The complexity of dominating set reconfiguration

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by $O(n)$, where $n$ is the number of vertices in the input graph

Symmetries of Holographic Super-Minimal Models

We compute the asymptotic symmetry of the higher-spin supergravity theory in AdS_3 and obtain an infinite-dimensional non-linear superalgebra, which we call the super-W_infinity[lambda] algebra. According to the recently proposed supersymmetric duality between higher-spin supergravity in an AdS_3 background and the 't Hooft limit of the N=2 CP^n Kazama-Suzuki model on the boundary, this symmetry algebra should agree with the 't Hooft limit of the chiral algebra of the CFT, SW_n. We provide two nontrivial checks of the duality. By comparing the algebras, we explicitly match the lowest-spin commutation relations in the super-W_infinity[lambda] with the corresponding commutation relations in the 't Hooft limit on the CFT side. We also consider the degenerate representations of the two algebras and find that the spectra of the chiral primary fields are identical.Comment: 33 pages, references added, some errors corrected, discussions about the truncation of the shs[lambda] algebra and reobtaining the original shs[lambda] algebra from the super-W_infinity[lambda] algebra adde

The Large N 't Hooft Limit of Kazama-Suzuki Model

We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known that the N=2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from the generalized GKO coset construction previously. For N=4, we construct one of the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N=2 classical W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected and to appear in JHE

Supersymmetric holography on AdS3

The proposed duality between Vasiliev's supersymmetric higher spin theory on AdS3 and the 't Hooft limit of the 2d superconformal Kazama-Suzuki models is analysed in detail. In particular, we show that the partition functions of the two theories agree in the large N limit.Comment: 25 pages, 3 figures, improved fig.

The Operator Product Expansion of the Lowest Higher Spin Current at Finite N

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the presentations in the whole paper improved and to appear in JHE

Higher spin AdS_3 supergravity and its dual CFT

Vasiliev's higher spin supergravity theory on three dimensional anti-de Sitter space is studied and, in particular, the partition function is computed at one loop level. The dual conformal field theory is proposed to be the N=(2,2) CP^N Kazama-Suzuki model in two dimensions. The proposal is based on symmetry considerations and comparison of the bulk partition function with the conformal field theory. Our findings suggest that the theory is strong-weak self-dual.Comment: 36 page

On Non-linear Action for Gauged M2-brane

We propose a non-linear extension of U(1) \times U(1) (abelian) ABJM model including T_{M2} (higher derivative) corrections. The action proposed here is expected to describe a single M2-brane proving C^4/Z_k target space. The model includes couplings with the 3-form background in the eleven-dimensional supergravity which is consistent with the orbifold projection. We show that the novel higgs mechanism proposed by Mukhi and Papageorgakis does work even in the presence of higher derivative corrections and couplings with the background field, giving the correct structure of the Dirac-Born-Infeld action with Wess-Zumino term for a D2-brane. We also find half BPS solutions in the full non-linear theory which is interpreted as an another M2-brane intersecting with the original M2-brane. A possible generalization to U(N) \times U(N) gauge group is briefly discussed.Comment: 19 pages, no figure, references added, typos correcte

Use of low-dose oral theophylline as an adjunct to inhaled corticosteroids in preventing exacerbations of chronic obstructive pulmonary disease: study protocol for a randomised controlled trial.

BACKGROUND: Chronic obstructive pulmonary disease (COPD) is associated with high morbidity, mortality, and health-care costs. An incomplete response to the anti-inflammatory effects of inhaled corticosteroids is present in COPD. Preclinical work indicates that 'low dose' theophylline improves steroid responsiveness. The Theophylline With Inhaled Corticosteroids (TWICS) trial investigates whether the addition of 'low dose' theophylline to inhaled corticosteroids has clinical and cost-effective benefits in COPD. METHOD/DESIGN: TWICS is a randomised double-blind placebo-controlled trial conducted in primary and secondary care sites in the UK. The inclusion criteria are the following: an established predominant respiratory diagnosis of COPD (post-bronchodilator forced expiratory volume in first second/forced vital capacity [FEV1/FVC] of less than 0.7), age of at least 40 years, smoking history of at least 10 pack-years, current inhaled corticosteroid use, and history of at least two exacerbations requiring treatment with antibiotics or oral corticosteroids in the previous year. A computerised randomisation system will stratify 1424 participants by region and recruitment setting (primary and secondary) and then randomly assign with equal probability to intervention or control arms. Participants will receive either 'low dose' theophylline (Uniphyllin MR 200 mg tablets) or placebo for 52 weeks. Dosing is based on pharmacokinetic modelling to achieve a steady-state serum theophylline of 1-5 mg/l. A dose of theophylline MR 200 mg once daily (or placebo once daily) will be taken by participants who do not smoke or participants who smoke but have an ideal body weight (IBW) of not more than 60 kg. A dose of theophylline MR 200 mg twice daily (or placebo twice daily) will be taken by participants who smoke and have an IBW of more than 60 kg. Participants will be reviewed at recruitment and after 6 and 12 months. The primary outcome is the total number of participant-reported COPD exacerbations requiring oral corticosteroids or antibiotics during the 52-week treatment period. DISCUSSION: The demonstration that 'low dose' theophylline increases the efficacy of inhaled corticosteroids in COPD by reducing the incidence of exacerbations is relevant not only to patients and clinicians but also to health-care providers, both in the UK and globally. TRIAL REGISTRATION: Current Controlled Trials ISRCTN27066620 was registered on Sept. 19, 2013, and the first subject was randomly assigned on Feb. 6, 2014

Prognostic parameters for recurrence of papillary thyroid microcarcinoma

<p>Abstract</p> <p>Background</p> <p>Papillary thyroid microcarcinoma (PTMC) is defined as a papillary thyroid carcinoma less than or equal to 1.0 cm in size. Independent prognostic factors for clinical recurrence of PTMC have not been clearly delineated.</p> <p>Methods</p> <p>Clinicopathological parameters predicting PTMC recurrence were determined by retrospective analysis of 307 patients.</p> <p>Results</p> <p>Of the 293 patients eligible for analysis, 14 (5%) had recurrence during a median follow-up time of 65 months. Recurrence was observed in 8 of 166 patients (0.5%) treated with total or near-total thyroidectomy; gender (P = 0.02) and presence of lateral cervical node metastases at initial surgery (P = 0.01) were associated with recurrence. Six of the 127 patients (0.5%) treated with hemi- or subtotal thyroidectomy experience recurrences, but no significant prognostic factor for recurrence was identified. Multivariate Cox-regression analysis showed that gender and cervical lymph node metastasis were significant variables</p> <p>Conclusion</p> <p>PTMC showed very diverse disease extent and could not be regarded as indolent, relatively benign disease based on the primary tumor size. The extent of surgery should be based on prognostic parameters, such as gender and lateral neck node metastasis, in patients with PTMC.</p

Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups

N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS states become massless. In a region of the moduli space, we compute dyon charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge groups respectively for rank r>1. From here we elucidate the connection to the wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the Argyres-Douglas loci, despite our emphasis being only at the massless sector of the BPS spectra. We also present 2r-1 candidates for the maximal Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.Comment: 81 pages, 41 figures, LaTeX; v2: Minor cosmetic changes and correction of a typographical error in acknowledgement. Final version to appear in JHE