Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d

For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of arithmetic genus n), and exhibit all (E,P) attaining this minimum. The minimal h^(P) was known to equal 1/30 for n=1 (Oguiso-Shioda) and 11/420 for n=2 (Nishiyama), but the formulas for the general (E,P) were not known, nor was the fact that these are also the minima for an elliptic curve of discriminant degree 12n over a function field of any genus. For n=3 both the minimal height (23/840) and the explicit curves are new. These (E,P) also have the property that that mP is an integral point (a point of naive height zero) for each m=1,2,...,M, where M=6,8,9 for n=1,2,3; this, too, is maximal in each of the three cases.Comment: 15 pages; some lines in the TeX source are commented out with "%" to meet the 15-page limit for ANTS proceeding

L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields

The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many examples of L-functions over function fields vanishing to high order at the center point of their functional equation. The main application is that for every prime p and every integer g>0 there are absolutely simple abelian varieties of dimension g over Fp(t) for which the BSD conjecture holds and which have arbitrarily large rank.Comment: To appear in Inventiones Mathematica

Non-liftable Calabi-Yau spaces

We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and D. van Straten.Comment: 16 pages, 5 tables; v2: minor corrections and addition

Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19

It is known that K3 surfaces S whose Picard number rho (= rank of the Neron-Severi group of S) is at least 19 are parametrized by modular curves X, and these modular curves X include various Shimura modular curves associated with congruence subgroups of quaternion algebras over Q. In a family of such K3 surfaces, a surface has rho=20 if and only if it corresponds to a CM point on X. We use this to compute equations for Shimura curves, natural maps between them, and CM coordinates well beyond what could be done by working with the curves directly as we did in ``Shimura Curve Computations'' (1998) = Comment: 16 pages (1 figure drawn with the LaTeX picture environment); To appear in the proceedings of ANTS-VIII, Banff, May 200

Magnetic-Field-Induced Antiferromagnetism in Two-Dimensional Hubbard Model: Analysis of CeRhIn5_5

We propose the mechanism for the magnetic-field-induced antiferromagnetic (AFM) state in a two-dimensional Hubbard model in the vicinity of the AFM quantum critical point (QCP), using the fluctuation-exchange (FLEX) approximation by taking the Zeeman energy due to the magnetic field $B$ into account. In the vicinity of the QCP, we find that the AFM correlation perpendicular to $B$ is enhanced, whereas that parallel to $B$ is reduced. This fact means that the finite magnetic field increases $T_N$, with the AFM order perpendicular to $B$. The increment in $T_N$ can be understood in terms of the reduction of both quantum and thermal fluctuations due to the magnetic field, which is caused by the self-energy effect within the FLEX approximation. The present study naturally explains the increment in $T_N$ in CeRhIn_5 under the magnetic field found recently.Comment: 5 page

Dose-Related Estrogen Effects on Gene Expression in Fetal Mouse Prostate Mesenchymal Cells

Developmental exposure of mouse fetuses to estrogens results in dose-dependent permanent effects on prostate morphology and function. Fetal prostatic mesenchyme cells express estrogen receptor alpha (ERα) and androgen receptors and convert stimuli from circulating estrogens and androgens into paracrine signaling to regulate epithelial cell proliferation and differentiation. To obtain mechanistic insight into the role of different doses of estradiol (E2) in regulating mesenchymal cells, we examined E2-induced transcriptomal changes in primary cultures of fetal mouse prostate mesenchymal cells. Urogenital sinus mesenchyme cells were obtained from male mouse fetuses at gestation day 17 and exposed to 10 pM, 100 pM or 100 nM E2 in the presence of a physiological concentration of dihydrotestosterone (0.69 nM) for four days. Gene ontology studies suggested that low doses of E2 (10 pM and 100 pM) induce genes involved in morphological tissue development and sterol biosynthesis but suppress genes involved in growth factor signaling. Genes involved in cell adhesion were enriched among both up-regulated and down-regulated genes. Genes showing inverted-U-shape dose responses (enhanced by E2 at 10 pM E2 but suppressed at 100 pM) were enriched in the glycolytic pathway. At the highest dose (100 nM), E2 induced genes enriched for cell adhesion, steroid hormone signaling and metabolism, cytokines and their receptors, cell-to-cell communication, Wnt signaling, and TGF- β signaling. These results suggest that prostate mesenchymal cells may regulate epithelial cells through direct cell contacts when estrogen level is low whereas secreted growth factors and cytokines might play significant roles when estrogen level is high

The IGF2 intronic miR-483 selectively enhances transcription from IGF2 fetal promoters and enhances tumorigenesis

