An infinite natural sum

As far as algebraic properties are concerned, the usual addition on the class of ordinal numbers is not really well behaved; for example, it is not commutative, nor left cancellative etc. In a few cases, the natural Hessemberg sum is a better alternative, since it shares most of the usual properties of the addition on the naturals. A countably infinite version of the natural sum has been used in a recent paper by V\"a\"an\"anen and Wang, with applications to infinitary logics. We provide an order theoretical characterization of this operation. We show that this countable natural sum differs from the more usual infinite ordinal sum only for an initial finite "head" and agrees on the remaining infinite "tail". We show how to evaluate the countable natural sum just by computing a finite natural sum. Various kinds of infinite mixed sums of ordinals are discussed.Comment: v3 added a remark connected with surreal number

Genetic algebras and time continuous models

It is shown how linear genetic algebras, ordinarily applied in situations with discrete time, will also simplify certain systems of differential equations in time continuous models. These models describe the variation of genotype frequencies in infinite populations in different mating systems. The cases considered include matings between individuals randomly drawn from the population at each moment, a population which is continuously backcrossed to a second, constant population, and a population divided into two age groups, which take part in the matings with different intensities. For the first case the general theory is applied to an example with tetraploids having a mixture of chromatid and chromosome segregation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33864/1/0000125.pd

A short-term clinical study of marginal bone level change around microthreaded and platform-switched implants

PURPOSE: The marginal bone levels around implants following restoration are used as a reference for evaluating implant success and survival. Two design concepts that can reduce crestal bone resorption are the microthread and platform-switching concepts. The aims of this study were to analyze the placement of microthreaded and platform-switched implants and their short-term survival rate, as well as the level of bone around the implants. METHODS: The subjects of this study were 27 patients (79 implants) undergoing treatment with microthreaded and platform-switched implants between October 2008 and July 2009 in the Dental Hospital of Yonsei University Department of Periodontology. The patients received follow-up care more than 6 months after the final setting of the prosthesis, at which time periapical radiographs were taken. The marginal bone level was measured from the reference point to the lowest observed point of contact between the marginal bone and the fixture. Comparisons were made between radiographs taken at the time of fixture installation and those taken at the follow-up visit. RESULTS: During the study period (average of 11.8 months after fixture installation and 7.4 months after the prosthesis delivery), the short-term survival rate of microthreaded and platform-switched implants was 100% and the marginal bone loss around implants was 0.16±0.08 mm, the latter of which is lower than the previously reported values. CONCLUSIONS: This short-term clinical study has demonstrated the successful survival rates of a microthread and platform-switched implant system, and that this system is associated with reduced marginal bone loss.ope

Bone Engineering of Maxillary Sinus Bone Deficiencies Using Enriched CD90+ Stem Cell Therapy: A Randomized Clinical Trial

Bone engineering of localized craniofacial osseous defects or deficiencies by stem cell therapy offers strong prospects to improve treatment predictability for patient care. The aim of this phase 1/2 randomized, controlled clinical trial was to evaluate reconstruction of bone deficiencies of the maxillary sinus with transplantation of autologous cells enriched with CD90+ stem cells and CD14+ monocytes. Thirty human participants requiring bone augmentation of the maxillary sinus were enrolled. Patients presenting with 50% to 80% bone deficiencies of the maxillary sinus were randomized to receive either stem cells delivered onto a β‐tricalcium phosphate scaffold or scaffold alone. Four months after treatment, clinical, radiographic, and histologic analyses were performed to evaluate de novo engineered bone. At the time of alveolar bone core harvest, oral implants were installed in the engineered bone and later functionally restored with dental tooth prostheses. Radiographic analyses showed no difference in the total bone volume gained between treatment groups; however, density of the engineered bone was higher in patients receiving stem cells. Bone core biopsies showed that stem cell therapy provided the greatest benefit in the most severe deficiencies, yielding better bone quality than control patients, as evidenced by higher bone volume fraction (BVF; 0.5 versus 0.4; p = 0.04). Assessment of the relation between degree of CD90+ stem cell enrichment and BVF showed that the higher the CD90 composition of transplanted cells, the greater the BVF of regenerated bone (r = 0.56; p = 0.05). Oral implants were placed and restored with functionally loaded dental restorations in all patients and no treatment‐related adverse events were reported at the 1‐year follow‐up. These results provide evidence that cell‐based therapy using enriched CD90+ stem cell populations is safe for maxillary sinus floor reconstruction and offers potential to accelerate and enhance tissue engineered bone quality in other craniofacial bone defects and deficiencies (Clinicaltrials.gov NCT00980278). © 2015 American Society for Bone and Mineral Research. © 2015 American Society for Bone and Mineral ResearchPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112016/1/jbmr2464.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/112016/2/jbmr2464-sup-0009-SupLegend-S1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/112016/3/jbmr2464-sup-0008-SupTab-S4.pd

Multipotential stromal cell abundance in cellular bone allograft: comparison with fresh age-matched iliac crest bone and bone marrow aspirate

