Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

Counting points on hyperelliptic curves over finite fields

International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm à la Schoof for genus 2 using Cantor's division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature

D-cycloserine augmentation of exposure-based cognitive behavior therapy for anxiety, obsessive-compulsive, and posttraumatic stress disorders: a systematic review and meta-analysis of individual participant data

Importance: Whether and under which conditions D-cycloserine (DCS) augments the effects of exposure-based cognitive behavior therapy for anxiety, obsessive-compulsive, and posttraumatic stress disorders is unclear. Objective: To clarify whether DCS is superior to placebo in augmenting the effects of cognitive behavior therapy for anxiety, obsessive-compulsive, and posttraumatic stress disorders and to evaluate whether antidepressants interact with DCS and the effect of potential moderating variables. Data Sources: PubMed, EMBASE, and PsycINFO were searched from inception to February 10, 2016. Reference lists of previous reviews and meta-analyses and reports of randomized clinical trials were also checked. Study Selection: Studies were eligible for inclusion if they were (1) double-blind randomized clinical trials of DCS as an augmentation strategy for exposure-based cognitive behavior therapy and (2) conducted in humans diagnosed as having specific phobia, social anxiety disorder, panic disorder with or without agoraphobia, obsessive-compulsive disorder, or posttraumatic stress disorder. Data Extraction and Synthesis: Raw data were obtained from the authors and quality controlled. Data were ranked to ensure a consistent metric across studies (score range, 0-100). We used a 3-level multilevel model nesting repeated measures of outcomes within participants, who were nested within studies. Results: Individual participant data were obtained for 21 of 22 eligible trials, representing 1047 of 1073 eligible participants. When controlling for antidepressant use, participants receiving DCS showed greater improvement from pretreatment to posttreatment (mean difference, -3.62; 95% CI, -0.81 to -6.43; P = .01; d = -0.25) but not from pretreatment to midtreatment (mean difference, -1.66; 95% CI, -4.92 to 1.60; P = .32; d = -0.14) or from pretreatment to follow-up (mean difference, -2.98, 95% CI, -5.99 to 0.03; P = .05; d = -0.19). Additional analyses showed that participants assigned to DCS were associated with lower symptom severity than those assigned to placebo at posttreatment and at follow-up. Antidepressants did not moderate the effects of DCS. None of the prespecified patient-level or study-level moderators was associated with outcomes. Conclusions and Relevance: D-cycloserine is associated with a small augmentation effect on exposure-based therapy. This effect is not moderated by the concurrent use of antidepressants. Further research is needed to identify patient and/or therapy characteristics associated with DCS response.2018-05-0

Fusicoccin Counteracts the Toxic Effect of Cadmium on the Growth of Maize Coleoptile Segments

The effects of cadmium (Cd; 0.1–1000 μM) and fusicoccin (FC) on growth, Cd2+ content, and membrane potential (Em) in maize coleoptile segments were studied. In addition, the Em changes and accumulation of Cd and calcium (Ca) in coleoptile segments treated with Cd2+ combined with 1 μM FC or 30 mM tetraethylammonium (TEA) chloride (K+-channel blocker) were also determined. In this study, the effects of Ca2+-channel blockers [lanthanum (La) and verapamil (Ver)] on growth and content of Cd2+ and Ca2+ in coleoptile segments were also investigated. It was found that Cd at high concentrations (100 and 1000 μM) significantly inhibited endogenous growth of coleoptile segments and simultaneously measured proton extrusion. FC combined with Cd2+ counteracted the toxic effect of Cd2+ on endogenous growth and significantly decreased Cd2+ content (not the case for Cd2+ at the highest concentration) in coleoptile segments. Addition of Cd to the control medium caused depolarization of Em, the extent of which was dependent on Cd concentration and time of treatment with Cd2+. Hyperpolarization of Em induced by FC was suppressed in the presence of Cd2+ at 1000 μM but not Cd2+ at 100 μM. It was also found that treatment of maize coleoptile segments with 30 mM TEA chloride caused hyperpolarization of Em and decreased Cd2+ content in coleoptile segments, suggesting that, in the same way as for FC, accumulation of Cd2+ was dependent on plasma membrane (PM) hyperpolarization. Similar to FC, TEA chloride also decreased Ca2+ content in coleoptile segments. La and Ver combined with Cd2+ (100 μM) significantly decreased Cd content in maize coleoptile segments, but only La completely abolished the toxic effect of Cd2+ on endogenous growth and growth in the presence of FC. Taken together, these results suggest that the mechanism by which FC counteracts the toxic effect of Cd2+ (except at 1000 μM Cd2+) on the growth of maize coleoptile segments involves both stimulation of PM H+-ATPase activity by FC as well as Cd2+-permeable, voltage-dependent Ca channels, which are blocked by FC and TEA chloride-induced PM hyperpolarization

Trapdooring Discrete Logarithms on Elliptic Curves over Rings

This paper introduces three new probabilistic encryption schemes using elliptic curves over rings. The cryptosystems are based on three specific trapdoor mechanisms allowing the recipient to recover discrete logarithms on di#erent types of curves. The first scheme is an embodiment of Naccache and Stern's cryptosystem and realizes a discrete log encryption as originally wanted in [23] by Vanstone and Zuccherato

Document collections, mobilized regulations, and the making of customary law at the end of the Middle Ages

Using late medieval examples from Switzerland, this paper argues that the emergence of formally organized archives around 1500 was part of an important shift in how documents could be deployed. However, this shift was not away from an oral and toward a literate culture, as argued in some earlier studies, but rather away from seeing documents as testimony that reminded a community about past authoritative actors, and toward relating the texts of documents to other texts, that is, to contexts. This shift took place largely through the appropriation of methods for using and organizing written material that had been developed in the realms of scholastic theology and liturgy, and applying them to secular lordship and administration. These methods provided new models for organizing collections of parchments and papers into connected archives and gave rise to new forms of text collection such as reorganized versions of law books (Spiegel, Coutumiers) containing new search tools such as tables of contents (capitulationes) and indices (abecedaria). Individual charters and scattered legal norms were also organized into textus–glossae structures in larger and smaller administrative units. In the Swiss case, the contextualization of legal texts was accompanied by an increased attribution of authority to ‘custom’ in general, because the community-oriented attribution of meaning found in earlier use was lost. Ultimately, recasting individual documents as part of larger textual contexts increased the power of rulers and ushered in an age of lawyers and of archives

The equivalence between the DHP and DLP for elliptic curves used in practical applications, revisited

The theoretical equivalence between the DLP and DHP problems was shown by Maurer in 1994. His work was then reexamined by Muzereau et al. [11] for the special case of elliptic curves used in practical cryptographic applications. This paper improves on the latter and tries to get the tightest possible reduction in terms of computational equivalence, using Maurer’s method