The multi-indexed partitional

In this paper we present the multi-indexed partitional. The structure is a generalization of the partitional of Foata and Schützenberger, and gives a combinatorial interpretation for certain multivariate polynomial sequences of binomial type.     

Session 6 environmental biotechnology

Applied Biochemistry and Biotechnology -     

JADE for Tensor-Valued Observations

Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely, matrices or tensors (e.g., images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth-order blind identification (FOBI) specially suited for tensor-valued observations was proposed and showed to outperform its vector version for tensor data. In this article, we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background, we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors. Supplementary material including the proofs of the theorems and the codes for running the simulations and the real data example are available online.     

Expansion formulas. I. A general method

Using the MacMahon Master Theorem, Carlitz, in (SIAM J. Appl. Math. 26 (1974), 431–436; 8 (1977), 320–336) obtains the expansion . A “factorial” analog of this expansion and other related results are also given. In this paper we derive one general formula from which these expanions follow as special cases. This formula demonstrates a bijection between a class of expansion formulas and Sheffer sequences of polynomials.     

The Use of Megamolecular Polysaccharide Sacran in Food and Biomedical Applications

Natural polymer is a frequently used polymer in various food applications and pharmaceutical formulations due to its benefits and its biocompatibility compared to synthetic polymers. One of the natural polymer groups (i.e., polysaccharide) does not only function as an additive in pharmaceutical preparations, but also as an active ingredient with pharmacological effects. In addition, several natural polymers offer potential distinct applications in gene delivery and genetic engineering. However, some of these polymers have drawbacks, such as their lack of water retention and elasticity. Sacran, one of the high-molecular-weight natural polysaccharides (megamolecular polysaccharides) derived from Aphanothece sacrum (A. sacrum), has good water retention and elasticity. Historically, sacran has been used as a dietary food. Moreover, sacran can be applied in biomedical fields as an active material, excipient, and genetic engineering material. This article discusses the characteristics, extraction, isolation procedures, and the use of sacran in food and biomedical applications.     

In Vitro Evaluation of the Squaramide-Conjugated Fibroblast Activation Protein Inhibitor-Based Agents AAZTA5.SA.FAPi and DOTA.SA.FAPi

Recently, the first squaramide-(SA) containing FAP inhibitor-derived radiotracers were introduced. DATA^5m.SA.FAPi and DOTA.SA.FAPi with their non-radioactive complexes showed high affinity and selectivity for FAP. After a successful preclinical study with [⁶⁸Ga]Ga-DOTA.SA.FAPi, the first patient studies were realized for both compounds. Here, we present a new squaramide-containing compound targeting FAP, based on the AAZTA⁵ chelator 1,4-bis-(carboxylmethyl)-6-[bis-(carboxymethyl)-amino-6-pentanoic-acid]-perhydro-1,4-diazepine. For this molecule (AAZTA⁵.SA.FAPi), complexation with radionuclides such as gallium-68, scandium-44, and lutetium-177 was investigated, and the in vitro properties of the complexes were characterized and compared with those of DOTA.SA.FAPi. AAZTA⁵.SA.FAPi and its derivatives labelled with non-radioactive isotopes demonstrated similar excellent inhibitory potencies compared to the previously published SA.FAPi ligands, i.e., sub-nanomolar IC₅₀ values for FAP and high selectivity indices over the serine proteases PREP and DPPs. Labeling with all three radiometals was easier and faster with AAZTA⁵.SA.FAPi compared to the corresponding DOTA analogue at ambient temperature. Especially, scandium-44 labeling with the AAZTA derivative resulted in higher specific activities. Both DOTA.SA.FAPi and AAZTA⁵.SA.FAPi showed sufficiently high stability in different media. Therefore, these FAP inhibitor agents could be promising for theranostic approaches targeting FAP.