Dimension Of Class Research Articles

Scaling solutions in the derivative expansion

Scalar field theories with $\mathbb{Z}_{2}$-symmetry are the traditional playground of critical phenomena. In this work these models are studied using functional renormalization group (FRG) equations at order $\partial^2$ of the derivative expansion and, differently from previous approaches, the spike plot technique is employed to find the relative scaling solutions in two and three dimensions. The anomalous dimension of the first few universality classes in $d=2$ is given and the phase structure predicted by conformal field theory is recovered (without the imposition of conformal invariance), while in $d=3$ a refined view of the standard Wilson-Fisher fixed point is found. Our study enlightens the strength of shooting techniques in studying FRG equations, suggesting them as candidates to investigate strongly non-perturbative theories even in more complex cases.

Uniquely identifying the edges of a graph: The edge metric dimension

Let G=(V,E) be a connected graph, let v∈V be a vertex and let e=uw∈E be an edge. The distance between the vertex v and the edge e is given by dG(e,v)=min{dG(u,v),dG(w,v)}. A vertex w∈V distinguishes two edges e1,e2∈E if dG(w,e1)≠dG(w,e2). A set S of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertex of S. The smallest cardinality of an edge metric generator for G is called the edge metric dimension and is denoted by edim(G). In this paper, we introduce the concept of edge metric dimension and initiate the study of its mathematical properties. We make a comparison between the edge metric dimension and the standard metric dimension of graphs while presenting some realization results concerning the edge metric dimension and the standard metric dimension of graphs. We prove that computing the edge metric dimension of connected graphs is NP-hard and give some approximation results. Moreover, we present some bounds and closed formulae for the edge metric dimension of several classes of graphs.

Class Dimension of Social Inequality

In this article we look at some of the most influential theories of class, which try to explain class inequality in west and east European societies. Social stratification is considered as a system of social inequality, social differentiation, based on differences in the occupied position and functions performed. Social inequality is the basis of stratification of society and is perceived as its main feature. The theory of social stratification reveals the essence of social inequality in such factors as social status, social role and prestige of functionally describing the social structure.

Complexity of concept classes induced by discrete Markov networks and Bayesian networks

Markov networks and Bayesian networks are two popular models for classification. Vapnik–Chervonenkis dimension and Euclidean dimension are two measures of complexity of a class of functions, which can be used to measure classification capability of classifiers. One can use Vapnik–Chervonenkis dimension of the class of functions associated with a classifier to construct an estimate of its generalization error. In this paper, we study Vapnik–Chervonenkis dimension and Euclidean dimension of concept classes induced by discrete Markov networks and Bayesian networks. We show that these two dimensional values of the concept class induced by a discrete Markov network are identical, and the value equals dimension of the toric ideal corresponding to this Markov network as long as the toric ideal is nontrivial. Based on this result, one can compute the dimensional value in terms of a computer algebra system directly. Furthermore, for a general Bayesian network, we show that dimension of the corresponding toric ideal offers an upper bound of Euclidean dimension. In addition, we illustrate how to use Vapnik–Chervonenkis dimension to estimate generalization error in binary classification.

Double-trace flows and the swampland

We explore the idea that large N, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite k, deformed by {displaystyle int {mathcal{O}}^2} , where mathcal{O} is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1/N. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large N CFT3 with an Einstein gravity dual.

