Compositions of invertibility preserving maps for some monoids and their application to Clifford algebras

For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensional algebras over a field." As examples, we give invertibility preserving maps for Clifford algebras into a field and determinants for Clifford algebras into a field, where we assume that the algebras are generated by less than or equal to 5 generators over the field. On the other hand, "determinant formulas for Clifford algebras" are known. We understand these formulas as an expression that connects invertibility preserving maps for Clifford algebras and determinants for Clifford algebras. As a result, we have a better sense of determinant formulas. In addition, we show that there is not such a determinant formula for Clifford algebras generated by greater than 5 generators

Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup

We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard Mansfield, where they show that two groups with the same group determinant are isomorphic. The derived condition leads to a generalization of this result.Comment: 6 page

Integer group determinants for C42C_{4}^{2}

We determine all possible values of the integer group determinant of $C_{4}^{2}$, where $C_{4}$ is the cyclic group of order $4$

Integer group determinants for abelian groups of order 16

For any positive integer $n$, let $C_{n}$ be the cyclic group of order $n$. We determine all possible values of the integer group determinant of $C_{4} \times C_{2}^{2}$, which is the only unsolved abelian group of order $16$

Integer group determinants for C24C_{2}^{4}

We determine all possible values of the integer group determinant of $C_{2}^{4}$, where $C_{2}$ is the cyclic group of order $2$

Inequality for the variance of an asymmetric loss

We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss

Minimizing the expected value of the asymmetric loss and an inequality of the variance of the loss

For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a solution by correcting any predictions so that the prediction error follows a general normal distribution. In our method, we can not only minimize the expected value of the asymmetric loss, but also lower the variance of the loss

Insight into single cell cloning in serum-free media

Chinese hamster ovary (CHO) cells have been used as host cells for the manufacturing of therapeutic recombinant proteins over the past decade. It is thought that the development of high performance cell lines, which satisfy both productivity and regulatory expectations, is one of the key success drivers to establish good manufacturing processes. The cell line for the clinical and commercial productions should be derived from a single progenitor or clone, and so the single cell cloning is an essential step during the cell line development. Recently serum-free media have been widely applied for this step. But under such conditions, the cloning efficiency varies significantly among the clones. This might be because the serum-free conditions can be stressful for the CHO cells exposed to such an unexpected cloning process. In this study, we performed re-cloning from two pre-cloned cell lines to evaluate the impact of serum-free cloning on the resulting cell line characteristics; various parameters such as cell growth, productivity, fed-batch culture performance, product quality and cell stability were evaluated. As a result, most of the clones showed exactly the same performance before and after the cloning process, but some clones did not. The detail of these results will be presented and also the proper evaluation to be needed during cell line development, especially after the single cell isolation, will be discusse

Identification of diabetes susceptibility loci in db mice by combined quantitative trait loci analysis and haplotype mapping

To identify the disease-susceptibility genes of type 2 diabetes, we performed quantitative trait loci (QTL) analysis in F2 populations generated from a BKS.Cg-m+/+Leprdb and C3H/HeJ intercross, taking advantage of genetically determined obesity and diabetes traits associated with the db gene. A genome-wide scan in the F2 populations divided by sex and db genotypes identified 14 QTLs in total and 3 major QTLs on chromosome (Chr) 3 (LOD 5.78) for fat pad weight, Chr 15 (LOD 6.64) for body weight, and Chr 16 (LOD 8.15) for blood glucose concentrations. A linear-model-based genome scan using interactive covariates allowed us to consider sex- or sex-by db-specific effects of each locus. For the most significant QTL on Chr 16, the high-resolution haplotype comparison between BKS and C3H strains reduced the critical QTL interval from 20 to 4.6 Mb by excluding shared haplotype regions and identified 11 nonsynonymous single-nucleotide polymorphisms in six candidate genes

Detection of miRNA in Cell Cultures by Using Microchip Electrophoresis with a Fluorescence-Labeled Riboprobe

The analysis of a microRNA (miRNA), miR-222 isolated from the PC12 cell line, was performed by use of the ribonuclease (RNase) protection assay, cyanine 5 (Cy5)-labeled miR-222 riboprobe, and a Hitachi SV1210 microchip electrophoresis system, which can be used to evaluate the integrity of total RNA. The fluorescence intensity corresponding to the protected RNA fragment increased in a dose-dependent manner with respect to the complementary-strand RNA. More highly sensitive detection of miRNA by microchip electrophoresis than by conventional method using fluorescence-labeled riboprobe could be obtained in 180 s. An obvious increase in miR-222 expression induced by nerve growth factor in PC12 cells could be observed. These results clearly indicate the potential of microchip electrophoresis for the analysis of miRNA using RNase protection assay with a fluorescence-labeled riboprobe