Dimension Of Class Research Articles

Fault-Tolerant Metric Dimension of Barycentric Subdivision of Cayley Graphs

Metric dimension and fault-tolerant metric dimension of any graph G is subject to size of resolving set. It has become more important in modern GPS and sensors based world as resolving set ensures that in case of semi outage system is still scalable using redundant interfaces. Metric dimension of several interesting classes of graphs have been investigated like Cayley digraphs, Cartesian product of graphs, wheel graphs, convex polytopes and certain networks for categorical product of graphs. In this paper we used the phenomena of barycentric subdivision of graph and proved that fault-tolerant metric dimension of barycentric subdivision of Cayley graph is constant.

Metric Dimension of Irregular Convex Triangular Networks

Irregular convex triangular networks consist of the interior of a 6-sided convex polygon drawn on the infinite triangular network. Formal description of these applicable networks is provided. In the main result it is proved that the metric dimension of an irregular convex triangular network is either 2 or 3 and the determination of which value is the right one is specified. Metric dimensions of various graph classes and interconnection networks are also collected.

Volumetric analysis of pharyngeal airway dimensions and hyoid bone position following orthognathic surgery in skeletal class III patients: a cross sectional cephalometric study

Background: Objective of the study was to determine linear and volumetric changes in pharyngeal airway dimensions in class III patients treated by different modalities of orthognathic surgery and to compare the results of different orthognathic surgical modalities, and determine the change at the position of the hyoid bone. Methods: Pre and post-treatment lateral cephalogram of 53 class III adult patients who were treated by different modalities of orthognathic surgery studied to assess the changes in pharyngeal airway dimensions and hyoid bone position after orthognathic surgery. 28 patients were treated with mandibular set back, and 25 patients were treated with Bijaw surgery. Lateral cephalogram records were taken before treatment (T1), after surgery (T2), the end of the fixed treatment (T3) and 1 year after debonding (T4). Results: Interception of both surgical modalities has significant impact on various skeletal and pharyngeal parameters i.e., BMeH (0.00), PNS (0.009), MPS (0.13), GOP (0.001), IPS (0.007), SAS (0.006), and MAS (0.00). OJ (overjet) and OB (overbite) was significant especially after time interval of one year. In Bijaw groups, PPST4 parameter was significantly increased (0.0000), SPST4 (0.000), GOP (0.000), EPS (0.000) and IPS parameter was significantly decreased (0.045). Significant difference was observed in T4 time interval in superior pharyngeal airway space, posterior airway space and middle airway space with (p<0.05). Conclusions: Pharyngeal airway is significantly altered following orthognathic surgery in class III patients and it depends on the type of surgical modality employed were Bijaw surgery has significant impact on oropharyngeal and hypopharyngeal airway space.

Modification of Space Debris Trajectories through Lasers: Dependence of Thermal and Impulse Coupling on Material and Surface Properties

Environmental pollution exists not only within our atmosphere but also in space. Space debris is a critical problem of modern and future space infrastructure. Congested orbits raise the question of spacecraft disposal. Therefore, state-of-the-art satellites come with a deorbit system in cases of low Earth orbit (LEO) and with thrusters for transferring into the graveyard orbit for geostationary and geosynchronous orbits. No practical solution is available for debris objects that stem from fragmentation events. The present study focuses on objects in LEO orbits with dimensions in the dangerous class of 1 to 10 cm. Our assumed method for the change of trajectories of space debris is laser ablation for collision avoidance or complete removal by ground-based laser systems. Thus, we executed an experimental feasibility study with focus on thermal and impulse coupling between laser and sample. Free-fall experiments with a 10 ns laser pulse at nominally 60 J and 1064 nm were conducted with GSI Darmstadt’s nhelix laser on various sample materials with different surfaces. Ablated mass, heating, and trajectory were recorded. Furthermore, we investigated the influence of the sample surface roughness on the laser-object interaction. We measured impulse coupling coefficients between 7 and 40 µNs/J and thermal coupling coefficients between 2% and 12.5% both depending on target fluence, surface roughness, and material. Ablated mass and changes in surface roughness were considered via simulation to discriminate their relevance for a multiple shot concept.