Numerical integration of KPZ equation with restrictions

In this paper, we introduce a novel integration method of Kardar–Parisi–Zhang (KPZ) equation. It is known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical value, instabilities appear and the integration diverges. One way to avoid these instabilities is to replace the KPZ nonlinear-term by a function of the same term that depends on a single adjustable parameter which is able to control pillars or grooves growing on the interface. Here, we propose a different integration method which consists of directly limiting the value taken by the KPZ nonlinearity, thereby imposing a restriction rule that is applied in each integration time-step, as if it were the growth rule of a restricted discrete model, e.g. restricted-solid-on-solid (RSOS). Taking the discrete KPZ equation with restrictions to its dimensionless version, the integration depends on three parameters: the coupling constant g, the inverse of the time-step k, and the restriction constant ε which is chosen to eliminate divergences while keeping all the properties of the continuous KPZ equation. We study in detail the conditions in the parameters’ space that avoid divergences in the 1-dimensional integration and reproduce the scaling properties of the continuous KPZ with a particular parameter set. We apply the tested methodology to the d-dimensional case () with the purpose of obtaining the growth exponent β, by establishing the conditions of the coupling constant g under which we recover known values reached by other authors, particularly for the RSOS model. This method allows us to infer that d = 4 is not the critical dimension of the KPZ universality class, where the strong-coupling phase disappears.

Effective Hausdorff Dimension in General Metric Spaces

We introduce the concept of effective dimension for a wide class of metric spaces whose metric is not necessarily based on a measure. Effective dimension was defined by Lutz (Inf. Comput., 187(1), 49–79, 2003) for Cantor space and has also been extended to Euclidean space. Lutz effectivization uses gambling, in particular the concept of gale and supergale, our extension of Hausdorff dimension to other metric spaces is also based on a supergale characterization of dimension, which in practice avoids an extra quantifier present in the classical definition of dimension that is based on Hausdorff measure and therefore allows effectivization for small time-bounds. We present here the concept of constructive dimension and its characterization in terms of Kolmogorov complexity, for which we extend the concept of Kolmogorov complexity to any metric space defining the Kolmogorov complexity of a point at a certain precision. Further research directions are indicated.

An Evaluation of Mandibular Dental and Basal Arch Dimensions in Class I and Class II Division 1 Adult Syrian Patients using Cone-beam Computed Tomography

Aim: The aim of this study is (1) to inspect any difference in mandibular arch widths between males and females in class I and class II division 1 (class malocclusions using cone-beam computed tomography (CBCT), (2) to compare the mandibular dental and basal widths between the two groups, and (3) to investigate any possible correlation between dental and basal arch widths in both groups. Materials and methods: The CBCT images of 68 patients aged between 18 and 25 years consisted of 34 class I (17 males and 17 females) and 34 class (17 males and 17 females) who were recruited at the Department of Orthodontics, University of Damascus Dental School (Syria). Using on-demand three-dimensional (3D) on axial views, facial axis points for dental measurements and basal bone center (BBC) points for basal measurements were identified on lower canines and first molars. Dental and basal intercanine width (ICW) and intermolar width (IMW) were measured. Results: Independent t-test showed a statistically significant difference between males and females in several variables in both groups and a statistically significant difference between class I and class groups in the basal ICW for both genders and in the dental ICW for females only (p < 0.05). In class I group, Pearson's correlation coefficients between dental and basal measurements showed a strong correlation in the IMW for both genders (r > 0.73; p < 0.01) and a moderate correlation in females' ICW (r = 0.67; p < 0.01). In the class group, a moderate correlation in females' IMW (r = 0.67; p < 0.01) was found. Conclusion: Females compared with males had narrower dimensions. Class I patients had larger ICW than class II-1 patients in all measurements and had narrower IMW than class in most measurements for both genders. There were moderate-to-strong correlations between dental and basal dimensions. BBC points might be landmarks that accurately represent the basal bone arch. Clinical significance: CBCT-based assessments of dental and basal arch dimensions provide a great opportunity to accurately evaluate these aspects, to enhance clinicians' decisions regarding proper tooth movements, and to achieve good dentoalveolar intra-arch harmony. Keywords: Basal arch, Class I, Class Cone-beam computed tomography, Dental arch, Intercanine width, Intermolar width.

