The deep structure of the Salair fold-cover structure according to magnetotelluric studies

The results of magnetotelluric studies (MTS) performed within the Salair cover-folded structure on two profiles are considered: the Zabrodino village – the Rodnikovy village (1) and the Smaznevo village – the Kotino village (2). The profiles are oriented crosswise along the main structures and intersect Salair and the western part of the Kuznetskiy trough. The analysis of the obtained data showed that a subhorizontal underlying conducting zone is distinguished in the Earth’s crust of the Salair fold-cover structure, such zone is typical for intracontinental orogens. The zone is considered as a deep separation failure. The nature of the electrical resistance values distribution confirms the presence of the Salair thrust on the Kuznetskiy deflection. The Alambay ophiolite zone on the geoelectric section corresponds to a highly gradient region, indicating the suture zone of this structure. High resistivity values in the northern part of the Khmelevskoy trough are associated with the widespread development of granitoid massifs that are not covered by erosion.

Linking Numbers in Three-Manifolds

Let M be a connected, closed, oriented three-manifold and K, L two rationally null-homologous oriented simple closed curves in M. We give an explicit algorithm for computing the linking number between K and L in terms of a presentation of M as an irregular dihedral three-fold cover of $$S^3$$ S 3 branched along a knot $$\alpha \subset S^3$$ α ⊂ S 3 . Since every closed, oriented three-manifold admits such a presentation, our results apply to all (well-defined) linking numbers in all three-manifolds. Furthermore, ribbon obstructions for a knot $$\alpha $$ α can be derived from dihedral covers of $$\alpha $$ α . The linking numbers we compute are necessary for evaluating one such obstruction. This work is a step toward testing potential counter-examples to the Slice-Ribbon Conjecture, among other applications.

The Multi-Cover Persistence of Euclidean Balls

Given a locally finite $$X \subseteq {{{\mathbb {R}}}}^d$$ X ⊆ R d and a radius $$r \ge 0$$ r ≥ 0 , the k-fold cover of X and r consists of all points in $${{{\mathbb {R}}}}^d$$ R d that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in $${{{\mathbb {R}}}}^{d+1}$$ R d + 1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.

On a two-fold cover 2.(2⁶˙G₂(2)) of a maximal subgroup of Rudvalis group Ru

The Schur multiplier M(Ḡ1) ≅4 of the maximal subgroup Ḡ1 = 2⁶˙G₂(2)of the Rudvalis sporadic simple group Ru is a cyclic group of order 4. Hence a full representative group R of the type R = 4.(2⁶˙G₂(2)) exists for Ḡ1. Furthermore, Ḡ1 will have four sets IrrProj(Ḡ1;αi) of irreducible projective characters, where the associated factor sets α1, α2, α3 and α4, have orders of 1, 2, 4 and 4, respectively. In this paper, we will deal with a 2-fold cover 2. Ḡ1 of Ḡ1 which can be treated as a non-split extension of the form Ḡ = 27˙G2(2). The ordinary character table of Ḡ will be computed using the technique of the so-called Fischer matrices. Routines written in the computer algebra system GAP will be presented to compute the conjugacy classes and Fischer matrices of Ḡ and as well as the sizes of the sets |IrrProj(Hi; αi)| associated with each inertia factor Hi. From the ordinary irreducible characters Irr(Ḡ) of Ḡ, the set IrrProj(Ḡ1; α2) of irreducible projective characters of Ḡ1 with factor set α2 such that α22= 1, can be obtained.

Minor Structural Alterations of the Vocal Fold Cover: Vocal Quality before and after Treatment

Introduction Minor structural alterations of the vocal fold cover are important causes of dysphonia. The variability in the type of alteration and the grade of vocal deviation affects the definition of the conduit and the results of treatment. Objective To characterize the occurrence, the selected treatments adopted and vocal quality before and after treatment in patients with minor structural alterations of the vocal folds cover. Methods This was a cross-sectional study based on the records of patients treated by an interdisciplinary team at the laryngology outpatient clinic of a public university hospital from 2010 to 2018. Data collection consisted of access to a database of information on otorhinolaryngological diagnostic hypotheses, intervention and perceptual-auditory vocal assessments before and after the treatment. Data from 102 subjects were analyzed. Association tests were applied between the perceptual-auditory vocal results and the different alterations found and between these and the adopted treatments. The results of the degrees of vocal deviation before and after treatment were also compared. Results The degree of roughness was associated with the sulcus vocalis, and in this alteration the highest occurrence was mild degree of roughness. There was an improvement in the breathiness and general grade of vocal deviation after treatment. Conclusion Cysts were the most frequent structural alteration in the population studied. There was an association between the degree of general deviation and that of roughness in sulcus vocalis cases. The breathiness and the general grade of vocal deviation improved after treatment regardless of the type of treatment and alteration.

q-nonabelianization for line defects

We consider the q-nonabelianization map, which maps links L in a 3-manifold M to combinations of links $$ \tilde{L} $$ L ˜ in a branched N -fold cover $$ \tilde{M} $$ M ˜ . In quantum field theory terms, q-nonabelianization is the UV-IR map relating two different sorts of defect: in the UV we have the six-dimensional (2, 0) superconformal field theory of type $$ \mathfrak{gl} $$ gl (N ) on M × ℝ2,1, and we consider surface defects placed on L × {x4 = x5 = 0}; in the IR we have the (2, 0) theory of type gl (1) on $$ \tilde{M} $$ M ˜ × ℝ2,1, and put the defects on $$ \tilde{L} $$ L ˜ × {x4 = x5 = 0}. In the case M = ℝ3, q-nonabelianization computes the Jones polynomial of a link, or its analogue associated to the group U(N ). In the case M = C × ℝ, when the projection of L to C is a simple non-contractible loop, q-nonabelianization computes the protected spin character for framed BPS states in 4d $$ \mathcal{N} $$ N = 2 theories of class S. In the case N = 2 and M = C × ℝ, we give a concrete construction of the q-nonabelianization map. The construction uses the data of the WKB foliations associated to a holomorphic covering $$ \tilde{C}\to C $$ C ˜ → C .

Prevalence of Minor Larynx Structural Alterations: Influence on the Concept of a Normal Vocal Fold

Objective To determine the prevalence of minor structural alterations (MSA) in the vocal fold cover in a population submitted to extralaryngeal site surgery and to characterize them according to morphological and epidemiological parameters. Study Design This was a cross-sectional and observational study. Setting Tertiary referral medical center. Subjects and Methods A total of 147 patients underwent general anesthesia for extralaryngeal site surgery indicated for a procedure extraneous to the study and irrespective of the presence of vocal complaint. Next, detection and morphological characterization of MSAs in the vocal fold cover were performed by means of suspension microlaryngoscopy with laryngeal inspection and palpation without surgical intervention related to this procedure. The laryngeal findings were compared with variables from a clinical and demographic characteristics questionnaire given to these individuals. Results A 21.1% prevalence of MSAs was identified in the sample, which included a majority of individuals without vocal complaint (95.9%). Of these, 5.4% of individuals had laryngeal microdiaphragms, 16.3% sulcus vocalis, and 4.1% epidermoid cysts. No pouch sulcus or mucosal bridges were found. The identification of these alterations occurred mainly after 10 years of age, without effects of sex, vocal abuse, or upper airway conditions. The most common combination of MSAs was bilateral sulcus vocalis. Conclusions The prevalence of MSAs in laryngeal coverage in this predominantly vocally asymptomatic population was 21.1%, with identification of sulcus vocalis, epidermoid cyst, and laryngeal microdiaphragm. Age was the only clinical or demographic characteristic associated with these alterations.