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This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187 , 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes.

Melatonin is probably produced in all cells but is only secreted by the pineal gland. The pineal secretion of melatonin is determined by the light–dark cycle, and it is only released at night. Melatonin regulates biological rhythms via its receptors located in the suprachiasmatic nuclei of the hypothalamus. Melatonin also has strong antioxidant activities to scavenge free radicals such as reactive oxygen species (ROS). The direct free radical scavenging actions are receptor independent. ROS play an important role in reproductive function including in the ovulatory process. However, excessive ROS can also have an adverse effect on oocytes because of oxidative stress, thereby causing infertility. It is becoming clear that melatonin is located in the ovarian follicular fluid and in the oocytes themselves, which protects these cells from oxidative damage as well as having other beneficial actions in oocyte maturation, fertilization, and embryo development. Trials on humans have investigated the improvement of outcomes of assisted reproductive technology (ART), such as in vitro fertilization and embryo transfer (IVF-ET), by way of administering melatonin to patients suffering from infertility. In addition, clinical research has examined melatonin as an anti-aging molecule via its antioxidative actions, and its relationship with the aging diseases, e.g., Alzheimer’s and Parkinson’s disease, is also underway. Melatonin may also reduce ovarian aging, which is a major issue in assisted reproductive technology. This review explains the relationship between melatonin and human reproductive function, as well as the clinical applications expected to improve the outcomes of assisted reproductive technology such as IVF, while also discussing possibilities for melatonin in preventing ovarian aging.

The ordinary differential equation (ODE) models of optimization methods allow for concise proofs of convergence rates through discussions based on Lyapunov functions. The weak discrete gradient (wDG) framework discretizes ODEs while preserving the properties of convergence, serving as a foundation for deriving optimization methods. Although various optimization methods have been derived through wDG, their properties and practical applicability remain underexplored. Hence, this study elucidates these aspects through numerical experiments. Particularly, although wDG yields several implicit methods, we highlight the potential utility of these methods in scenarios where the objective function incorporates a regularization term.

The incidence of prostate cancer (PC) has been increasing in Asian countries, where it was previously low. Although the adoption of a Westernized lifestyle is a possible explanation, the incidence is statistically biased due to the increase in prostate-specific antigen (PSA) screening and the accuracy of national cancer registration systems. Studies on latent PC provide less biased information. This review included studies evaluating latent PC in several countries after excluding studies using random or single-section evaluations and those that did not mention section thickness. The findings showed that latent PC prevalence has been stable since 1950 in Western countries, but has increased over time in Asian countries. Latent PC in Asian men has increased in both prevalence and number of high-grade cases. Racial differences between Caucasian and Asian men may explain the tumor location of latent PC. In conclusion, the recent increase in latent PC in Asian men is consistent with an increase in clinical PC. Evidence suggests that this increase is caused not only by the increase in PSA screening, but also by the adoption of a more Westernized lifestyle. Autopsy findings suggest the need to reconsider the definition of clinically insignificant PC.

Somatic mutations in Mediator complex subunit 12 (MED12m) have been reported as a biomarker of uterine fibroids (UFs). However, the role of MED12m is still unclear in the pathogenesis of UFs. Therefore, we investigated the differences in DNA methylome, transcriptome, and histological features between MED12m-positive and -negative UFs. DNA methylomes and transcriptomes were obtained from MED12m-positive and -negative UFs and myometrium, and hierarchically clustered. Differentially expressed genes in comparison with the myometrium and co-expressed genes detected by weighted gene co-expression network analysis were subjected to gene ontology enrichment analyses. The amounts of collagen fibers and the number of blood vessels and smooth muscle cells were histologically evaluated. Hierarchical clustering based on DNA methylation clearly separated the myometrium, MED12m-positive, and MED12m-negative UFs. MED12m-positive UFs had the increased activities of extracellular matrix formation, whereas MED12m-negative UFs had the increased angiogenic activities and smooth muscle cell proliferation. The MED12m-positive and -negative UFs had different DNA methylation, gene expression, and histological features. The MED12m-positive UFs form the tumor with a rich extracellular matrix and poor blood vessels and smooth muscle cells compared to the MED12m-negative UFs, suggesting MED12 mutations affect the tissue composition of UFs.

This paper deals with the geometric numerical integration of gradient flow and its application to optimization. Gradient flows often appear as model equations of various physical phenomena, and their dissipation laws are essential. Therefore, dissipative numerical methods, which are numerical methods replicating the dissipation law, have been studied in the literature. Recently, Cheng, Liu, and Shen proposed a novel dissipative method, the Lagrange multiplier approach, for gradient flows, which is computationally cheaper than existing dissipative methods. Although their efficacy is numerically confirmed in existing studies, the existence results of the Lagrange multiplier approach are not known in the literature. In this paper, we establish some existence results. We prove the existence of the solution under a relatively mild assumption. In addition, by restricting ourselves to a special case, we show some existence and uniqueness results with concrete bounds. As gradient flows also appear in optimization, we further apply the latter results to optimization problems.

