Stochastic Model of Block Segmentation Based on Improper Quadtree and Optimal Code under the Bayes Criterion

Most previous studies on lossless image compression have focused on improving preprocessing functions to reduce the redundancy of pixel values in real images. However, we assumed stochastic generative models directly on pixel values and focused on achieving the theoretical limit of the assumed models. In this study, we proposed a stochastic model based on improper quadtrees. We theoretically derive the optimal code for the proposed model under the Bayes criterion. In general, Bayes-optimal codes require an exponential order of calculation with respect to the data lengths. However, we propose an algorithm that takes a polynomial order of calculation without losing optimality by assuming a novel prior distribution.     

Towers of function fields over finite fields corresponding to elliptic modular curves

In this paper, we find several equations of recursive towers of function fields over finite fields corresponding to sequences of elliptic modular curves. This is a continuation of the work of Noam D. Elkies [8], [9] on modular equations of higher degrees.     

Alternative Synthesis of Dibenzo-and Dipyrido-[1,3]Diazepines from Thioamides and o,o′-Diaminobiaryls

Thioamides were treated with iodomethane, and then o,o′-diaminobiphenyl or bipyridyl to afford 6-substituted-5H-dibenzo- or dipyrido [1,3]diazepines in good yields.     

Selective and random syntheses of [n]cycloparaphenylenes (n=8-13) and size dependence of their electronic properties

[n]Cycloparaphenylenes (n = 8-13, CPPs) were synthesized, and their physical properties were systematically investigated. [8] and [12]CPPs were selectively prepared from the reaction of 4,4'-bis(trimethylstannyl)biphenyl and 4,4'-bis(trimethylstannyl)terphenyl, respectively, with Pt(cod)Cl(2) (cod = 1,5-cyclooctadiene) through square-shaped tetranuclear platinum intermediates. A mixture of [8]-[13]CPPs was prepared in good combined yields by mixing biphenyl and terphenyl precursors with platinum sources. Products were easily separated and purified by using gel permeation chromatography. In (1)H NMR spectra, the proton of the CPPs shifts to a lower field as n increased due to an anisotropic effect from the nearby PP moieties. Although the UV-vis spectra were rather insensitive to the size of the CPPs, the fluorescence spectra changed significantly in relation to their size. A larger Stokes shift was observed for the smaller CPPs. Redox properties of the CPPs were measured for the first time by using cyclic voltammetry, and the smaller CPPs had lower oxidation potentials. The results are consistent with the HOMO energies of CPPs, of which the smaller CPPs had higher energies.     

Microwave-assisted organic functionalization of silica surfaces: Effect of selectively heating silylating agents

Microwave (MW)-assisted (2.45 GHz) organic functionalization of silica surfaces was investigated using (3-chloropropyl)dimethylsilanes with alkoxy, allyl, or aryl leaving groups in heptane or toluene at 80 °C. ²⁹Si and ¹³C CP/MAS spectroscopy confirmed the 3-chloropropyldimethylsilyl moiety was covalently grafted onto silica for all the samples. The effect of MW irradiation on the loading amount strongly depended on the leaving group as well as the solvent; using methoxysilane and p-anisylsilane in heptane caused a distinct acceleration. The correlation with the dielectric loss factors of the silylating agents suggested that the MW acceleration effect resulted from selectively heating the strongly MW-absorbing silylating agent. For the grafting reaction in toluene, the MW effect was not observed possibly because toluene masked the selective heating effect of the silylating agent.     

Thermoelectric properties of Bi-Sb semiconducting alloys prepared by quenching and annealing

Bi_100−xSb_x (x=8-17) alloys were prepared by direct melting of constituent elements, which was followed by quenching and annealing. The synthesis of high-homogeneity alloys was confirmed by X-ray diffraction, differential thermal analyses and electron microprobe analysis. The semiconducting and thermoelectric properties of the samples were investigated by measuring Hall coefficient, electrical resistivity and Seebeck coefficient in the temperature range from 20 to 300 K for both the as-quenched and annealing samples. The properties change gradually with the Sb concentration x, which is attributed to the variation of the energy gap. The Hall mobility was enhanced by annealing, which leads to a small electrical resistivity and a large Seebeck coefficient. Consequently, large values of about 8.5 mW/mK² for the power factor were obtained in the annealed alloys of x=8,12, and 14.     

Meta-Tree Random Forest: Probabilistic Data-Generative Model and Bayes Optimal Prediction

This paper deals with a prediction problem of a new targeting variable corresponding to a new explanatory variable given a training dataset. To predict the targeting variable, we consider a model tree, which is used to represent a conditional probabilistic structure of a targeting variable given an explanatory variable, and discuss statistical optimality for prediction based on the Bayes decision theory. The optimal prediction based on the Bayes decision theory is given by weighting all the model trees in the model tree candidate set, where the model tree candidate set is a set of model trees in which the true model tree is assumed to be included. Because the number of all the model trees in the model tree candidate set increases exponentially according to the maximum depth of model trees, the computational complexity of weighting them increases exponentially according to the maximum depth of model trees. To solve this issue, we introduce a notion of meta-tree and propose an algorithm called MTRF (Meta-Tree Random Forest) by using multiple meta-trees. Theoretical and experimental analyses of the MTRF show the superiority of the MTRF to previous decision tree-based algorithms.     

Synthesis,Characterization, and Properties of [4]Cyclo‐2,7‐pyrenylene: Effects of Cyclic Structure on the Electronic Properties of Pyrene Oligomers

A cyclic tetramer of pyrene, [4]cyclo‐2,7‐pyrenylene ([4]CPY), was synthesized from pyrene in six steps and 18 % overall yield by the platinum‐mediated assembly of pyrene units and subsequent reductive elimination of platinum. The structures of the two key intermediates were unambiguously determined by X‐ray crystallographic analysis. DFT calculations showed that the topology of the frontier orbitals in [4]CPY was essentially the same as those in [8]cycloparaphenylene ([8]CPP), and that all the pyrene units were fully conjugated. The electrochemical analyses proved the electronic properties of [4]CPY to be similar to those of [8]CPP. The results are in sharp contrast to those obtained for the corresponding linear oligomers of pyrene in which each pyrene unit was electronically isolated. The results clearly show a novel effect of the cyclic structure on cyclic π‐conjugated molecules.     

The synthesis of the 1-carbopenem antibiotic (±)-ps-5 and its 6-epi analogue

Total synthesis of the title compounds is described which includes, as the key step, regioselective Dieckmann reaction for constructing the 2-oxo-carbapenam ring system.     

Synthesis and spectral properties of perylene–rhodamine dyads with lipophilic dendritic auxiliaries

The present publication reports a new entry of perylene–rhodamine dyads, whose solubilities in organic solvents are enhanced by the lipophilic dendritic auxiliaries. Spectroscopic studies on these dyad systems have demonstrated that the intramolecular Förster resonance energy transfer (FRET) from the perylene donor to the rhodamine acceptor was activated upon protonation with either H₂SO₄ or TFA to result in drastic colour change of the fluorescence emissions. This phenomenon can be reasonably accounted for in terms of the switching behaviour of the FRET interactions, which is suppressed by disruptive interference from lone pair electrons of the amino moieties.