Insulin-like growth factor 2 (IGF2), a developmentally regulated and maternally imprinted gene, is frequently overexpressed in pediatric cancers. Although loss of imprinting (LOI) at fetal promoters contributes to increased IGF2 in tumors, the magnitude of IGF2 expression suggests the involvement of additional regulatory mechanisms. A microRNA (miRNA) screen of primary Wilms' tumors identified specific overexpression of miR-483-5p, which is embedded within the IGF2 gene. Unexpectedly, the IGF2 mRNA itself is transcriptionally up-regulated by miR-483-5p. A nuclear pool of miR-483-5p binds directly to the 5′ untranslated region (UTR) of fetal IGF2 mRNA, enhancing the association of the RNA helicase DHX9 to the IGF2 transcript and promoting IGF2 transcription. Ectopic expression of miR-483-5p in IGF2-dependent sarcoma cells is correlated with increased tumorigenesis in vivo. Together, these observations suggest a functional positive feedback loop of an intronic miRNA on transcription of its host gene

Reversal of age-related learning deficiency by the vertebrate PACAP and IGF-1 in a novel invertebrate model of aging: the pond snail (Lymnaea Stagnalis)

With the increase of life span, nonpathological age-related memory decline is affecting an increasing number of people. However, there is evidence that age-associated memory impairment only suspends, rather than irreversibly extinguishes, the intrinsic capacity of the aging nervous system for plasticity (1). Here, using a molluscan model system, we show that the age-related decline in memory performance can be reversed by administration of the pituitary adenylate cyclase activating polypeptide (PACAP). Our earlier findings showed that a homolog of the vertebrate PACAP38 and its receptors exist in the pond snail (Lymnaea stagnalis) brain (2), and it is both necessary and instructive for memory formation after reward conditioning in young animals (3). Here we show that exogenous PACAP38 boosts memory formation in aged Lymnaea, where endogenous PACAP38 levels are low in the brain. Treatment with insulin-like growth factor-1, which in vertebrates was shown to transactivate PACAP type I (PAC1) receptors (4) also boosts memory formation in aged pond snails. Due to the evolutionarily conserved nature of these polypeptides and their established role in memory and synaptic plasticity, there is a very high probability that they could also act as “memory rejuvenating” agents in humans

Expanding homogeneous culture of human primordial germ cell-like cells maintaining germline features without serum or feeder layers.

In vitro expansion of human primordial germ cell-like cells (hPGCLCs), a pluripotent stem cell-derived PGC model, has proved challenging due to rapid loss of primordial germ cell (PGC)-like identity and limited cell survival/proliferation. Here, we describe long-term culture hPGCLCs (LTC-hPGCLCs), which actively proliferate in a serum-free, feeder-free condition without apparent limit as highly homogeneous diploid cell populations maintaining transcriptomic and epigenomic characteristics of hPGCLCs. Histone proteomics confirmed reduced H3K9me2 and increased H3K27me3 marks in LTC-hPGCLCs compared with induced pluripotent stem cells (iPSCs). LTC-hPGCLCs established from multiple human iPSC clones of both sexes were telomerase positive, senescence-free cells readily passaged with minimal cell death or deviation from the PGC-like identity. LTC-hPGCLCs are capable of differentiating to DAZL-positive M-spermatogonia-like cells in the xenogeneic reconstituted testis (xrTestis) organ culture milieu as well as efficiently producing fully pluripotent embryonic germ cell-like cells in the presence of stem cell factor and fibroblast growth factor 2. Thus, LTC-hPGCLCs provide convenient access to unlimited amounts of high-quality and homogeneous hPGCLCs

PAC1 receptor-mediated clearance of tau in postsynaptic compartments attenuates tau pathology in mouse brain

Accumulation of pathological tau in synapses has been identified as an early event in Alzheimer's disease (AD) and correlates with cognitive decline in patients with AD. Tau is a cytosolic axonal protein, but under disease conditions, tau accumulates in postsynaptic compartments and presynaptic terminals, due to missorting within neurons, transsynaptic transfer between neurons, or a failure of clearance pathways. Using subcellular fractionation of brain tissue from rTg4510 tau transgenic mice with tauopathy and human postmortem brain tissue from patients with AD, we found accumulation of seed-competent tau predominantly in postsynaptic compartments. Tau-mediated toxicity in postsynaptic compartments was exacerbated by impaired proteasome activity detected by measuring lysine-48 polyubiquitination of proteins targeted for proteasomal degradation. To combat the accumulation of tau and proteasome impairment in the postsynaptic compartments of rTg4510 mouse brain, we stimulated the pituitary adenylate cyclase-activating polypeptide (PACAP) type 1 receptor (PAC1R) with its ligand PACAP administered intracerebroventricularly to rTg4510 mice. We observed enhanced synaptic proteasome activity and reduced total tau in postsynaptic compartments in mouse brain after PACAP treatment. The clearance of tau from postsynaptic compartments correlated with attenuated tauopathy and improved cognitive performance of rTg4510 transgenic mice on two behavioral tests. These results suggest that activating PAC1R could prevent accumulation of aggregate-prone tau and indicate a potential therapeutic approach for AD and other tauopathies