Gendered familialism in a Mediterranean context: women’s labor market participation and early childhood education and care in Turkey

AbstractThis article explores the relationship between women’s labor market participation and early childhood education and care (ECEC) in Turkey within a broader Mediterranean context. Since the 1990s, there have been significant changes in the familialist models in the Mediterranean region driven by women’s increased labor market participation and the expansion of ECEC services. The transformations in the region have unveiled a significant link between the expansion of preschool education and an increase in women’s labor market participation. Turkey missed this critical juncture in the 1990s, as indicated by the low employment rates of women and below-the-Organisation for Economic Co-operation and Development (OECD)-average preschool enrolment. Through a comparative perspective that examines the slow progress in both areas in Turkey as well as the gendered feature of its familialist model, the article emphasizes the need for closer analysis of the link between ECEC and the low labor force participation of women. Given that the expansion of ECEC in the 2000s has taken place through market-driven services, the article concludes that the link between ECEC and women’s labor market participation exhibits a class dimension. Thereby, women from lower socio-economic groups are increasingly experiencing the impact of the gendered characteristics inherent in the familialist regime in Turkey.

Working-class Palestinian mothers in Israel: agency, habitus, and maternal responsibility

ABSTRACT Mothers are perceived as responsible for both their children’s complementary education and their emotional well-being, a social construction that challenges the perception of maternal responsibility among working-class Palestinian mothers in Israel in their effort to function appropriately in the face of three power structures: the school system, welfare policies, and the family. This study reveals how working-class Palestinian mothers in Israel negotiate these three axes by exploring their actions as a form of agency from a specific cultural and class perspective, based on the concept of habitus as a theoretical framework that makes possible an examination of mothers’ personal experience as an integral part of the dimension of social class. Semi-structured interviews were conducted with 20 working-class Palestinian mothers. The findings indicate that mothers’ agency enables change within the spaces of institutionalized structures such as school and welfare services but is limited to directing change in the cultural patriarchal structure.

A note on hardness of computing recursive teaching dimension

In this short note, we show that the problem of computing the recursive teaching dimension (RTD) for a concept class (given explicitly as input) requires nΩ(log⁡n)-time, assuming the exponential time hypothesis (ETH). This matches the running time nO(log⁡n) of the brute-force algorithm for the problem.

Local Metric Dimension of Certain Classes of Circulant Networks

Let G(V,E) be a graph with a set of vertices V and a set of edges E. Then, a minimum subset Wl of V is said to be a local metric basis of G if for any two adjacent vertices u,v∈V∖Wl there exists a vertex w∈Wl such that d(u,w) ≠ d(v,w). The cardinality of a local metric basis is referred to as the local metric dimension of the graph G denoted by βl(G). In this paper, we investigate the local metric dimensions of certain circulant-related architectures such as Harary graphs Hk,n with even k or n, Toeplitz networks, and ILLIAC networks.

Assessment of Soft Tissue, Airway Dimension and Hyoid Bone Position in Class II Patients Treated by PowerScope Class 2 Corrector.

This study aims to assess the changes in the soft tissue, pharyngeal airway dimensions, and hyoid bone position in patients treated with PowerScope Class 2 corrector to correct the skeletal Class II pattern. This study was conducted on a sample of 20 cases diagnosed with Class II malocclusion. The lateral cephalograms were taken before (T1) and after functional appliance therapy (T2) and were traced. The outcomes were compared for the mean changes in soft tissue, airway way dimension, and hyoid bone position. The paired t-test was used for the data comparisons wherein p < 0.05 was kept for statistical significance. The mean values before and after treatment for H angle, mentolabial angle, lower lip E-line, upper lip S-line, lower lip S-line, and lip strain were 19.88 ± 2.77 vs 17.13 ± 1.659, 94.09 ± 12.164 vs 101.75 ± 11.28, -2.47 ± 1.213 vs -1.38 ± 0.976, 3.99 ± 0.19 vs 2.64 ± 0.32, 9.01 ± 0.247 vs 9.43 ± 0.238, 10.24 ± 0.510 vs 10.64 ± 0.52, respectively, which were statistically significant (p < 0.05). All airway spaces (except for lower pharyngeal space) and hyoid bone parameters were significantly improved posttreatment. The facial convexity, upper E-line, Z-angle, nasolabial angle, and lower pharyngeal space did not show statistically significant changes. The rest of the soft tissue parameters, oropharyngeal air spaces, and hyoid positioning measured in the study showed significant improvement after treatment with the PowerScope appliance in Class II patients. Class II malocclusion is the most common dental anomaly with a high degree of prevalence in the population. This study will help the clinician in understanding the improvement of soft tissue, airway dimension, and hyoid bone position changes on treatment with a fixed functional appliance for the correction of Class II cases, thereby ensuring the greater success of orthodontic therapy in the future.

