Explicit Hopcroft's Trick in Categorical Partition Refinement

Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of Hopcroft's trick. Our contribution is twofold. Firstly, we present a novel formulation of Hopcroft's trick in terms of general trees with weights. This clean and explicit formulation -- we call it Hopcroft's inequality -- is crucially used in our second contribution, namely a general partition refinement algorithm that is \emph{functor-generic} (i.e. it works for a variety of systems such as (non-)deterministic automata and Markov chains). Here we build on recent works on coalgebraic partition refinement but depart from them with the use of fibrations. In particular, our fibrational notion of $R$-partitioning exposes a concrete tree structure to which Hopcroft's inequality readily applies. It is notable that our fibrational framework accommodates such algorithmic analysis on the categorical level of abstraction

Rapid decomposition of asbestos and with various additives

The toxicity of asbestos is widely known, and various methods are being investigated to decompose asbestos into harmless compounds. The authors previously reported that asbestos-cement composites, a general waste material including asbestos, can be decomposed into harmless substances by adding small amounts of CaCl2 and then heating to 700℃ [1-3]. Recycling decomposed asbestos as a raw ingredient for cement is crucial in using this result industrially. However, compounds including chlorine form in decomposed asbestos, preventing of use in production of cement. The authors investigated additives other than CaCl2 in decomposition, and found that reagent-grade asbestos can be decomposed by adding 5mass% of additive and heating for 15 seconds at a low temperature of 900℃

Rapid decomposition of asbestos and with various additives

The toxicity of asbestos is widely known, and various methods are being investigated to decompose asbestos into harmless compounds. The authors previously reported that asbestos-cement composites, a general waste material including asbestos, can be decomposed into harmless substances by adding small amounts of CaCl2 and then heating to 700℃ [1-3]. Recycling decomposed asbestos as a raw ingredient for cement is crucial in using this result industrially. However, compounds including chlorine form in decomposed asbestos, preventing of use in production of cement. The authors investigated additives other than CaCl2 in decomposition, and found that reagent-grade asbestos can be decomposed by adding 5mass% of additive and heating for 15 seconds at a low temperature of 900℃

Development of hydroxyapatite-coated nonwovens for efficient isolation of somatic stem cells from adipose tissues

Adipose-derived stem cells (ASCs) are an attractive cell source for cell therapy. Despite the increasing number of clinical applications, the methodology for ASC isolation is not optimized for every individual. In this study, we developed an effective material to stabilize explant cultures from small-fragment adipose tissues. Methods: Polypropylene/polyethylene nonwoven sheets were coated with hydroxyapatite (HA) particles. Adipose fragments were then placed on these sheets, and their ability to trap tissue was monitored during explant culture. The yield and properties of the cells were compared to those of cells isolated by conventional collagenase digestion. Results: Hydroxyapatite-coated nonwovens immediately trapped adipose fragments when placed on the sheets. The adhesion was stable even in culture media, leading to cell migration and proliferation from the tissue along with the nonwoven fibers. A higher fiber density further enhanced cell growth. Although cells on nonwoven explants could not be fully collected with cell dissociation enzymes, the cell yield was significantly higher than that of conventional monolayer culture without impacting stem cell properties. Conclusions: Hydroxyapatite-coated nonwovens are useful for the effective primary explant culture of connective tissues without enzymatic cell dissociation