Dynamical Optimal Transport on Discrete Surfaces

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation of quadratic optimal transport proposed for flat domains by Benamou and Brenier [2000], adapted to discrete surfaces. Our structure-preserving construction yields a Riemannian metric on the (finite-dimensional) space of probability distributions on a discrete surface, which translates the so-called Otto calculus to discrete language. From a practical perspective, our technique provides a smooth interpolation between distributions on discrete surfaces with less diffusion than state-of-the-art algorithms involving entropic regularization. Beyond interpolation, we show how our discrete notion of optimal transport extends to other tasks, such as distribution-valued Dirichlet problems and time integration of gradient flows

Evaluating 3D fit of lithium disilicate restorations with a novel virtual measuring technique

OBJECTIVE: To explore a novel virtual inspection approach with a 3D metrology software to provide a non-destructive in situ analysis in digital workflow. Also, to evaluate the fit discrepancies of lithium disilicate crowns by using such a novel virtual measuring technique. MATERIALS AND METHODS: Maxillary arch typodont was used to design abutment for tooth #8 and #14 (hand prepared) and #4 and #10 (titanium custom abutment). All four abutments were placed into a duplicated maxillary arch solid stone model for scanning with laboratory scanner. Four crown patterns were designed and exported as STL files. The internal control group consists of the four original digital STL files and the external control group which was the 32-milled lithium disilicate crowns (IPS e.max® CAD, Ivoclar Vivadent, Inc.), eight patterns for each tooth. Thirty-two pressable wax patterns (8 of each) was fabricated for each of the three different technique systems. Two printed wax systems, Varseo Wax CAD/Cast (BEGO) and Press-E-Cast (EnvisionTec). Two milled wax systems Harvest Wax (Ivoclar Vivadent, Inc.) and Polycon Cast (Straumann), and a set of conventional cutbacks of 1.5mm with applied marginal wax. All patterns were pressed into lithium disilicate crowns, then fine polished and scanned. Each file was imported into a quality control metrology software (Geomagic Control X, 3D Systems) for marginal fit and internal fit evaluation with respective digital abutment. RESULTS: Mean of marginal gap for all groups were all lower than the preset gap space of 40 microns. Statistically significant differences in the fit accuracy were found among tooth number, technique system and measurement locations, but the differences are in clinically acceptable range. New scope of analyzing a restoration in a 3D fashion can help solve clinical complications. The study has shown that lower marginal gap does not necessary indicates a better fit restoration, as every level of the crown should be evaluated for. CONCLUSION: This novel inspection method can be used as a replacement of fit checker and help clinician to work in a full digital workflow. Lithium disilicate restorations fabricated through printed wax pattern, milled wax pattern and conventional hand wax are all clinically acceptable techniques.2019-09-26T00:00:00

Barriers to Implementing Large-Scale Online Staff Development Programs for Teachers

This is the publisher's version, which may also be found here: http://www.westga.edu/~distance/ojdla/winter64/meyen64.pdfThis study on barriers to online staff development for classroom teachers was conducted as part of the planning activities of a delivery models project designed to develop guidelines for implementing large-scale online staff development programs. The study involved engaging 54 general and special educators in several professional roles from nine states in a series of focus groups to identify the barriers to online staff development. An instrument was designed to rank order the barriers in terms of perceived significance. Twenty-two barriers were identified. This project was in follow-up to the Online Academy (H029K73002) funded by the Office of Special Education Programs in the U.S. Department of Education (OSEP/USDOE)

Stochastic Wasserstein Barycenters

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.Comment: ICML 201

N-(4-Bromophenyl)methoxycarbothioamide

The synthesis, spectroscopic and crystallographic characterisation of the title compound, O-methyl-N-4-bromophenyl thiocarbamate, MeOC(=S)N(H)PhBr-4 (1), are described. Spectroscopy confirmed the formation of the compound and the molecular structure was determined crystallographically. Two independent but chemically similar molecules comprise the asymmetric unit of 1. The C-S and C-N bond lengths confirm the presence of the thioamide tautomer. The thione-S and amide-N-H atoms are syn, enabling the formation of amide-N-H . . . S(thione) hydrogen bonds between the two independent molecules that generates a two-molecule aggregate via an eight-membered { . . . HNCS}2 synthon. The aggregates are connected into a three-dimensional architecture via weak intermolecular interactions, including Br. . . π(4-bromophenyl), S . . . π(4-bromophenyl), and weak Br. . . S halogen bonding contacts. The overall molecular conformation, thioamide tautomer, and the presence of amide-N-H . . . S(thione) hydrogen bonding in the crystal conform with expectation for this class of compound

O-Methyl m-Tolylcarbamothioate

The synthesis, spectroscopic, and crystallographic characterisation of the title compound,O-methyl m-tolylcarbamothioate, MeOC(=S)N(H)(m-tolyl) (1), are described. The crystallographic study confirms the structure determined by spectroscopy and shows the presence of the thioamide tautomer, a syn-disposition of the thione-S and thioamide-N-H atoms and, in the crystal, thioamide-N-H . . . S(thione) hydrogen bonding leading to an eight-membered { . . . HNCS}2 synthon

Crystal structure of the (E)-O-methyl-N-phenyl-thiocarbamate – 4,4′-bipyridine (1/1), C18H17N3OS

C18H17N3OS, monoclinic, C2/c (no. 15), a=13.4754(3) Å, b=13.8997(3) Å, c=18.0300(4) Å, β=107.202(3)°, V =3226.03(13) Å3, Z =8, Rgt(F)=0.0341, wRref(F2)=0.0878, T =100(2) K

Crystal structure of N-(3-chlorophenyl)(propan-2-yloxy)carbothioamide, C10H12ClNOS

C10H12ClNOS, monoclinic, P21/n (no. 14), a=13.2003(12) Å, b=6.0448(6) Å, c=13.9403(13) Å, β=101.9180(10)°, V =1088.36(18) Å3, Z =4, Rgt(F)=0.0291, wRref(F2)=0.0807, T =100(2) K

Crystal structure of the bis((E)-O-ethyl-N-phenylthiocarbamate) – 4,4′-bipyridine co-crystal (2/1), C28H30N4O2S2

C12H11N5, monoclinic, P21/n (no. 14), a=7.3455(1) Å, b=12.2470(1) Å, c=12.1689(1) Å, β=103.505(1)°, V =1064.45(2) Å3, Z =4, Rgt(F)=0.0365, wRref(F2)=0.0987, T =100 K