This study evaluated 3 implant surfaces in a dog model: (1) resorbable-blasting media + acid-etched (RBMa), alumina-blasting + acid-etching (AB/AE), and AB/AE + RBMa (hybrid). All of the surfaces were minimally rough, and Ca and P were present for the RBMa and hybrid surfaces. Following 2 weeks in vivo, no significant differences were observed for torque, bone-to-implant contact, and bone-area fraction occupied measurements. Newly formed woven bone was observed in proximity with all surfaces.

Objective: this study aimed to histomorphologically and histomorphometrically evaluate the in vivo response to three variations in the resorbable blasting media (RBM) surface processing in a rabbit femur model. Study Design: screw root form implants with 3.75 mm in diameter by 8 mm in length presenting four surfaces (n=8 each): alumina-blasted/acid-etched (AB/AE), bioresorbable ceramic blasted (TCP), TCP + acid etching, and AB/AE + TCP were characterized by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The implants were placed at the distal femur of 8 New Zeland rabbits, remaining for 2 weeks in vivo. After sacrifice, the implants were nondecalcified processed to 30 micro m thickness slides for histomorphology and bone-to-implant contact (BIC) determination. Statistical analysis was performed by one-way ANOVA at 95% level of significance considering implant surface as the independent variable and BIC as the dependent variable. Results: SEM and AFM showed that all surfaces presented rough textures and that calciu-hosohate particles were observed at the TCP group surface. Histologic evaluation showed intimate interaction between newly formed woven bone and all implant surfaces, demonstrating that all surfaces were biocompatible and osseoconductive. Significant differences in BIC were observed between the AB/AE and the AB/AE + TCP, and intermediate values observed for the TCP and TCP + Acid surfaces. Conclusion: irrespective of RBM processing variation, all surfaces were osseoconductive and biocaompatible. The differences in BIC between groups warrant further bone-implant interface biomechanical characterization.

Given two graphs X and Y on n vertices, the friends-and-strangers graph FS(X, Y ) has as its vertices all n! bijections from V (X) to V (Y ), with bijections σ, τ adjacent if and only if they differ on two elements of V (X), whose mappings are adjacent in Y . In this work, we study the diameters of friends-and-strangers graphs, which correspond to the largest number of swaps necessary to achieve one configuration from another. We provide families of constructions XL and YL for all integers L ≥ 1 to show that diameters of connected components of friends-and-strangers graphs fail to be polynomially bounded in the size of X and Y , resolving a question raised by Alon, Defant, and Kravitz in the negative. Specifically, our construction yields that there exist infinitely many values of n for which there are n-vertex graphs X and Y with the diameter of a component of FS(X, Y ) at least n (log n)/(log log n) . We also study the diameters of components of friends-and-strangers graphs when X is taken to be a path graph or a cycle graph, showing that any component of FS(Pathn, Y ) has diameter at most |E(Y )|, and diam(FS(Cycle n , Y )) is O(n 3 ) whenever FS(Cycle n , Y ) is connected. We conclude the work with several conjectures that aim to generalize this latter result.

Given two graphs X and Y with the same number of vertices, the friends-and-strangers graph FS(X, Y ) has as its vertices all n! bijections from V (X) to V (Y ), with bijections σ, τ adjacent if and only if they differ on two elements of V (X), whose mappings are adjacent in Y . In this article, we study necessary and sufficient conditions for FS(X, Y ) to be connected for all graphs X from some set. In the setting that we take X to be drawn from the set of all biconnected graphs, we prove that FS(X, Y ) is connected for all biconnected X if and only if Y is a forest with trees of jointly coprime size; this resolves a conjecture of Defant and Kravitz. We also initiate and make significant progress toward determining the girth of FS(X, Starn) for connected graphs X, and in particular focus on the necessary trajectories that the central vertex of Starn takes around all such graphs X to achieve the girth.