A Lie algebra attached to a projective variety

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra \slt on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding \slt-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori, hyperk\"ahler manifolds and flag varieties. We pay special attention to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.Comment: AMSTeX v2.1, 46 page

Monodromy of Cyclic Coverings of the Projective Line

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae

Constraining the Kahler Moduli in the Heterotic Standard Model

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to determine lower and upper bounds to the region of the Kaehler moduli space where such compactifications can exist. We show how small these regions can be, working out in full detail the case of the recently proposed Heterotic Standard Model. More explicitely, we exhibit Kaehler classes in these regions for which the visible vector bundle is stable. On the other hand, there is no polarization for which the hidden bundle is stable.Comment: 28 pages, harvmac. Exposition improved, references and one figure added, minor correction

The structure of 2D semi-simple field theories

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio

N- and KRAS mutations in primary testicular germ cell tumors: Incidence and possible biological implications

Recently, conflicting results have been reported on the incidence of RAS mutations in primary testicular germ cell tumors of adults (TGCTs). In four studies a low incidence of mutations (less than 15%) in a variety of TGCTs or derived cell lines was found, whereas in two other studies a high incidence of N- or KRAS mutations (over 40%) was shown. A total of 62 testicular seminomas (SE) and 34 nonseminomatous TGCTs (NS) were studied thus far. The largest series consisted of 42 TGCTs, studied on paraffin embedded tissue. We present the results of analysis for the presence of N- and KRAS mutations, in codons 12, 13, and 61, in snap frozen samples of 100 primary TGCTs, comprising 40 SE and 60 NS. Using the polymerase chain reaction (PCR) and allele specific oligonucleotide hybridization (ASO), mutations were found in five SE (three in NRAS and two in KRAS, all codon 12), and in one NS (KRAS, codon 12). To exclude underestimation of the incidence of RAS mutations in TGCTs due to the presence of an excess of wild type alleles in the analyzed sample, a PCR technique preferentially ampli

Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality

We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich intersection theory over the moduli space of N-pointed closed Riemann surfaces of the same genus. We also discuss various aspects of the geometrical setting which connects this model to PSL(2,C) Chern-Simons theory.Comment: 35 pages, references added, slightly revised introductio

Specific detection of OCT3/4 isoform A/B/B1 expression in solid (germ cell) tumours and cell lines: Confirmation of OCT3/4 specificity for germ cell tumours

Background: OCT3/4 (POU5F1) is an established diagnostic immunohistochemical marker for specific histological variants of human malignant germ cell tumours (GCTs), including the seminomatous types and the stem cell component of non-seminomas, known as embryonal carcinoma. OCT3/4 is crucial for the regulation of pluripotency and the self-renewal of normal embryonic stem-and germ cells. Detection of expression of this transcription factor is complicated by the existence of multiple pseudogenes and isoforms. Various claims have been made about OCT3/4 expression in non-GCTs, possibly related to using nonspecific detection methods. False-positive findings undermine the applicability of OCT3/4 as a specific diagnostic tool in a clinical setting. In addition, false-positive findings could result in misinterpretation of pluripotency regulation in solid somatic cancers and their stem cells. Of the three identified isoforms-OCT4A, OCT4B and OCT4B1-only OCT4A proved to regulate pluripotency. Up until now, no convincing nuclear OCT4A protein expression has been shown in somatic cancers or tissues. Methods: This study investigates expression of the various OCT3/4 isoforms in GCTs (both differentiated and undifferentiated) and somatic (non-germ cell) cancers, including representative cell lines and xenografts. Results: Using specific methods, OCT4A and OCT4B1 are shown to be preferentially expressed in undifferentiated GCTs. The OCT4B variant shows no difference in expression between GCTs (either differentiated or undifferentiated) and somatic cancers. In spite of the presence of OCT4A mRNA in somatic cancer-derived cell lines, no OCT3/4

On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem

We prove that the number of limit cycles generated by a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing tangential Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection (Gauss-Manin connection) with a quasiunipotent monodromy group.Comment: Final revisio

Serum microRNA profiles in athyroid patients on and off levothyroxine therapy

Background Levothyroxine replacement treatment in hypothyroidism is unable to restore physiological thyroxine and triiodothyronine concentrations in serum and tissues completely. Normal serum thyroid stimulating hormone (TSH) concentrations reflect only pituitary euthyroidism and, therefore, novel biomarkers representing tissue-specific thyroid state are needed. MicroRNAs (miRNAs), small non-coding regulatory RNAs, exhibit tissue-specific expression patterns and can be detectable in serum. Previous studies have demonstrated differential expression of (precursors of) miRNAs in tissues under the influence of thyroid hormone. Objective To study if serum miRNA profiles are changed in different thyroid states. Design and methods We studied 13 athyroid patients (6 males) during TSH suppressive therapy and after 4 weeks of thyroid hormone withdrawal. A magnetic bead capture system was used to isolate 384 defined miRNAs from serum. Subsequently, the TaqMan Array Card 3.0 platform was used for profiling after individual target amplification. Results Mean age of the subjects was 44.0 years (range 20–61 years). Median TSH levels were 88.9 mU/l during levothyroxine withdrawal and 0.006 mU/l during LT4 treatment with a median dosage of 2.1 μg/kg. After normalization to allow inter-sample analysis, a paired analysis did not demonstrate a significant difference in expression of any of the 384 miRNAs analyzed on and off LT4 treatment

Serum and CSF microRNAs in paediatric malignant GCTs

BACKGROUND: The current biomarkers alpha-fetoprotein and human chorionic gonadotropin have limited sensitivity and specificity for diagnosing malignant germ-cell tumours (GCTs). MicroRNAs (miRNAs) from the miR-371-373 and miR-302/367 clusters are overexpressed in all malignant GCTs, and some of these miRNAs show elevated serum levels at diagnosis. Here, we developed a robust technical pipeline to quantify these miRNAs in the serum and cerebrospinal fluid (CSF). The pipeline was used in samples from a cohort of exclusively paediatric patients with gonadal and extragonadal malignant GCTs, compared with appropriate tumour and non-tumour control groups. METHODS: We developed a method for miRNA quantification that enabled sample adequacy assessment and reliable data normalisation. We performed qRT-PCR profiling for miR-371-373 and miR-302/367 cluster miRNAs in a total of 45 serum and CSF samples, obtained from 25 paediatric patients. RESULTS: The exogenous non-human spike-in cel-miR-39-3p and the endogenous housekeeper miR-30b-5p were optimal for obtaining robust serum and CSF qRT-PCR quantification. A four-serum miRNA panel (miR-371a-3p, miR-372-3p, miR-373-3p and miR-367-3p): (i) showed high sensitivity/specificity for diagnosing paediatric extracranial malignant GCT; (ii) allowed early detection of relapse of a testicular mixed malignant GCT; and (iii) distinguished intracranial malignant GCT from intracranial non-GCT tumours at diagnosis, using CSF and serum samples. CONCLUSIONS: The pipeline we have developed is robust, scalable and transferable. It potentially promises to improve clinical management of paediatric (and adult) malignant GCTs.Grant funding was from CwCUK/GOSHCC (M.J. Murray, K.L. Raby, J.C. Nicholson, N. Coleman), SPARKS (M.J. Murray, J.C. Nicholson, N. Coleman), AstraZeneca (E. Bell, H. Brown and B. Destenaves), CRUK (N. Coleman), MRC (M.J. Murray) and an Erasmus MC MRACE grant (M.A. Rijlaarsdam). The authors also thank the Max Williamson Fund and The Perse Preparatory School, Cambridge for supporting this study.This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/bjc.2015.42