Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.     

Fq-linear codes over Fq-algebras

Huffman (2013) [12] studied ${\mathbb{F}}_q$-linear codes over ${\mathbb{F}}_{q^m}$ and he proved the MacWilliams identity for these codes with respect to ordinary and Hermitian trace inner products. Let S be a finite commutative ${\mathbb{F}}_q$-algebra. An ${\mathbb{F}}_q$-linear code over S of length n is an ${\mathbb{F}}_q$-submodule of $S^n$. In this paper, we study ${\mathbb{F}}_q$-linear codes over S. We obtain some bounds on minimum distance of these codes, and some large classes of MDR codes are introduced. We generalize the ordinary and Hermitian trace products over ${\mathbb{F}}_q$-algebras and we prove the MacWilliams identity with respect to the generalized form. In particular, we obtain Huffman's results on the MacWilliams identity. Among other results, we give a theory to construct a class of quantum codes and the structure of ${\mathbb{F}}_q$-linear codes over finite commutative graded ${\mathbb{F}}_q$-algebras.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Development of a highly sensitive imaged cIEF immunoassay for studying AAV capsid protein charge heterogeneity

Post-translational modifications (PTMs) of adeno-associated virus (AAV) capsid proteins tune and regulate the AAV infective life cycle, which can impact the safety and efficacy of AAV gene therapy products. Many of these PTMs induce changes in protein charge heterogeneity, including deamidation, oxidation, glycation, and glycosylation. To characterize the charge heterogeneity of a protein, imaged capillary isoelectric focusing (icIEF) has become the gold standard method. We have previously reported an icIEF method with native fluorescence detection for denatured AAV capsid protein charge heterogeneity analysis. Although well suited for final products, the method does not have sufficient sensitivity for upstream, low-concentration AAV samples, and lacks the specificity for capsid protein detection in complex samples like cell culture supernatants and cell lysates. In contrast, the combination of icIEF, protein capture, and immunodetection affords significantly higher sensitivity and specificity, addressing the challenges of the icIEF method. By leveraging different primary antibodies, the icIEF immunoassay provides additional selectivity and affords a detailed characterization of individual AAV capsid proteins. In this study, we describe an icIEF immunoassay method for AAV analysis that is 90 times more sensitive than native fluorescence icIEF. This icIEF immunoassay provides AAV stability monitoring, where changes in individual capsid protein charge heterogeneity can be observed in response to heat stress. When applied to different AAV serotypes, this method also provides serotype identity with reproducible quantification of VP protein peak areas and apparent isoelectric point (pI). Overall, the described icIEF immunoassay is a sensitive, reproducible, quantitative, specific, and selective tool that can be used across the AAV biomanufacturing process, especially in upstream process development where complex sample types are often encountered.