Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Observation on A-PRF promoting regeneration of osteochondral defects in rabbit knee joints

Objective·To explore the role of advanced platelet-rich fibrin (A-PRF) in osteochondral regeneration.Methods·Bone-marrow mesenchymal stem cells (BMSCs) and knee joint chondrocytes were obtained from New Zealand rabbits. A-PRF was obtained by low-speed centrifugation of the heart blood of rabbits. The histological structure of A-PRF was observed by an optical microscope. The release of growth factors in A-PRF was detected by ELISA, including platelet-derived growth factor, transforming growth factor-β, insulin-like growth factor, vascular endothelial growth factor, epidermal growth factor and fibroblast growth factor. A-PRF's cytotoxicity and capability for promoting the proliferation of rabbit BMSCs were detected by live/dead double staining and MTT methods. The effect of A-PRF on the gene expression of type Ⅱ collagen, aggrecan, alkaline phosphatase (ALP) and osteocalcin (OCN) in rabbit BMSCs was detected by real-time fluorescence quantitative polymerase chain reaction (qRT-PCR). Transwell chambers were used to determine the effect of A-PRF on the migration ability of rabbit BMSCs and the chondrocytes. Rabbit knee osteochondral defect models were established, and 18 rabbits were randomly divided into 3 groups. The A-PRF group (n=6) was implanted with A-PRF in the defect, the A-PRF+BMSCs group (n=6) was implanted with rabbit BMSCs on A-PRF, and the control group (n=6) did not undergo implantation. The rabbits were sacrificed 12 weeks after surgery and the knee joint specimens were stained with hematoxylin-eosin (H-E), toluidine blue and safranin O/fast green. Based on the surface morphology and histology of the knee joints, the International Cartilage Repair Society (ICRS) scoring system was used for macroscopic and histological scoring.Results·A-PRF had a loose network structure and can slowly release growth factors. No cytotoxicity to rabbit BMSCs was observed after adding A-PRF, and the the capability for promoting the proliferation of rabbit BMSCs was significantly increased at 24, 48 and 72 h after adding A-PRF (all P<0.05). Chondrogenesis-related gene Ⅱ collagen and aggrecan, as well as osteogenesis-related genes ALP and OCN were significantly up-regulated (all P<0.05). After adding A-PRF, the migration abilities of rabbit BMSCs and chondrocytes were significantly enhanced (both P<0.05), and the migration ability of rabbit BMSCs was significantly higher than that of chondrocytes (P=0.025). The joint surface morphology in the rabbit knee joint defect models was observed. It can be seen that the defects in the A-PRF group and the A-PRF+BMSCs group were basically restored, while the the defects in the control group were only covered by soft tissue. In the ICRS macroscopic score, there was no statistical difference between the A-PRF group and the A-PRF+BMSCs group, but the scores of the two groups were all significantly higher than those of the control group (all P<0.05). According to the histological results, both the A-PRF group and the A-PRF+BMSCs group formed osteochondral repair, but the cartilage in the A-PRF group was more mature, while the control group formed fibrous repair. In the ICRS histological score, there was no statistical difference between the A-PRF group and the A-PRF+BMSCs group, but the scores of both the groups were significantly higher than those of the control group (both P<0.05).Conclusion·Autologous A-PRF has good biocompatibility and the capability for promoting the proliferation of BMSCs. It can promote the repair of cartilage and subchondral bone both in vitro and in vivo

Intrinsic Surface Effects of Tantalum and Titanium on Integrin α5β1/ ERK1/2 Pathway-Mediated Osteogenic Differentiation in Rat Bone Mesenchymal Stromal Cells

