An Observation about Variations of the Diffie-Hellman Assumption

We generalize the Strong Boneh-Boyen (SBB) signature scheme to sign vectors; we call this scheme GSBB. We show that if a particular (but most natural) average case reduction from SBB to GSBB exists, then the Strong Diffie-Hellman (SDH) and the Computational Diffie-Hellman (CDH) have the same worst-case complexity.

A Poster about the Recent History of Fractional Calculus

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22

A Poster about the Old History of Fractional Calculus

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22

Global variations and time trends in the prevalence of childhood myopia, a systematic review and quantitative meta-analysis:implications for aetiology and early prevention

The aim of this review was to quantify the global variation in childhood myopia prevalence over time taking account of demographic and study design factors. A systematic review identified population-based surveys with estimates of childhood myopia prevalence published by February 2015. Multilevel binomial logistic regression of log odds of myopia was used to examine the association with age, gender, urban versus rural setting and survey year, among populations of different ethnic origins, adjusting for study design factors. 143 published articles (42 countries, 374 349 subjects aged 1- 18 years, 74 847 myopia cases) were included. Increase in myopia prevalence with age varied by ethnicity. East Asians showed the highest prevalence, reaching 69% (95% credible intervals (CrI) 61% to 77%) at 15 years of age (86% among Singaporean-Chinese). Blacks in Africa had the lowest prevalence; 5.5% at 15 years (95% CrI 3% to 9%). Time trends in myopia prevalence over the last decade were small in whites, increased by 23% in East Asians, with a weaker increase among South Asians. Children from urban environments have 2.6 times the odds of myopia compared with those from rural environments. In whites and East Asians sex differences emerge at about 9 years of age; by late adolescence girls are twice as likely as boys to be myopic. Marked ethnic differences in age-specific prevalence of myopia exist. Rapid increases in myopia prevalence over time, particularly in East Asians, combined with a universally higher risk of myopia in urban settings, suggest that environmental factors play an important role in myopia development, which may offer scope for prevention.

Ammonite biostratigraphy, lithofacies variations, and paleoceanographic implications for Barremian-Aptian sequences of northeastern Mexico

Two Barremian-Aptian sequences studied in Durango and Nuevo Leon States, northeastern Mexico include three lithic units which have been described as the Cupido Formation of Barremian-early Early Aptian age, its lateral equivalent, the Lower Tamaulipas Formation, and the La Peña Formation extending through the early Albian. ^ The present work improves the existing ammonite Aptian biozonation by considering constraints associated with a discontinuous spatial and temporal record of the different taxa within the La Peña Formation. ^ Four ammonite biozones are established: (1) The Dufrenoyia justinae Zone for the late Early Aptian, (2) The Burckhardtites nazasensis/Rhytidoplites robertsi Zone for the middle Aptian, (3) The Cheloniceras inconstans Zone for the early Late Aptian, and (4) The Hypacanthoplites cf. leanzae Zone for the late late Aptian. ^ Also, a detailed sedimentological analysis of the sections shed further light on the possible causes that controlled intermittent occurrences of the ammonites in relation to the prevailing paleoceanographic and paleoecologic conditions in northeastern Mexico during the late Barremian-Aptian. ^ Microfacies analyses show that the upper part of the Cupido facies are represented by biocalcirudite with rudists, biocalcarenites with oolites and algae, and rich benthonic foraminifera assemblages with ostracods. These facies are related to paleoceanographic conditions of sedimentation within a shallow-marine carbonate platform. Its lateral equivalent, deep-water facies extended to the southeast and it is represented by the Lower Tamaulipas Formation, which includes planktonic foraminifera, ostracods, and mollusk and echinoid fragments. The beginning of deposition of the La Peña Formation in the late Early Aptian is characterized by an increase in terrigenous materials and significant decrease in the abundance of benthic fauna. The La Peña Formation is recognized by an alternation of marls and shale limestones containing ammonites, planktonic foraminifera, ostracods, and radiolaria toward the top. Accumulation of the La Peña continued throughout the end of the Aptian and records changes in conditions of sedimentation and productivity in the water column, which abruptly terminated the carbonate deposition in the Cupido Platform. ^ Results of carbon/carbonate content analyses show that changes from the Cupido to the La Peña facies are also characterized by an increase of organic carbon, which indicate the onset of enhanced dysoxic/anoxic conditions in the lower water column. ^