0.1. The kinds of homotopy theories under consideration in this paper are Waldhausen ∞-categories [2, Df. 2.7]. (We employ the quasicategory model of∞-categories for technical convenience.) These are ∞-categories with a zero object and a distinguished class of morphisms (called cofibrations or ingressive morphisms) that satisfies the following conditions. (0.1.1) Any equivalence is ingressive. ...

INTRODUCTION The objective of this study was to determine if a synthetic bone substitute would provide results similar to bone from osteoporotic femoral heads during in vitro testing with orthopaedic implants. If the synthetic material could produce results similar to those of the osteoporotic bone, it could reduce or eliminate the need for testing of implants on bone. METHODS Pushout studies...

We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, pushout, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgemental equality rul...

This controlled study compared the strength and porosity of 48 polymethylmethacrylate cement-implant constructs prepared with open bowl versus vacuum mix technique. Forty-eight blast finished stainless steel rods of 13 mm diameter were implanted with centralizers into 17-mm inner diameter tubes that had been retrograde filled with polymethylmethacrylate cement. The eight cement preparations use...

Chemical reaction networks can be automatically generated from graph grammar descriptions, where rewrite rules model reaction patterns. Because a molecule graph is connected and reactions in general involve multiple molecules, the rewriting must be performed on multisets of graphs. We present a general software package for this type of graph rewriting system, which can be used for modelling che...

In this paper, we present: 1) design of a single-rail energy-efficient 64-b Han–Carlson ALU, operating at 482 ps in 1.5 V, 0.18m bulk CMOS; 2) direct port of this ALU to 0.18m partially depleted SOI process; 3) SOI-optimal redesign of the ALU using a novel deep-stack quaternary-tree architecture; 4) margining for max-delay pushout due to reverse body bias in SOI designs; and 5) performance scal...

A plug-in for the 3D modeling application CINEMA 4D is presented which allows to use the graph transformation language XL to transform the 3D scene graph of CINEMA 4D. XL extends Java by graph query and rewrite facilities via a data model interface, the default rewrite mechanism is that of relational growth grammars which are based on parallel single-pushout derivations. We illustrate the plug-...

For terminating double-pushout (DPO) graph rewriting systems confluence is, in general, undecidable. We show that confluence is decidable for an extension of DPO rewriting to graphs with interfaces. This variant is important due to it being closely related to rewriting of string diagrams. We show that our result extends, under mild conditions, to decidability of confluence for terminating rewri...

We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the...

0AHU The goal of this chapter is to discuss pushouts in the category of algebraic spaces. This can be done with varying assumptions. A fairly general pushout construction is given in [TT13]: one of the morphisms is affine and the other is a closed immersion. We discuss a particular case of this in Section 2 where we assume one of the morphisms is affine and the other is a thickening, a situatio...