Background/Aims: Accumulating evidence demonstrates the superior osteoinductivity of tantalum (Ta) to that of titanium (Ti); however, the mechanisms underlying these differences are unclear. Thus, the objective of the present study was to examine the effects of Ta and Ti surfaces on osteogenesis using rat bone mesenchymal stromal cells (rBMSCs) as a model. Methods: Ta and Ti substrates were polished to a mirror finish to minimize the influences of structural factors, and the intrinsic surface effects of the two materials on the integrin α5β1/mitogen-activated protein kinases 3 and 1 (ERK1/2) cascade-mediated osteogenesis of rBMSCs were evaluated. Alkaline phosphatase (ALP) activity, Alizarin Red staining, real-time polymerase chain reaction, and western blot assays of critical osteogenic markers were conducted to evaluate the effects of the two substrates on cell osteogenesis. Moreover, the role of the integrin α5β1/ERK1/2 pathway on the osteoinductive performance of Ta and Ti was assessed by up- and down-regulation of integrin α5 and β1 with RNA interference, as well as through ERK1/2 inhibition with U0126. Results: Osteogenesis of rBMSCs seeded on the Ta surface was superior to that of cells seeded on the Ti surface in terms of ALP activity, extracellular matrix calcification, and the expression of integrin α5, integrin β1, ERK1/2, Runt-related transcription factor 2, osteocalcin, collagen type I, and ALP at both the mRNA and protein levels. Moreover, down-regulation of integrin α5 or integrin β1, or ERK1/2 inhibition severely impaired the osteoblastic differentiation on the Ta surface. By contrast, over-expression of integrin α5 or integrin β1 improved osteogenesis on the Ti substrates, while subsequent ERK1/2 inhibition abrogated this effect. Conclusion: The integrin α5β1/ERK1/2 pathway plays a crucial role in regulating rBMSCs osteogenic differentiation; thus, the greater ability of a Ta surface to trigger integrin α5β1/ERK1/2 signaling may explain its better osteoinductivity. The different effects of Ta and Ti surfaces on rBMSC osteogenesis are considered to be related to the conductive behaviors between integrin α5β1 and the oxides spontaneously formed on the two metals. These results should facilitate the development of engineering strategies with Ta and Ti surfaces for improved osteogenesis in endosteal implants

Ridge Alterations following Socket Preservation Using a Collagen Membrane in Dogs

Background. The healing process following tooth extraction results in alveolar ridge resorption. The dimensional changes may complicate the subsequent implant procedure. Socket preservation using absorbable collagen membranes or a combination of membranes with calcium phosphate cement (CPC) particles might ensure that the alveolar ridge retains a suitable morphology for implant placement. Objective. To evaluate the quality and quantity of new bone regenerated after application of either collagen membranes alone covering the sockets or a combination of membranes with CPC particles added into the sockets in dogs. Materials and Methods. Six dogs were included in this study. The mandibular premolars were extracted. For each hemimandible, three premolar extraction sites were randomly assigned to one of the following treatments: a covering collagen membrane, CPC with a covering collagen membrane, and a socket left empty. Cone-beam computed tomography (CBCT) measurements, polyfluorochrome sequential labeling, and histological assessments were performed to investigate the healing ability and repair processes within a 6-month observation period. Results. Buccal bone height in the membrane group was significantly higher than that in the membrane+CPC and blank groups at 4 and 6 months after extraction. The mineral apposition rate over 2-4 months and the alizarin red-stained area in the membrane group were significantly higher than those in the other two groups. Histological analysis after 6 months of healing showed significantly higher amounts of newly formed bone in the membrane group than in the other groups. Conclusion. Extraction sites treated with collagen barrier membranes showed better protection than sites not covered with membranes. And the buccal bone wall of the socket was well preserved by collagen membrane without extra CPC materials. Socket preservation using absorbable membranes alone yielded better quality and quantity of regenerated bone inside the socket site

The Effect of Asymmetrical Occlusion on Surface Electromyographic Activity in Subjects with a Chewing Side Preference: A Preliminary Study