Understanding the social geographies of urban regions through the socio‐economic and cultural dimension of class

AbstractEconomic restructuring and changing demographic and migration patterns have significantly altered the population compositions of urban regions. Whereas there is evidence that employees in various sectors of the economy have different residential preferences, there exists much less insight into the social geography of various class fractions at the level of urban regions. The aims of this paper are (1) to describe the spatial orientations of various employment groups in the largest urban regions in the Netherlands and (2) to understand the extent to which spatial orientations towards various residential urban and suburban milieus can be explained by belonging to a specific class fraction. We draw on individual‐level register data for the whole population of urban regions, applying a multidimensional and detailed perspective on social class that takes into account both economic and cultural capital. We demonstrate a strong urban orientation among the cultural classes, who are often working in the new economies—irrespective of their income status—and an over‐representation in suburban areas of more economically orientated class fractions. Despite the differences in terms of economic structure of the researched urban regions, these variegated residential orientations are remarkably consistent.

Quotidian realities of organic mothering in Turkey

AbstractThis article explores how mothers in Turkey respond to the current atmosphere of food fear and the neoliberal rhetoric of the individualization of risks, as well as interrogating the class dimension of the varying ways in which mothers experience pressures regarding feeding their children in an organic manner. The article primarily suggests that mothers adopt different organic food strategies across class divisions—particularly through class-specific definitions of “organic”—so as to deal in stratified ways with the challenges organic feeding brings. It indicates that organic mothering practices have been incorporated into the lifestyle and cultural distinctions of middle-class families and reinforced by rural nostalgia. Contrary to this, ideas about “the organic” and rural nostalgia are mostly translated as “home-made” for lower-class families. Relying on sixteen in-depth interviews with mothers in İstanbul and on an analysis of posts and comments found on a mothering blog, this article offers empirical findings on analyses of organic mothering and risk from a standpoint and location that have been largely ignored in the existing literature. It also contributes to analyses about neoliberal transformations in the Turkish food market and the growing literature on family and neoliberalism under the government of the Justice and Development Party (Adalet ve Kalkınma Partisi, AKP) by bringing a research-based view on the subjective experiences of mothers into a discourse that is rather political in nature as well as into policy research discussions.

Random Euclidean matching problems in one dimension.

We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the problem in a compact set with the topology both of the interval and of the circumference. Afterwards, we assume the points' positions to be random variables identically and independently distributed on the considered domain. We analytically obtain the average optimal cost in the asymptotic regime of very large number of points N and some correlation functions for a power-law-type cost function in the form c(z)=z^{p}, both in the p>1 case and in the p<0 case. The scaling of the optimal mean cost with the number of points is N^{-p/2} for the assignment and N^{-p} for the matching when p>1, whereas in both cases it is a constant when p<0. Finally, our predictions are compared with the results of numerical simulations.

ANALISIS KEMAMPUAN PESERTA DIDIK KELAS XI MIA SMA DI KABUPATEN ENREKANG DALAM MENYELESAIKAN SOAL-SOAL BERDIMENSI PENGETAHUAN FAKTUAL, KONSEPTUAL, PROSEDURAL DAN METAKOGNITIF

This descriptive research aims to discover the students’ ability in solving question in Factual, Conceptual, Prosedural and Metacognitive dimension in class XI MIA of Senior High School in Enrekang District. The population of the research was all of the students class XI MIA of Senior High School in Enrekang Discrict which consisted of 39 classes with the total 907 students. The sample of the research was selected by using stratified purposive random sampling technique and obtained SMA 1 Alla, SMA 1 Anggeraja, SMA 1 Baraka, SMA Masalle and SMA Muhammadiyah Kalosi, 5 classes with the total 150 student. The instrument of the research were questionnaire and learning result test. The result of the research show that (i) the ability of the students in solving the question in factual dimension is in sufficient category; conceptual dimension is in low category; procedural dimension is in low category; metecognitif dimension is in very low category in class XI MIA of Senior High School in Enrekang Discrict; (ii) there is no difference in the achievement of factual, conceptual, and procedural ability of the school in the city or in the main road with the school in the suburb (out of town) and the favorite schools with non-favorite school; (iii) there are difference in the achievement of metacognitif ability of the school in the city or in the main road with the school in the suburb (out of town) and the favorite schools with non-favorite school; (iv) there are difference of the students’ leaning result of the school in the city or in the main road with the school in the suburb (out of town) and the favorite schools with non-favorite school.

