Efficient Network Structures with Separable Heterogeneous Connection Costs

We introduce a heterogeneous connection model for network formation to capture the effect of cost heterogeneity on the structure of efficient networks. In the proposed model, connection costs are assumed to be separable, which means the total connection cost for each agent is uniquely proportional to its degree. For these sets of networks, we provide the analytical solution for the efficient network and discuss stability impli- cations. We show that the efficient network exhibits a core-periphery structure, and for a given density, we find a lower bound for clustering coefficient of the efficient network.Comment: 9 page

The reduction number of an algebra

Abstract. We introduce the technique of tracking numbers of graded algebras and modules. It is a modified version of the first Chern class of its free resolution relative to any of its standard Noether normalizations. Several estimations are obtained which are used to bound the length of chains of algebras occurring in the construction of the integral closure of a graded domain. Noteworthy is a quadratic bound on the multiplicity for all chains of algebras that satisfy the condition S2 of Serre. 1

Assessing joint space and condylar position in the people with normal function of temporomandibular joint with cone-beam computed tomography

Background: The optimal position of the condyle in glenoid fossa is a fundamental question in dentistry. There is no quantitative standard for the optimal position of mandibular condyle in the glenoid fossa in our population. The purpose of this study is to assess the position of the condyle by cone beam computed tomography (CBCT) images in patient with normal function of temporomandibular joint (TMJ). Materials and Methods: In this cross-sectional study, CBCT images of 40 class I skeletal patients (15 males and 25 females) without history of TMJ disorders were selected. Next, the anterior, superior and posterior joint spaces (Ajs, Sjs, Pjs) were measured on the two true central sagittal slices. Then medial (M) and lateral (L) joint spaces on true coronal view were measured in the right and left sides, separately. After that, P/A ratio, S/A ratio and M/L ratio were calculated. Finally, a paired t-test and independent samples t-test were employed for analysis. Results: The centric position of the condyle in glenoid fossa was more common (92.5%) than other positions. Significant differences in Ajs, Sjs, Pjs, Mjs and Ljs values between two sides were observed (P ≤ 0.05). Additionally, Sjs showed statistically significant differences between the sexes (P = 0.05). P/A ratio and S/A ratio had significant differences between two sides but not between those sexes. Conclusion: The assessment of joint spaces in right and left sides should be done independently. Overall, the measured joint spaces except Sjs are not different in two sexes. The data from this study could be a useful and comparable reference for the clinical assessment of condylar position in patients with normal functional joints

Evaluation of the nasopalatine canal with cone-beam computed tomography in an Iranian population

Background: Implant placement plays a vital role in oral rehabilitation following loss of the incisors. Thus, having knowledge of anatomical variations of adjacent neurovascular structures especially the nasopalatine canal (NPC) is essential. Due to the lack of basic information in Iran about the morphology of this canal and the probability of its variety in different populations, this study was designed on an Iranian population. Materials and Methods: In this descriptive study, we selected cone-beam computed tomography images of 198 patients comprising of 98 males and 100 females in two dental groups (edentulous or dentate). The shape of the nasopalatine foramen and the form of the canal in axial views were assessed. Then, the canal height and its diameter at the palatal, middle and nasal levels in cross-sectional images were measured. The available bone in the buccal and palatal sides of the canal was assessed. Data analysis was carried out using a Chi-square test and an independent t-test (P ≤ 0.05). Results: The majority of the samples (81.8%) presented a single foramen. Cylindrical shape (57.6%) was the most frequently detected canal form. The mean of the estimated canal height was 12.84 ± 2.88 mm. The canal diameter at the palatal level between the sexes and dental groups showed statistically significant differences. Conclusion: In our investigated population, the NPC form was mainly cylindrical with a single opening foramen. The mean of the canal height was higher than that found in other populations. Furthermore, the canal diameter in the edentulous group was greater than that observed in the other group