Analisis Pemahaman Konsep dalam Menyelesaikan Soal Geometri Dimensi Tiga Pada Peserta Didik SMK di Kota Makassar

This type of research is descriptive research. This study aims to determine the understanding of concepts in solving three-dimensional geometry problems in class XI students of SMK Muhammadiyah 3 Makassar. The population in this study were all students of class XI SMK Muhammadiyah 3 Makassar. Furthermore, selecting samples with Cluster Random Sampling technique. The selected sample in this study is class XI Accounting Department. From this sample, interviews will be continued with 9 students consisting of 3 students in the high category, 3 students in the medium category, and 3 students in the low category. The instruments in this study in the form of concept understanding tests and interview guidelines used to determine the understanding of concepts in solving three-dimensional geometry problems in class XI students of SMK Muhammadiyah 3 Makassar. The data analysis technique in this study is descriptive statistical analysis with the aim of describing the understanding of mathematical concepts of students in class XI SMK Muhammadiyah 3 Makassar. Based on the results of data analysis and discussion that has been stated, the conclusion in this study is the understanding of concepts in solving geometry problems of three dimensions in class XI students of SMK Muhammadiyah 3 Makassar is on the indicators: (1) Concept understanding on indicator I, namely giving examples and not examples of a concept by 91%, (2) Concept understanding on indicator II, namely presenting concepts in various forms of mathematical representation by 53%, and (3) Concept understanding on indicator III, namely applying concepts or algorithms in problem solving by 57%.

Associations of Specific Indicators of Adult–Child Interaction Quality and Child Language Outcomes: What Teaching Practices Influence Language?

ABSTRACT Research Findings: This study aims to extend our knowledge regarding contributions of educator–child interactions to child language outcomes by examining the extent to which specific dimensions of the CLASS observational tool of educator–child interactions are associated with child language abilities, utilizing data from an Australian longitudinal study of over 2,000 children attending formal Early Childhood Education and Care (ECEC). The analysis included a novel measurement model fitted to the data to allow each CLASS dimension to be modeled separately. Results showed that each CLASS dimension was associated with initial average language abilities. Small, negative effects of Emotional Support dimensions on growth of children’s average Understanding Directions score were found, but there were no associations between any of the dimensions and average growth in Verbal Ability. None of the Instructional Support dimensions (which are language focused) predicted growth in language abilities. These null findings are addressed in the discussion. Practice or Policy: Findings from this study illustrate that, typically, ECEC programs rate low on dimensions of quality developed to capture language-promoting educator–child interactions. Findings also suggest a selection effect related to equity of access to classroom quality with children with the highest initial language abilities in the highest quality classrooms.

ACTN3 gene variations in various Ethnic populations and its association with Malocclusion – A Literature Review

Genetic etiology of Skeletal Malocclusion has been explored extensively over recent years with the advent of advances in molecular technologies. Studies have been reported that the masticatory muscles regulate skeletal development and few recent works of literature report that the muscle growth regulators influence the facial proportions in sagittal and vertical dimensions in Skeletal Class II malocclusion. This review is a humble attempt to highlight the role of one such muscle gene known as ACTN3 and its association with Skeletal Class II malocclusion.