Borel–Padé Re-summation of the β-functions Describing Anderson Localisation in the Wigner–Dyson Symmetry Classes

We describe a Borel-Pad\'e re-summation of the $\beta$-function in the three Wigner-Dyson symmetry classes. Using this approximate $\beta$-function we discuss the dimensional dependence of the critical exponent and compare with numerical estimates. We also estimate the lower critical dimension of the symplectic symmetry class.

Religious Tastes and Styles as Markers of Class Belonging: A Bourdieuian Perspective on Pentecostalism in South America

Studies on the relationship between social class and religion tend to highlight the demographic dimension of class, but neglect its symbolic dimension. By addressing the symbolic dimensions through a Bourdieuian approach, this article contends that religious tastes and styles can be employed as class markers within the sphere of religion. A case study on Argentinean Pentecostalism and in-depth analysis of a lower and middle class church illustrate how symbolic class differences are cultivated in the form of distinctive religious styles. While the lower class church displays a style marked by emotional expressiveness and the search for life improvement through spiritual practices, the middle class church performs a sober and calm style of Pentecostalism. The study highlights the role of styles in the reproduction of class boundaries, while shedding a critical light on the importance of tastes.

Class and politics in twenty-first century Norway: a homology of positions and position-taking

ABSTRACTThis article draws on Pierre Bourdieu’s rethinking of social class to investigate the connection between class and politics in contemporary society. We introduce a new class scheme that incorporates an often neglected hallmark of Bourdieu’s approach, namely the distinction between class fractions based on the preponderance of economic or cultural capital possessed. By relating our two-dimensional concept of class to a two-dimensional political space, we will show that the relationship between class and politics is homological – the systems of class divisions and political divisions exhibit a corresponding structure. The hierarchical dimension of class is associated with the divide between liberal and anti-liberal views on what is sometimes dubbed ‘new’ politics, whereas the capital composition dimension is connected with the classical left vs. right divide in terms of issues of redistribution, social spending and government interventions in the economy. We conclude by discussing whether political attitudes should be seen as a form of taste and as such on par with cultural tastes.

Hypergraphs with high projective dimension and 1-dimensional hypergraphs

(Dual) hypergraphs have been used by Kimura, Rinaldo and Terai to characterize squarefree monomial ideals [Formula: see text] with [Formula: see text], i.e. whose projective dimension equals the minimal number of generators of [Formula: see text] minus 1. In this paper, we prove sufficient and necessary combinatorial conditions for [Formula: see text]. The second main result is an effective explicit procedure to compute the projective dimension of a large class of 1-dimensional hypergraphs [Formula: see text] (the ones in which every connected component contains at most one cycle). An algorithm to compute the projective dimension is also provided. Applications of these results are given; they include, for instance, computing the projective dimension of monomial ideals whose associated hypergraph has a spanning Ferrers graph.

Treatment and post-treatment effects of functional therapy on the sagittal pharyngeal dimensions in Class II subjects

