Solutions of xqk+⋯+xq+x=ax^{q^k}+\cdots+x^{q}+x=a in GF2nGF{2^n}

Though it is well known that the roots of any affine polynomial over a finite field can be computed by a system of linear equations by using a normal base of the field, such solving approach appears to be difficult to apply when the field is fairly large. Thus, it may be of great interest to find an explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over a binary finite field. This paper gives an explicit representation of solutions for a much wider class of affine polynomials over a binary prime field

A weak solution for free vibration of multi-span beams with general elastic boundary and coupling conditions

A weak solution of free vibration is developed for multi-span beams, which can adapt general elastic boundary and coupling conditions. Firstly, create the energy functional of the multi-span beam system based on the small deformation theory. Then, adopt the modified Fourier series method to rewrite the displacement functions. Compared with the traditional Fourier series method, the present series representations provide a solution for general elastic restrains. Lastly, combined with the Rayleigh-Ritz technique, all the series expansion coefficients can be obtained as the generalized coordinates. Numerical results demonstrate that the current weak solution has good convergence and high accuracy compared with the existing results in literature and FEM results

A Proof of the Beierle-Kranz-Leander’s Conjecture related to Lightweight Multiplication in F2nF_{2^n}

Lightweight cryptography is an important tool for building strong security solutions for pervasive devices with limited resources. Due to the stringent cost constraints inherent in extremely large applications, the efficient implementation of cryptographic hardware and software algorithms is of utmost importance to realize the vision of generalized computing. In CRYPTO 2016, Beierle, Kranz and Leander have considered lightweight multiplication in ${F}_{2^n}$. Specifically, they have considered the fundamental question of optimizing finite field multiplications with one fixed element and investigated which field representation, that is which choice of basis, allows for an optimal implementation. They have left open a conjecture related to two XOR-count. Using the theory of linear algebra, we prove in the present paper that their conjecture is correct. Consequently, this proved conjecture can be used as a reference for further developing and implementing cryptography algorithms in lightweight devices

The number of primitive endoderm cells in the inner cell mass is regulated by platelet-derived growth factor signaling in porcine preimplantation embryos

Objective Discovering the mechanism of cell specification is important to manipulate cellular lineages. To obtain lineage-specific cell lines, the target lineage needs to be promoted, and counterpart lineages should be suppressed. Embryos in the early blastocyst stage possess two different cell populations, the inner cell mass (ICM) and trophectoderm. Then, cells in the ICM segregate into epiblasts (Epi) and primitive endoderm (PrE). PrE cells in embryos show specific expression of platelet-derived growth factor (PDGF) and its receptor, PDGF receptor A (PDGFRA). In this study, we suppressed PDGF signaling using two methods (CRISPR/Cas9 injection and inhibitor treatment) to provide insight into the segregation of embryonic lineages. Methods CRISPR/Cas9 RNAs were injected into parthenogenetically activated and in vitro fertilized embryos. The PDGF receptor inhibitor AG1296 was treated at 0, 5, 10, and 20 μM concentration. The developmental competence of the embryos and the number of cells expressing marker proteins (SOX2 for ICM and SOX17 for PrE) were measured after the treatments. The expression levels of the marker genes with the inhibitor were examined during embryo development. Results Microinjection targeting the PDGF receptor (PDGFR) A reduced the number of SOX17-positive cell populations in a subset of day 7 blastocysts (n = 9/12). However, microinjection accompanied diminution of Epi cells in the blastocyst. The PDGF receptor inhibitor AG1296 (5 μM) suppressed SOX17-positive cells without reducing SOX2-positive cells in both parthenogenetic activated and in vitro fertilized embryos. Within the transcriptional target of PDGF signaling, the inhibitor significantly upregulated the Txnip gene in embryos. Conclusion We identified that PDGF signaling is important to sustain the PrE population in porcine blastocysts. Additionally, treatment with inhibitors was a better method to suppress PrE cells than CRISPR/Cas9 microinjection of anti-PDGF receptor α gene, because microinjection suppressed number of Epi cells. The PDGF receptor might control the number of PrE cells by repressing the proapoptotic gene Txnip. Our results can help to isolate Epi-specific cell lines from blastocysts

Combination of cell signaling molecules can facilitate MYOD1-mediated myogenic transdifferentiation of pig fibroblasts

Background Myogenic transdifferentiation can be accomplished through ectopic MYOD1 expression, which is facilitated by various signaling pathways associated with myogenesis. In this study, we attempted to transdifferentiate pig embryonic fibroblasts (PEFs) myogenically into skeletal muscle through overexpression of the pig MYOD1 gene and modulation of the FGF, TGF-β, WNT, and cAMP signaling pathways. Results The MYOD1 overexpression vector was constructed based on comparative sequence analysis, demonstrating that pig MYOD1 has evolutionarily conserved domains across various species. Although forced MYOD1 expression through these vectors triggered the expression of endogenous muscle markers, transdifferentiated muscle cells from fibroblasts were not observed. Therefore, various signaling molecules, including FGF2, SB431542, CHIR99021, and forskolin, along with MYOD1 overexpression were applied to enhance the myogenic reprogramming. The modified conditions led to the derivation of myotubes and activation of muscle markers in PEFs, as determined by qPCR and immunostaining. Notably, a sarcomere-like structure was observed, indicating that terminally differentiated skeletal muscle could be obtained from transdifferentiated cells. Conclusions In summary, we established a protocol for reprogramming MYOD1-overexpressing PEFs into the mature skeletal muscle using signaling molecules. Our myogenic reprogramming can be used as a cell source for muscle disease models in regenerative medicine and the production of cultured meat in cellular agriculture.This work was supported by the BK21 Four program, the Korea Evaluation Institute of Industrial Technology (KEIT; 20012411), and the National Research Foundation of Korea (NRF) grant (2021R1A2C4001837)

Regulation of mouse steroidogenesis by WHISTLE and JMJD1C through histone methylation balance

The dynamic exchange of histone lysine methylation status by histone methyltransferases and demethylases has been previously implicated as an important factor in chromatin structure and transcriptional regulation. Using immunoaffinity TAP analysis, we purified the WHISTLE-interacting protein complexes, which include the heat shock protein HSP90α and the jumonji C-domain harboring the histone demethylase JMJD1C. In this study, we demonstrate that JMJD1C specifically demethylates histone H3K9 mono- and di-methylation, and mediates transcriptional activation. We also provide evidence suggesting that both WHISTLE and JMJD1C performs functions in the development of mouse testes by regulating the expression of the steroidogenesis marker, p450c17, via SF-1-mediated transcription. Furthermore, we demonstrate that WHISTLE is recruited to the p450c17 promoter via SF-1 and represses the transcription of prepubertal stages of steroidogenesis, after which JMJD1C replaces WHISTLE and activates the expression of target genes via SF-1-mediated interactions. Our results demonstrate that the histone methylation balance mediated by HMTase WHISTLE and demethylase JMJD1C perform a transcriptional regulatory function in mouse testis development

Necessity of negative serial correlation for mean-reversion of stock prices

In this paper, we show that the widespread common perception that stock returns must necessarily exhibit negative first-order autocorrelation for the mean-reverting components of stock prices is not quite correct. The necessity of negative autocorrelation in one-period returns is an artifact of assuming an AR(1) process for the transitory components of the underlying stock price and assuming independence between innovations in the transitory process and innovations in the permanent components. The sign of first-order return autocorrelation for mean-reverting property could be positive under a different lag structure of the transitory components of stock prices