Twin-width I: Tractable FO Model Checking

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA’14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, K t -free unit d -dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes (except map graphs without geometric embedding) we show how to compute in polynomial time a sequence of d -contractions , witness that the twin-width is at most d . We show that FO model checking, that is deciding if a given first-order formula ϕ evaluates to true for a given binary structure G on a domain D , is FPT in |ϕ| on classes of bounded twin-width, provided the witness is given. More precisely, being given a d -contraction sequence for G , our algorithm runs in time f ( d ,|ϕ |) · |D| where f is a computable but non-elementary function. We also prove that bounded twin-width is preserved under FO interpretations and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-parameter tractability of FO model checking on non-monotone classes, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS’15].

Principal bundles on two-dimensional CW-complexes with disconnected structure group

Given any topological group G, the topological classification of principal G-bundles over a finite CW-complex X is long known to be given by the set of free homotopy classes of maps from X to the corresponding classifying space BG. This classical result has been long-used to provide such classification in terms of explicit characteristic classes. However, even when X has dimension 2, there is a case in which such explicit classification has not been explicitly considered. This is the case where G is a Lie group, whose group of components acts nontrivially on its fundamental group $\pi_1G$ . Here, we deal with this case and obtain the classification, in terms of characteristic classes, of principal G-bundles over a finite CW-complex of dimension 2, with G is a Lie group such that $\pi_0G$ is abelian.

Acylindrical hyperbolicity for Artin groups of dimension 2

In this paper, we show that every irreducible 2-dimensional Artin group $$A_{\Gamma }$$ A Γ of rank at least 3 is acylindrically hyperbolic. We do this by studying the action of $$A_\Gamma $$ A Γ on its modified Deligne complex. Along the way, we prove results of independent interests on the geometry of links of this complex.

Design characteristics of showering aeration system

The showering aeration system (SAS) was designed and its performance was evaluated by conducting the aeration experiments in a tank of dimension 2 × 4 × 1.5 m. Initially, the aeration experiments were conducted to optimize the radius of curvature of the SAS with different values, such as = 0, 5, 10, 15, and 20 mm, and maintain other geometric parameters, i.e. number of holes in the shower (); height of water fall (H); diameter of the shower hole (d); volume of water under aeration (V) and water flow rate (Q) as constants. The optimum radius of curvature () was found to be 10 mm. The aeration experiments were further conducted with four different non-dimensional geometric parameters such as the number of holes , the ratio of the height of water fall to the length of shower arm the ratio of the diameter of the hole to the length of shower arm and the ratio of the volume of water to the cube of the length of shower arm The Response Surface Methodology and Box–Behnken Design were used to optimize the non-dimensional geometric parameters of the SAS to maximize the Non-Dimensional Standard Aeration Efficiency. The result indicates that the maximum NDSAE of 16.98 × 106 was obtained from the SAS performance at = 80; = 2; = 4 and = 48. HIGHLIGHT The optimized non-dimensional geometric parameters (H/l; d/l; V/l3; n) for the showering aeration system were experimentally validated, and the final NDSAE value was found to be 16.98 × 106 against the predicted NDSAE value of 17.70 × 106.

1-form symmetries of 4d N=2 class S theories

We determine the 1-form symmetry group for any 4d4d\mathcal{N}=2𝒩=2 class S theory constructed by compactifying a 6d6d\mathcal{N}=(2,0)𝒩=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d4d, modulo screening and flavor charges. Complete specification of a 4d4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.

Factor Influencing Vaccine Rejection of Complete Basic Immunization in Indonesia

AIM: This study aims to identify psychological factors against vaccine rejection in Indonesia. The study also provides a review of the group of different factors on psychological factors in social media. METHODS: This study uses secondary data sourced from Facebook, Twitter, YouTube and Instagram about vaccines rejection from 2018 to 2019. That text is labeled based on seven psychological factors that influence vaccine rejection. The factor analysis method is used to determine the relationship between vaccine rejection and psychological factors. RESULTS: Dimension 1 focused on individual and group influences, where the correlation value between factors such as vaccine misinformation, health worker trust, perception of side effect is 0.906 (>0.5). Dimension 2 used different factors such as trust in the goverment, negative opinion about vaccine efficacy, and social influence as contextual/environmental influencers,with a correlation value of 0.866 (>0.5). Meanwhile, Dimension 3 with general perception is a factor in vaccine and vaccination specific problems with a correlation value of 0.940 (>0.5). CONCLUSION: Psychological factors are mainly associated with vaccine rejection. Stakeholders need to observe these factors in identifying conditions for childhood vaccines rejection posted on social media in Indonesia.

On the influence of ideals and self-idealizing subalgebras on the structure of Leibniz algebras

The subalgebra A of a Leibniz algebra L is self-idealizing in L, if A = IL (A) . In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing. More precisely, we obtain a description of such Leibniz algebras for the cases where the locally nilpotent radical is Abelian non-cyclic, non-Abelian noncyclic, and cyclic of dimension 2.