Correlating condylar dimensions with growth pattern: A radiographicstudy

As lateral cephalograms are one of the mandatory pretreatment diagnostic radiographs for identifying the structural changes of the craniofacial skeleton including the mandibular condylar region, the present study attempts to evaluate the condylar dimensions in skeletal Class I cases with three different growth patterns using lateral cephalograms. This study aimed to evaluate the dimensions of the mandibular condyle and to determine any correlation with growth patterns in skeletal Class I patients. This retrospective study was conducted on the lateral cephalogram of the patients reported for orthodontic treatment. After applying inclusion and exclusion criteria 60 lateral cephalograms were selected and distributed in three groups. The measurements of condylar neck length, condylar neck inclination, condylar width, and ramal length were measured on lateral cephalograms. The mean condylar dimensions were 12.18 ±1.44 mm of condylar width, condylar neck length of 16.82 ± 3.23 mm, and condylar inclination of 114.43⁰ ± 13.98⁰. The differences in condylar width among the three groups were not statistically significant. Pearson correlation reveals a statistically highly significant positive correlation between condylar neck length and ramal length. The condylar inclination was negatively correlated with the condylar neck length and ramal length but was not statistically significant. Within the scope of this study, it can be concluded that condylar width does not have a significant correlation with growth patterns. With the increase in condylar neck length, the overall ramal length also increases. There exists a negative correlation of condylar inclination with ramal length and condylar neck length but it was statistically not significant.

Primal and dual combinatorial dimensions

We give tight bounds on the relation between the primal and dual of various combinatorial dimensions, such as the pseudo-dimension and fat-shattering dimension, for multi-valued function classes. These dimensional notions play an important role in the area of learning theory. We first review some (folklore) results that bound the dual dimension of a function class in terms of its primal, and after that give (almost) matching lower bounds. In particular, we give an appropriate generalization to multi-valued function classes of a well-known bound due to Assouad (1983), that relates the primal and dual VC-dimension of a binary function class.

RootSlice-A novel functional-structural model for root anatomical phenotypes.

Root anatomy is an important determinant of root metabolic costs, soil exploration, and soil resource capture. Root anatomy varies substantially within and among plant species. RootSlice is a multicellular functional-structural model of root anatomy developed to facilitate the analysis and understanding of root anatomical phenotypes. RootSlice can capture phenotypically accurate root anatomy in three dimensions of different root classes and developmental zones, of both monocotyledonous and dicotyledonous species. Several case studies are presented illustrating the capabilities of the model. For maize nodal roots, the model illustrated the role of vacuole expansion in cell elongation; and confirmed the individual and synergistic role of increasing root cortical aerenchyma and reducing the number of cortical cell files in reducing root metabolic costs. Integration of RootSlice for different root zones as the temporal properties of the nodal roots in the whole-plant and soil model OpenSimRoot/maize enabled the multiscale evaluation of root anatomical phenotypes, highlighting the role of aerenchyma formation in enhancing the utility of cortical cell files for improving plant performance over varying soil nitrogen supply. Such integrative in silico approaches present avenues for exploring the fitness landscape of root anatomical phenotypes.

An Offline-Online Decomposition Method for Efficient Linear Bayesian Goal-Oriented Optimal Experimental Design: Application to Optimal Sensor Placement

Bayesian optimal experimental design (OED) plays an important role in minimizing model uncertainty with limited experimental data in a Bayesian framework. In many applications, rather than minimizing the uncertainty in the inference of model parameters, one seeks to minimize the uncertainty of a model-dependent quantity of interest (QoI). This is known as goal-oriented OED (GOOED). Here, we consider GOOED for linear Bayesian inverse problems governed by large-scale models represented by partial differential equations (PDE) that are computationally expensive to solve. In particular, we consider optimal sensor placement by maximizing an expected information gain (EIG) for the QoI. We develop an efficient method to solve such problems by deriving a new formulation of the goal-oriented EIG. Based on this formulation we propose an offline-online decomposition scheme that achieves significant computational reduction by computing all of the PDE-dependent quantities in an offline stage just once, and optimizing the sensor locations in an online stage without solving any PDEs. Moreover, in the offline stage we need only to compute low-rank approximations of two Hessian-related operators. The computational cost of these low-rank approximations, measured by the number of PDE solves, does not depend on the parameter or data dimensions for a large class of elliptic, parabolic, and sufficiently dissipative hyperbolic inverse problem that exhibit dimension-independent rapid spectra decay. We carry out detailed error analysis for the approximate goal-oriented EIG due to the low-rank approximations of the two operators. Furthermore, in the online stage we extend a swapping greedy method to optimize the sensor locations developed in our recent work that is demonstrated to be more efficient than a standard greedy method. We conduct a numerical experiment for a contaminant transport inverse problem with an infinite-dimensional parameter field to demonstrate the efficiency, accuracy, and both data- and parameter-dimension independence of the proposed algorithm.