Aim: To enumerate and characterize multipotential stromal cells (MSCs) in a cellular bone allograft and compare with fresh age-matched iliac crest bone and bone marrow (BM) aspirate. Materials and methods: MSC characterization used functional assays, confocal/scanning electron microscopy and whole-genome microarrays. Resident MSCs were enumerated by flow cytometry following enzymatic extraction. Results: Allograft material contained live osteocytes and proliferative bone-lining cells defined as MSCs by phenotypic and functional capacities. Without cultivation/expansion, the allograft displayed an 'osteoinductive' molecular signature and the presence of CD45-CD271+CD73+CD90+CD105+ MSCs; with a purity over 100-fold that of iliac crest bone. In comparison with BM, MSC numbers enzymatically released from 1 g of cellular allograft were equivalent to approximately 45 ml of BM aspirate. Conclusion: Cellular allograft bone represents a unique nonimmune material rich in MSCs and osteocytes. This osteoinductive graft represents an attractive alternative to autograft bone or composite/synthetic grafts in orthopedics and broader regenerative medicine settings

Exploring the Fundamental Dynamics of Error-Based Motor Learning Using a Stationary Predictive-Saccade Task

The maintenance of movement accuracy uses prior performance errors to correct future motor plans; this motor-learning process ensures that movements remain quick and accurate. The control of predictive saccades, in which anticipatory movements are made to future targets before visual stimulus information becomes available, serves as an ideal paradigm to analyze how the motor system utilizes prior errors to drive movements to a desired goal. Predictive saccades constitute a stationary process (the mean and to a rough approximation the variability of the data do not vary over time, unlike a typical motor adaptation paradigm). This enables us to study inter-trial correlations, both on a trial-by-trial basis and across long blocks of trials. Saccade errors are found to be corrected on a trial-by-trial basis in a direction-specific manner (the next saccade made in the same direction will reflect a correction for errors made on the current saccade). Additionally, there is evidence for a second, modulating process that exhibits long memory. That is, performance information, as measured via inter-trial correlations, is strongly retained across a large number of saccades (about 100 trials). Together, this evidence indicates that the dynamics of motor learning exhibit complexities that must be carefully considered, as they cannot be fully described with current state-space (ARMA) modeling efforts

Quantificação de fatores de crescimento na pele de equinos tratada com plasma rico em plaquetas

O plasma rico em plaquetas (PRP) é um produto derivado da centrifugação do sangue total, sendo rico em fatores bioativos, como os de crescimento. Apesar da ampla utilização em processos cicatriciais, há controvérsia sobre a eficácia da terapia na cicatrização cutânea. O objetivo desse estudo foi quantificar e comparar a concentração dos fatores TGF-β1 e PDGF-BB no PRP, plasma sanguíneo e pele, durante diferentes fases do processo de cicatrização da pele tratada ou não com PRP. Foram utilizados sete equinos machos castrados, mestiços, hígidos, com idade entre 16 e 17 (16,14±0,63) anos. Três lesões em formato quadrangular (6,25cm²) foram produzidas cirurgicamente nas regiões glúteas direita e esquerda de todos os animais. Doze horas após indução das feridas, 0,5mL do PRP foi administrado em cada uma das quatro extremidades das feridas de uma das regiões glúteas (Grupo tratado = GT), escolhida aleatoriamente. A região contralateral foi utilizada como controle (GC). As feridas foram submetidas à limpeza diária com água Milli Q, e amostras foram obtidas mediante biópsias realizadas com Punch de 6mm. Foram obtidas seis biópsias de pele, sendo a primeira realizada logo após a produção da ferida (T0), e as demais com 1 (T1) 2 (T2) 7 (T3) e 14 (T4) dias após a indução da lesão. A sexta biópsia (T5) foi obtida após completo fechamento da pele, que ocorreu aproximadamente aos 37 dias (36,85±7,45, GC; 38,85±6,46, GT). Também foram obtidas amostras de sangue com EDTA em todos os tempos mencionados. A quantificação dos fatores de crescimento TGF-β1 e PDGF-BB na pele, PRP e plasma sanguíneo foi realizada pela técnica ELISA. Os dados foram analisados estatisticamente pelo teste t, correlação de Pearson e regressão, utilizando nível de significância de 5%. Não houve diferença entre os grupos, nos valores dos dois fatores de crescimento mensurados na pele, nos diferentes tempos. Também não houve correlação entre a quantidade dos fatores de crescimento presentes na pele e no plasma. Por outro lado, correlação positiva foi observada entre PRP e pele no grupo tratado, para os fatores de crescimento TGF-β1 (r=0,31) e PDGF-BB (r=0,38), bem como entre ambos os fatores de crescimento presentes no PRP (r=0,81). Considerando as concentrações dos fatores de crescimento no T0, os maiores valores cutâneos (p<0,05) do TGF-β1, em ambos os grupos, ocorreram nos tempos T3 e T5. Valores mais elevados (p<0,05) do PDGF-BB ocorreram no T4 (GT) e T5 (GC). No plasma não houve alteração nas concentrações desses fatores em relação ao T0, o que sugere que o PRP não acarreta efeito sistêmico, quando os procedimentos adotados na presente pesquisa são utilizados. A administração local de PRP no volume estudado, 12 h após indução cirúrgica de ferida cutânea na região glútea de equinos não ocasiona maiores concentrações dos fatores de crescimento TGF-β1 e PDGF-BB no plasma sanguíneo e pele, durante o processo de cicatrização