A non-negative matrix factorization model based on the zero-inflated Tweedie distribution

Non-negative matrix factorization (NMF) is a technique of multivariate analysis used to approximate a given matrix containing non-negative data using two non-negative factor matrices that has been applied to a number of fields. However, when a matrix containing non-negative data has many zeroes, NMF encounters an approximation difficulty. This zero-inflated situation occurs often when a data matrix is given as count data, and becomes more challenging with matrices of increasing size. To solve this problem, we propose a new NMF model for zero-inflated non-negative matrices. Our model is based on the zero-inflated Tweedie distribution. The Tweedie distribution is a generalization of the normal, the Poisson, and the gamma distributions, and differs from each of the other distributions in the degree of robustness of its estimated parameters. In this paper, we show through numerical examples that the proposed model is superior to the basic NMF model in terms of approximation of zero-inflated data. Furthermore, we show the differences between the estimated basis vectors found using the basic and the proposed NMF models for \(\beta \) divergence by applying it to real purchasing data.     

Amplified Chirality Transfer to Aromatic Molecules through Non-specific Inclusion by Amorphous,Hyperbranched Poly(fluorenevinylene) Derivatives

Optically active, hyperbranched, poly(fluorene-2,4,7-triylethene-1,2-diyl) [poly(fluorenevinylene)] derivatives bearing a neomenthyl group and a pentyl group at the 9-position of the fluorene backbone at various ratios acted as a chirality donor (host polymers) efficiently included naphthalene, anthracene, pyrene, 9-phenylanthracene, and 9,10-diphenyanthracene as a chirality acceptor (guest molecules) in their interior space in film as well as in solution, with the guest molecules exhibiting intense circular dichroism through chirality transfer with chirality amplification. The efficiency of the chirality transfer was much higher with higher-molar-mass polymers than lower-molar-mass ones as well as with hyperbranched polymers compared to the analogous linear ones. The hyperbranched polymers include the small molecules in their complex structure without any specific interactions at various stoichiometries. The included molecules may have ordered intermolecular arrangement that may be somewhat similar to those of liquid crystals. Naphthalene, anthracene, and pyrene included in the polymer exhibited efficient circularly polarized luminescence, where the chirality was remarkably amplified in excited states, and anthracene exhibited especially high anisotropies in the emission on the order of 10⁻².     

A novel approach for LC-MS/MS-based chiral metabolomics fingerprinting and chiral metabolomics extraction using a pair of enantiomers of chiral derivatization reagents

Chiral metabolites are found in a wide variety of living organisms and some of them are understood to be physiologically active compounds and biomarkers. However, the overall analysis of chiral metabolomics is quite difficult due to the high number of metabolites, the significant diversity in their physicochemical properties, and concentration range from metabolite-to-metabolite. To solve this difficulty, we developed a novel approach for chiral metabolomics fingerprinting and chiral metabolomics extraction, which is based on the labeling of a pair of enantiomers of chiral derivatization reagents (i.e., DMT-(S,R)-Pro-OSu and DMT-3(S,R)-Apy) and precursor ion scan chromatography of the derivatives. The multivariate statistics is also required for this strategy. The proposed procedures were evaluated by the detection of a diagnostic marker (i.e., d-lactic acid) using the saliva of diabetic patients. This method was used for the determination of biomarker candidates of chiral amines and carboxyls in Alzheimer's disease (AD) brain homogenates. As the results, l-phenylalanine (L-Phe) and l-lactic acid (L-LA) were identified as the decreased and increased biomarker candidates in the AD brain, respectively. Therefore, the proposed approach seems to be helpful for the determination of non-target chiral metabolomics possessing amines and carboxyls.     

Influence of RNA Strand Rigidity on Polyion Complex Formation with Block Catiomers

Polyion complexes (b‐PICs) are prepared by mixing single‐ or double‐stranded oligo RNA (aniomer) with poly(ethylene glycol)‐b‐poly(l ‐lysine) (PEG‐PLL) (block catiomer) to clarify the effect of aniomer chain rigidity on association behaviors at varying concentrations. Here, a 21‐mer single‐stranded RNA (ssRNA) (persistence length: 1.0 nm) and a 21‐mer double‐stranded RNA (small interfering RNA, siRNA) (persistence length: 62 nm) are compared. Both oligo RNAs form a minimal charge‐neutralized ionomer pair with a single PEG‐PLL chain, termed unit b‐PIC (uPIC), at low concentrations (<≈0.01 mg mL⁻¹). Above the critical association concentration (≈0.01 mg mL⁻¹), ssRNA b‐PICs form secondary associates, PIC micelles, with sizes up to 30–70 nm, while no such multimolecular assembly is observed for siRNA b‐PICs. The entropy gain associated with the formation of a segregated PIC phase in the multimolecular PIC micelles may not be large enough for rigid siRNA strands to compensate with appreciably high steric repulsion derived from PEG chains. Chain rigidity appears to be a critical parameter in polyion complex association.

     

An Ultrastable,Small {Ag7}5+ Nanocluster within a Triangular Hollow Polyoxometalate Framework

Small Ag_n nanoclusters (n<10) have been emerging as promising materials as sensing, biolabeling, and catalysis because of their unique electronic states and optical properties. However, studying synthesis, structure determination, and exploration of their properties remain major challenges as a result of the low stability of small Ag nanoclusters. Herein, we synthesized an atomically precise face‐centered‐cubic‐type small {Ag₇}⁵⁺ nanocluster supported by a novel triangular hollow polyoxometalate (POM) framework [Si₃W₂₇O₉₆]^18?. The cluster showed unique {Ag₇}⁵⁺‐to‐POM charge transfer bands in both visible and UV light regions. Furthermore, this small {Ag₇}⁵⁺ nanocluster exhibited an unprecedented ultrastability in solution, despite having exposed Ag sites that can be accessed by small molecules, such as O₂, water, and solvents.