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

Pressure-Induced Ferromagnetic to Nonmagnetic Transition and the Enhancement of Ferromagnetic Interaction in the Thiazyl-Based Organic Ferromagnet γ-BBDTA·GaCl4

A thiazyl-based ferromagnet, the γ-phase of BBDTA (i.e., benzo[1,2- d :4,5- d \u27]bis[1,3,2]dithiazole)·GaCl 4 , has a high ferromagnetic ordering temperature of 7.0 K in organic radical ferromagnets. In this system, pressurization generated more compact molecular packing, resulting in that the ferromagnetic state at P = 16.2 kbar is stabilized over a temperature range of more than twice of the initial range. However, the saturation magnetic moment was reduced with increasing pressure, decreasing to about 12% of the initial value even at the low pressure level of P = 1.0 kbar. This suggests that the ferromagnetic molecular packing of the monoclinic γ-phase is easily transformed into that of the diamagnetic phase. Powder X-ray diffraction experiments revealed that the diamagnetic non-monoclinic (α- or β-) phase became stable instead of the monoclinic γ-phase across the pressure of 2.5–5.8 kbar. The increase in the temperature of onset of ferromagnetic state occurs in the surviving ferromagnetic domain surrounded by the diamagnetic domains

Gonadal sex differentiation and development during early ontogenesis in the breeding kisslip cuttlefish (Sepia lycidas)

To understand and obtain basic information on sex differentiation in the kisslip cuttlefish (Sepia lycidas), the gonadal sex differentiation process was investigated histologically. An undifferentiated gonad consisting of germ cells and somatic cells was found to form at a caudal site in the space between the internal yolk sacks of cuttlefish embryos at 14 and 21 days after spawning (DAS). Sexual dimorphism in the gonad was first detected at around 28 DAS. Meiotic oocytes were observed as the first visible morphological characteristic of ovaries in the gonads of some cuttlefish embryos at 28 DAS. In other individuals, neither meiotic germ cells,nor the appearance of a testicular structure, were observed in the gonad even after 10 days post hatching (DPH). Seminiferous tubules, consisting of a small number of spermatogonia and a surrounding basement membrane,were the first visible morphological characteristic of the testis in the male gonad, detected at around 20 DPH. This is the third report on the gonadal sex differentiation process in cephalopods

Manipulating quantum-well states by surface alloying: Pb on ultrathin Ag films

The electronic structure of ultrathin Ag films with 1/3 monolayer (ML) of Pb alloyed at the surface was investigated by angle-resolved photoemission spectroscopy. Compared to clean ultrathin Ag films, the energy positions of the quantum-well states (QWSs) moved closer to the Fermi level due to the change of the potential barrier at the film/vacuum interface. We found that the parabolic band dispersion of the QWSs become disturbed where they cross the surface-state bands, and furthermore, they were shown to follow the periodicity that is only present at the surface. Our results suggest that it is possible to tune the properties of the QWSs whose thickness is more than 10 ML just by submonolayer deposition of heteroelements at the surface

Effects of pressure on maghemite nanoparticles with acore/shell structure

The magnetic property and intraparticle structure of the γ phase of Fe2O3 (maghemite) nanoparticles with a diameter (D) of 5.1±0.5 nm were investigated through AC and DC magnetic measurements and powder X-ray diffraction (XRD) measurements at pressures (P) up to 27.7 kbar. Maghemite originally exhibits ferrimagnetic ordering below 918 K, and has an inverse-spinel structure with vacancies. Maghemitenanoparticles studied here consist of acore with structural periodicity and a disordered shell without the periodicity, and core shows superparamagnetism. The DC and AC susceptibilities reveal that the anisotropy energy barrier (ΔE/kB) and the effective value of the core moment decrease against the initial pressure (P≤3.8 kbar), recovering at P≥3.8 kbar. The change of ΔE/kB with P is qualitatively identical with that of the core moment, suggesting a down-and-up fluctuation of the number of Fe3+ ions constituting the core at the pressure threshold of about 4 kbar. This phenomenon was confirmed by the analysis of the XRD measurement using Scherrer’s formula. The core volume decreased for P≤2.5 kbar, whereas at higher pressure the core was restructured. For 2.5≤P≤10.7 kbar, the volume shrinkage of particle hardly occurs. There, ΔE/kB is approximately proportional to the volume associated to the ordered fraction of the nanoparticles as seen from XRD, Vcore. From this dependence it is possible to separate the core/shell contribution to ΔE/kB and estimate core and surface anisotropy constants. As for the structural experiments, similar experimental data have been obtained for D=12.8±3.2 nm as well.This work in Japan was supported by the CREST project of the Japan Science and Technology Agency (JST) and a Grant-in-Aidfor Young Scientists (B) (19750118) from the MEXT of Japan. The work in Zaragoza has been supported by the research grants MAT2007-61621 and CSD2007-00010 from the Ministry of Education. The Aveiro-Zaragoza collaboration has been supported by the Integrated Spanish-Portuguese Action PT2009-0131. N.J.O. Silva acknowledges CSIC for an I3Pcontract and FCT for a Ciencia 2008 contract.Peer Reviewe