Compact Minimal Submanifolds in a Large Class of Riemannian Manifolds

Through a new technique, we provide uniqueness, rigidity and non-existence results for compact minimal submanifolds of arbitrary dimension in a large class of Riemannian manifolds, which include between others, Riemannian double-twisted and warped products. Moreover, we show that our results can be applied in particular, to space forms and Cartan–Hadamard manifolds, re-obtaining several classic results in a different approach. Interesting applications to Geometric Analysis are also showed.

Ethnic residential segregation in the city of Milan at the interplay between social class, housing and labour market

This article analyses the spatial distribution of foreigners living in the city of Milan, based on data from the civil registry and relying on theories and methods from the residential segregation literature, exploring the dimensions of evenness, exposure, concentration, centralisation and clustering, as well as analysing migrants’ over/under-representation in specific areas through maps of their location quotients. Despite the low degree of ethnic residential segregation detected, we highlight the presence of persistent dynamics that exclude ethnic minorities from the wealthiest areas of the city. The most relevant case is that of the Chinese, clustering in some peripheral areas north of the historic centre, where they have established an enclave economy, often making their residence coincide with their workplace and running commercial activities mostly directed towards their compatriots. The Egyptians, constituting the most numerous foreign group in the city, show a completely different settlement pattern, being more integrated into the social tissue and more scattered throughout the city. In the context of a city strongly polarised between a wealthy centre and progressively deprived peripheral belts, the only foreign groups with a marked presence in the city core are those traditionally employed in domestic work, which are however excluded from life in the public places in which they reside. Overall, the class dimension seems to prevail over the ethnic in shaping population settlement patterns within the city.

Evaluation of Hard Tissue, Soft Tissue and Airway Changes Post Twin Block Therapy: An In-vitro Study

Introduction: Aesthetic improvement happens to be one of the main reasons for seeking orthodontic treatment in patients with Angle’s Class II malocclusion. Prognathic maxilla, retrognathic mandible or a combination of both are the main aetiological factors for this malocclusion. Growth modification treatment with different methods can be performed in order to correct skeletal class II malocclusion. Appliance therapy to correct similar malocclusions should immaculately be directed towards addressing the dentoskeletal discord, in order to gain a favourable facial aesthetic result. Aim: To assess the effects of twin block on mandibular length, soft tissue profile and Oropharyngeal Airway (OAW) dimensions in skeletal class II malocclusion patients. Materials and Methods: An in-vitro study was carried out in the Department of Paedodontics at Sardar Patel Postgraduate Institute of Dental and Medical Sciences, Lucknow from June 2018 to March 2021. Study was done on lateral cephalograms of 15 growing children with Angle’s Class II Division 1 malocclusion in the age group of 9-12 years, who had undergone functional appliance therapy with twin block appliance. Standardised lateral cephalograms were evaluated at pretreatment (0 month) and postactive phase of twin-block therapy (9-12 months). Selected hard tissue, soft tissue and airway landmarks were marked and traced to evaluate hard tissue, soft tissue and airway changes. The data was analysed using statistical package for social sciences (SPSS) version 21. Results: There was a statistically significant increase in effective mandibular length (Condyle-Gnathion) and mandibular base length Gonion-Pogonion (Go-Pog) values (p&lt;0.001). Significant decrease in the facial convexity Glabella- Soft tissue Nasion (G-Sn) Soft tissue Nasion- Soft tissue Pogonion (Sn-Pog) was observed and airway dimensions showed significant increase after twin block therapy. Conclusion: Correction of Class II malocclusion by twin block appliance resulted in significant cephalometric changes in the hard tissue profile (increase in mandibular length), together with clinically favourable soft tissue changes and OAW dimensions.

An exact computation for mixed multifractal dimensions of sets and measures

In the present work, we are concerned with the estimation of some mixed variants of multifractal dimensions for a special class of measures characterized by a weak Ahlfors assumption applying mixed multifractal generalizations of Hausdorff and packing measures. Exact computation of such dimensions is shown to be valid for a class of Moran-type measures in some special cases.