Gavin Kelsey and colleagues report methylation landscapes in mouse oocytes, sperm and blastocysts. They find that the majority of methylated CpG islands in oocytes display incomplete demethylation in preimplantation embryos. Elucidating how and to what extent CpG islands (CGIs) are methylated in germ cells is essential to understand genomic imprinting and epigenetic reprogramming 1 , 2 , 3 . Here we present, to our knowledge, the first integrated epigenomic analysis of mammalian oocytes, identifying over a thousand CGIs methylated in mature oocytes. We show that these CGIs depend on DNMT3A and DNMT3L 4 , 5 but are not distinct at the sequence level, including in CpG periodicity 6 . They are preferentially located within active transcription units and are relatively depleted in H3K4me3, supporting a general transcription-dependent mechanism of methylation. Very few methylated CGIs are fully protected from post-fertilization reprogramming but, notably, the majority show incomplete demethylation in embryonic day (E) 3.5 blastocysts. Our study shows that CGI methylation in gametes is not entirely related to genomic imprinting but is a strong factor in determining methylation status in preimplantation embryos, suggesting a need to reassess mechanisms of post-fertilization demethylation.

Eggs play important roles as food resources and nutraceuticals, to alleviate malnutrition and to improve health status in the world. Since free amino acids contribute to the nutritional values and food tastes, we investigated a total of 81 eggs from five chicken breeds, which are Australorp, Nagoya (NGY), Rhode Island Red (RIR), Shamo (SHA), Ukokkei, and two F 1 hybrids (NGYxRIR and SHAxRIR) to test impact on genetic differences in 10 egg traits, 20 yolk amino acid traits, and 18 albumen amino acid traits. One-way ANOVA revealed significant breed effects on 10 egg traits, 20 yolk amino acid traits, and 15 albumen amino acid traits. Moreover, a significant heterosis effect on yolk aspartic acid was identified. In addition, positive correlations were found broadly among traits within each trait category (egg traits, yolk amino acid traits, and albumen amino acid traits), whereas there were basically no or weak correlations among the trait categories. These results suggest that almost all traits can be dramatically modified by genetic factor, and there will be partially independent production systems of amino acids into yolk and albumen. Since there will be typical quantitative genetic architecture of egg contents, further genetic analyses will be needed.

Genome-wide dynamic changes in DNA methylation are indispensable for germline development and genomic imprinting in mammals. Here, we report single-base resolution DNA methylome and transcriptome maps of mouse germ cells, generated using whole-genome shotgun bisulfite sequencing and cDNA sequencing (mRNA-seq). Oocyte genomes showed a significant positive correlation between mRNA transcript levels and methylation of the transcribed region. Sperm genomes had nearly complete coverage of methylation, except in the CpG-rich regions, and showed a significant negative correlation between gene expression and promoter methylation. Thus, these methylome maps revealed that oocytes and sperms are widely different in the extent and distribution of DNA methylation. Furthermore, a comparison of oocyte and sperm methylomes identified more than 1,600 CpG islands differentially methylated in oocytes and sperm (germline differentially methylated regions, gDMRs), in addition to the known imprinting control regions (ICRs). About half of these differentially methylated DNA sequences appear to be at least partially resistant to the global DNA demethylation that occurs during preimplantation development. In the absence of Dnmt3L, neither methylation of most oocyte-methylated gDMRs nor intragenic methylation was observed. There was also genome-wide hypomethylation, and partial methylation at particular retrotransposons, while maintaining global gene expression, in oocytes. Along with the identification of the many Dnmt3L-dependent gDMRs at intragenic regions, the present results suggest that oocyte methylation can be divided into 2 types: Dnmt3L-dependent methylation, which is required for maternal methylation imprinting, and Dnmt3L-independent methylation, which might be essential for endogenous retroviral DNA silencing. The present data provide entirely new perspectives on the evaluation of epigenetic markers in germline cells.

Decidualization can be induced by culturing human endometrial stromal cells (ESCs) with several decidualization stimuli, such as cAMP, medroxyprogesterone acetate (MPA) or Estradiol (E 2 ). However, it has been unclear how decidualized cells induced by different stimuli are different. We compared transcriptomes and cellular functions of decidualized ESCs induced by different stimuli (MPA, E 2  + MPA, cAMP, and cAMP + MPA). We also investigated which decidualization stimulus induces a closer in vivo decidualization. Differentially expressed genes (DEGs) and altered cellular functions by each decidualization stimuli were identified by RNA-sequence and gene-ontology analysis. DEGs was about two times higher for stimuli that use cAMP (cAMP and cAMP + MPA) than for stimuli that did not use cAMP (MPA and E 2  + MPA). cAMP-using stimuli altered the cellular functions including angiogenesis, inflammation, immune system, and embryo implantation whereas MPA-using stimuli (MPA, E 2  + MPA, and cAMP + MPA) altered the cellular functions associated with insulin signaling. A public single-cell RNA-sequence data of the human endometrium was utilized to analyze in vivo decidualization. The altered cellular functions by in vivo decidualization were close to those observed by cAMP + MPA-induced decidualization. In conclusion, decidualized cells induced by different stimuli have different transcriptome and cellular functions. cAMP + MPA may induce a decidualization most closely to in vivo decidualization.