The relationship between asymmetrical occlusion and surface electromyographic activity (sEMG) in people with different chewing preferences is not clear. In this study, the 5 s sEMG changes in the masseter muscle (MM), sternocleidomastoid (SCM), lateral (LGA), and medial (MGA) gastrocnemius muscles were recorded in controls, and subjects with chewing side preference (CSP) during clench with bilateral (BCR), left (LCR), and right (RCR) posterior teeth placement of cotton rolls. The images of the middle 3 s were selected and expressed as the root mean square (unit: μV/s). The EMG waves of bilateral muscles were compared by computing the percentage overlapping coefficient (POC). Only the POCMM of the CSP showed gender differences at BCR and RCR. Between the control group and the CSP group, there were significant differences in the POCMM and the POCLGA at BCR. In addition, there was a significant difference in POCMM and POCSCM between the two populations in different occlusal positions. The change in the POCSCM correlated with the change in the POCMM (r = 0.415, p = 0.018). The experiment-induced asymmetrical occlusion showed that the altered symmetry of the MM correlated with the altered symmetry of the SCM. Long-term asymmetrical occlusion (i.e., CSP) not only affects MM but also has potential effects on other superficial muscles (e.g., LGA)

Masticatory efficiency in patients with partially dentate dentitions

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Multi-Agent Based Adaptive Consensus Control for Multiple Manipulators with Kinematic Uncertainties

Abstract — An adaptive control approach is proposed to deal with the multiple manipulators consensus problem based on the multi-agent theory. In the current multi-agent literature, agents were assumed to have determined models. However, the practical manipulator’s kinematics contains uncertain param-eters. By using the projection method, the adaptive updating law for uncertain kinematic parameters is derived. Then, the estimated manipulator Jacobian matrix can be obtained to design the decentralized controller. By the proposed controller, all the manipulators ’ end-effectors move towards the same configuration to achieve certain coordination tasks. In addition, performance of the control system is analyzed by the Lyapunov method, and the consensus error is proved to approach zero. Finally, the effectiveness of the proposed scheme is illustrated by simulations on a multiple PUMA 560 robots system. I

RETRACTED ARTICLE: Polymerase Spiral Reaction (PSR): A novel isothermal nucleic acid amplification method

Abstract In this study, we report a novel isothermal nucleic acid amplification method only requires one pair of primers and one enzyme, termed Polymerase Spiral Reaction (PSR) with high specificity, efficiency and rapidity under isothermal condition. The recombinant plasmid of bla NDM-1 was imported to Escherichia coli BL21 and selected as the microbial target. PSR method employs a Bst DNA polymerase and a pair of primers designed targeting the bla NDM-1 gene sequence. The forward and reverse Tab primer sequences are reverse to each other at their 5’ end (Nr and N), whereas their 3’ end sequences are complementary to their respective target nucleic acid sequences. The PSR method was performed at a constant temperature 61 °C–65 °C, yielding a complicated spiral structure. PSR assay was monitored continuously in a real-time turbidimeter instrument or visually detected with the aid of a fluorescent dye (SYBR Greenı) and could be finished within 1 h with a high accumulation of 109 copies of the target and a fine sensitivity of 6 CFU per reaction. Clinical evaluation was also conducted using PSR, showing high specificity of this method. The PSR technique provides a convenient and cost-effective alternative for clinical screening, on-site diagnosis and primary quarantine purposes

An Injectable Fibrin Scaffold Rich in Growth Factors for Skin Repair

Platelet aggregates, such as PRP, PRF, and CGF, have been used alone or in combination with other grafting materials to enhance restoration outcomes. The process for preparing these autografting materials requires two-step centrifugation or specific centrifuges. In this study, we obtained an injectable fibrin scaffold (IFS) rich in growth factors by one-step centrifugation of whole blood from rabbits. The purpose of this study is to introduce some characteristics of IFS. This scaffold was characterized using various techniques, including Masson’s trichrome staining, scanning electron microscopy, porosity measurements, and cell counting. The sustained release of growth factors, including PDGF, VEGF, TGF-β1, IGF, FGF, and EGF, was quantified using ELISA assay. The obtained IFS was tested for its effects on cell proliferation, extracellular matrix deposition, and full-thickness skin defect repair. The prepared IFS is characterized by a loose fibrin network structure with white blood cells and platelets that slowly release growth factors and can promote the healing of skin defects via the promotion of cell proliferation, collagen deposition, and tissue revascularization. In addition, its liquid properties and porous structure are conducive to its application as a therapeutic component in tissue engineering