The Formation of the First Massive Black Holes

Supermassive black holes (SMBHs) are common in local galactic nuclei, and SMBHs as massive as several billion solar masses already exist at redshift z=6. These earliest SMBHs may grow by the combination of radiation-pressure-limited accretion and mergers of stellar-mass seed BHs, left behind by the first generation of metal-free stars, or may be formed by more rapid direct collapse of gas in rare special environments where dense gas can accumulate without first fragmenting into stars. This chapter offers a review of these two competing scenarios, as well as some more exotic alternative ideas. It also briefly discusses how the different models may be distinguished in the future by observations with JWST, (e)LISA and other instruments.Comment: 47 pages with 306 references; this review is a chapter in "The First Galaxies - Theoretical Predictions and Observational Clues", Springer Astrophysics and Space Science Library, Eds. T. Wiklind, V. Bromm & B. Mobasher, in pres

Improved Structure Preserving Signatures under Standard Bilinear Assumptions

We show that the recent structure-preserving signature (SPS) scheme of Kiltz, Pan and Wee [CRYPTO 2015], provably secure under the standard bilinear pairings group assumption SXDH, can be improved to have one less group element and one less pairing product equation in the signature verification step. Our improved SPS scheme only requires six group elements (five in one group, and one in the other), and two pairing product equations for verification. The number of pairing product equations is optimal, as it matches a known lower bound of Abe et al [CRYPTO 2011]. The number of group elements in the signature also approaches the known lower bound of four for SXDH assumption. Further, while the earlier scheme had a security reduction which incurred a security loss that is quadratic in number of queries $Q$, our novel security reduction incurs only a $Q \log{Q}$ factor loss in security. Structure-preserving signatures are used pervasively in group signatures, group encryptions, blind signatures, proxy signatures and many other anonymous credential applications. Our work directly leads to improvements in these schemes. Moreover, the improvements are usually of a higher multiplicative factor order, as these constructions use Groth-Sahai NIZK proofs for zero-knowledge verification of pairing-product equations. We also give our construction under the more general and standard \D_k-MDDH (Matrix-DDH) assumption. The signature size in our scheme is $3k+2$ elements in one group, and one element in the other. The number of pairing product equations required for verification is only $2k$, whereas the earlier schemes required at least $2k+1$ equations

Germline variants and breast cancer survival in patients with distant metastases at primary breast cancer diagnosis

Breast cancer metastasis accounts for most of the deaths from breast cancer. Identification of germline variants associated with survival in aggressive types of breast cancer may inform understanding of breast cancer progression and assist treatment. In this analysis, we studied the associations between germline variants and breast cancer survival for patients with distant metastases at primary breast cancer diagnosis. We used data from the Breast Cancer Association Consortium (BCAC) including 1062 women of European ancestry with metastatic breast cancer, 606 of whom died of breast cancer. We identified two germline variants on chromosome 1, rs138569520 and rs146023652, significantly associated with breast cancer-specific survival (P = 3.19 × 10−8 and 4.42 × 10−8). In silico analysis suggested a potential regulatory effect of the variants on the nearby target genes SDE2 and H3F3A. However, the variants showed no evidence of association in a smaller replication dataset. The validation dataset was obtained from the SNPs to Risk of Metastasis (StoRM) study and included 293 patients with metastatic primary breast cancer at diagnosis. Ultimately, larger replication studies are needed to confirm the identified associations

Association of germline genetic variants with breast cancer-specific survival in patient subgroups defined by clinic-pathological variables related to tumor biology and type of systemic treatment

BACKGROUND: Given the high heterogeneity among breast tumors, associations between common germline genetic variants and survival that may exist within specific subgroups could go undetected in an unstratified set of breast cancer patients. METHODS: We performed genome-wide association analyses within 15 subgroups of breast cancer patients based on prognostic factors, including hormone receptors, tumor grade, age, and type of systemic treatment. Analyses were based on 91,686 female patients of European ancestry from the Breast Cancer Association Consortium, including 7531 breast cancer-specific deaths over a median follow-up of 8.1 years. Cox regression was used to assess associations of common germline variants with 15-year and 5-year breast cancer-specific survival. We assessed the probability of these associations being true positives via the Bayesian false discovery probability (BFDP < 0.15). RESULTS: Evidence of associations with breast cancer-specific survival was observed in three patient subgroups, with variant rs5934618 in patients with grade 3 tumors (15-year-hazard ratio (HR) [95% confidence interval (CI)] 1.32 [1.20, 1.45], P = 1.4E-08, BFDP = 0.01, per G allele); variant rs4679741 in patients with ER-positive tumors treated with endocrine therapy (15-year-HR [95% CI] 1.18 [1.11, 1.26], P = 1.6E-07, BFDP = 0.09, per G allele); variants rs1106333 (15-year-HR [95% CI] 1.68 [1.39,2.03], P = 5.6E-08, BFDP = 0.12, per A allele) and rs78754389 (5-year-HR [95% CI] 1.79 [1.46,2.20], P = 1.7E-08, BFDP = 0.07, per A allele), in patients with ER-negative tumors treated with chemotherapy. CONCLUSIONS: We found evidence of four loci associated with breast cancer-specific survival within three patient subgroups. There was limited evidence for the existence of associations in other patient subgroups. However, the power for many subgroups is limited due to the low number of events. Even so, our results suggest that the impact of common germline genetic variants on breast cancer-specific survival might be limited