ObjectiveTo evaluate the craniofacial changes induced by functional appliances with special regard to the oro and nasopharyngeal sagittal airway dimensions in subjects with dentoskeletal Class II malocclusions when compared with an untreated Class II control group immediately after therapy and at long-term observation. MethodsA group of 40 patients (21 females and 19 males) with Class II malocclusion treated consecutively either with a Bionator or an Activator followed by fixed appliances was compared with a matched control group of 31 subjects (16 females and 15 males) with untreated Class II malocclusion. The treated sample was evaluated at T1, start of treatment (mean age: 9.9 ± 1.4 years); T2, end of functional treatment and prior to fixed appliances (mean age: 11.9 ± 1.3 years); and T3, long-term observation at the end of growth (mean age: 18.2 ± 2.1 years). Statistical comparisons were performed with independent sample t tests at T1 (baseline characteristics) and for the T1−T2, T2-T3, and T1-T3 changes. ResultsDuring active treatment the treated group showed a significant increment in lower airway dimension (PNS-AD1), as well as a significant improvement in the upper airway dimension (PNS-AD2). A significant decrease in the upper adenoid size (AD2-H) was also found. In the longterm evaluation, a significant increase in both lower and upper airway thickness (PNS-AD1; PNS-AD2) and a significant decrease in the upper adenoid thickness were still present in the treated group. ConclusionThe treatment with functional appliances produced significant favorable changes during active treatment in the oro- and nasopharyngeal sagittal airway dimensions in dentoskeletal Class II subjects when compared with untreated controls, and these changes were stable in the long-term.

A Study on the Dimension Model of “Teaching Style, Study Style and Examination Discipline” of Teachers Evaluate Student Classes

The research on the evaluation of students’ class by university teachers is of great significance to promote the reform of education and teaching and to improve the study idea. In this paper, the use of teacher evaluation student class dimension model, focus on building processes of “teaching style, examination discipline, style of study”. Through the questionnaire survey on the six aspects of teachers’ teaching style, learning attitude, learning content, learning method and effect, students' ability and test conditions, the dimension model is established, and bring up with 4 recommendations to students learning, teachers teaching, teaching management and evaluation methods.

Qualitative correlation between postoperatively increased vertical dimension and mandibular position in skeletal class III using partial-least-square path modeling

BackgroundThis study constructed a partial-least-square path-modeling (PLS-PM) model and found the pathway by which the postsurgical vertical dimension (VD) affects the extent of the final mandibular setback on the B point at the posttreatment stage for the skeletal class III surgery-first approach (SFA).MethodsThis study re-analyzed the data from the retrospective study by Lee et al. on 40 patients with skeletal class III bimaxillary SFA. Variables were obtained from cone beam computed tomography (CBCT)-generated cephalograms. Authors investigated all variables at each time point to build a PLS-PM model to verify the effect of the VD on the final setback of the mandible.ResultsFrom PLS-PM, an increase in VD10 was found to decrease the absolute value of the final setback amount of the mandible, which reflects the postsurgical physiological responses to both surgery and orthodontic treatment, which, in turn, can be interpreted as an increase in postoperative mandibular changes.ConclusionsTo resolve the issue of collinear cephalometric data, the present study adopted PLS-PM to assess the orthodontic treatment. From PLS-PM, it was able to summarize the effect of increased postsurgery occlusal vertical dimension on the increased changeability of the B point position at the posttreatment stage.

Assessment and Comparison of Oropharyngeal Airway Dimensions in Skeletal Class II Cases Treated With Forsus FRD and Twin Block Appliances

Abstract Aims: To assess the changes in the oropharyngeal airway (OAW) dimensions in individuals with retrognathic mandible treated with Forsus FRD and Twin Block appliance to correct the skeletal Class II mal relationship. Methodology: 40 individuals, with Class II skeletal pattern were selected as per inclusion criteria. Pre-treatment lateral cephalograms and hand wrist radiographs were obtained and analyzed. Group 1 with 20 individuals were treated with Forsus FRD and Group 2 with 20 individuals were treated with conventional Twin Block Appliance. Post treatment records were taken after the Class I molar relationship had been obtained. Pre and post treatment cephalograms were compared and analyzed. The data obtained was statistically evaluated using paired t test and unpaired t test. Results: On comparison of pre-treatment and post-treatment cephalograms, increase in Oropharyngeal Airway (OAW) measurements, such as Superior posterior airway space (SPAS), Middle airway space (MAS) and Inferior airway space (IAS) was very highly significant. Conclusion: Our results suggest the existence of a relationship between functional-orthopaedic treatment and increases in OAW dimensions in skeletal Class II growing subjects.