficient conditions for the greedy strategy to be bounded by a factor of $(1-(1-1/K)^K)$, where $K$ is the optimization horizon length. Specifically, we introduce the notions of $K$-submodularity and $K$-GO-concavity, which together are sufficient for this bound to hold. By introducing a notion of \emph{curvature} $\eta\in(0,1]$, we prove an even tighter bound with the factor $(1/\eta)(1-e^{-\eta})$. Finally, we illustrate the strength of our results by considering two example applications. We show that our results provide weaker conditions on parameter values in these applications than in previous results.Comment: This paper has been accepted by 2015 IEEE CD