Quantum resource estimates for computing elliptic curve discrete logarithms

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ$Ui|\rangle$. We determine circuit implementations for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. We conclude that elliptic curve discrete logarithms on an elliptic curve defined over an $n$-bit prime field can be computed on a quantum computer with at most $9n + 2\lceil\log_2(n)\rceil+10$ qubits using a quantum circuit of at most $448 n^3 \log_2(n) + 4090 n^3$ Toffoli gates. We are able to classically simulate the Toffoli networks corresponding to the controlled elliptic curve point addition as the core piece of Shor's algorithm for the NIST standard curves P-192, P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to recent resource estimates for Shor's factoring algorithm. The results also support estimates given earlier by Proos and Zalka and indicate that, for current parameters at comparable classical security levels, the number of qubits required to tackle elliptic curves is less than for attacking RSA, suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added. ASIACRYPT 201

Microvascular function is selectively impaired in patients with hypertrophic cardiomyopathy and sarcomere myofilament gene mutations.

ObjectivesThe purpose of this study was to assess myocardial blood flow (MBF) using positron emission tomography in patients with hypertrophic cardiomyopathy (HCM) according to genetic status.BackgroundCoronary microvascular dysfunction is an important feature of HCM, associated with ventricular remodeling and heart failure. We recently demonstrated the increased prevalence of systolic dysfunction in patients with HCM with sarcomere myofilament gene mutations and postulated an association between genetic status and coronary microvascular dysfunction.MethodsMaximum MBF (intravenous dipyridamole, 0.56 mg/kg; Dip-MBF) was measured using 13N-labeled ammonia in 61 patients with HCM (age 38 ± 14 years), genotyped by automatic DNA sequencing of 8 myofilament-encoding genes (myosin-binding protein C, beta-myosin heavy chain, regulatory and essential light chains, troponin T, troponin I, troponin C, alpha-tropomyosin, and alpha-actin). In 35 patients, cardiac magnetic resonance imaging was performed.ResultsFifty-three mutations were identified in 42 of the 61 patients (genotype positive; 69%). Despite similar clinical profiles, genotype-positive patients with HCM showed substantially lower Dip-MBF compared with that of genotype-negative patients (1.7 ± 0.6 ml/min/g vs. 2.4 ± 1.2 ml/min/g; p < 0.02). A Dip-MBF <1.5 ml/min/g had 81% positive predictive value for genotype-positive status and implied a 3.5-fold independent increase in likelihood of carrying myofilament gene mutations (hazard ratio: 3.52; 95% confidence interval: 1.05 to 11.7; p = 0.04). At cardiac magnetic resonance imaging, the prevalence of late gadolinium enhancement was greater in genotype-positive patients (22 of 23 [96%] compared with 8 of 12 [67%] genotype-negative patients; p = 0.038).ConclusionsPatients with HCM with sarcomere myofilament mutations are characterized by more severe impairment of microvascular function and increased prevalence of myocardial fibrosis, compared with genotype-negative individuals. These findings suggest a direct link between sarcomere gene mutations and adverse remodeling of the microcirculation in HCM, accounting for the increased long-term prevalence of ventricular dysfunction and heart failure in genotype-positive patients

Simultaneous determination of wave speed and arrival time of reflected waves using the pressure-velocity loop

This is the post print version of the article. The official published version can be found at the link below.In a previous paper we demonstrated that the linear portion of the pressure–velocity loop (PU-loop) corresponding to early systole could be used to calculate the local wave speed. In this paper we extend this work to show that determination of the time at which the PU-loop first deviates from linearity provides a convenient way to determine the arrival time of reflected waves (Tr). We also present a new technique using the PU-loop that allows for the determination of wave speed and Tr simultaneously. We measured pressure and flow in elastic tubes of different diameters, where a strong reflection site existed at known distances away form the measurement site. We also measured pressure and flow in the ascending aorta of 11 anaesthetised dogs where a strong reflection site was produced through total arterial occlusion at four different sites. Wave speed was determined from the initial slope of the PU-loop and Tr was determined using a new algorithm that detects the sampling point at which the initial linear part of the PU-loop deviates from linearity. The results of the new technique for detecting Tr were comparable to those determined using the foot-to-foot and wave intensity analysis methods. In elastic tubes Tr detected using the new algorithm was almost identical to that detected using wave intensity analysis and foot-to-foot methods with a maximum difference of 2%. Tr detected using the PU-loop in vivo highly correlated with that detected using wave intensity analysis (r 2 = 0.83, P < 0.001). We conclude that the new technique described in this paper offers a convenient and objective method for detecting Tr, and allows for the dynamic determination of wave speed and Tr, simultaneously

Effects of seagrasses and algae of the Caulerpa family on hydrodynamics and particle-trapping rates

The widespread decline of seagrass beds within the Mediterranean often results in the replacement of seagrasses by opportunistic green algae of the Caulerpa family. Because Caulerpa beds have a different height, stiffness and density compared to seagrasses, these changes in habitat type modify the interaction of the seafloor with hydrodynamics, influencing key processes such as sediment resuspension and particle trapping. Here, we compare the effects on hydrodynamics and particle trapping of Caulerpa taxifolia, C. racemosa, and C. prolifera with the Mediterranean seagrasses Cymodocea nodosa and Posidonia oceanica. All macrophyte canopies reduced near-bed volumetric flow rates compared to bare sediment, vertical profiles of turbulent kinetic energy revealed peak values around the top of the canopies, and maximum values of Reynolds stress increased by a factor of between 1.4 (C. nodosa) and 324.1 (P. oceanica) when vegetation was present. All canopies enhanced particle retention rates compared to bare sediment. The experimental C. prolifera canopy was the most effective at particle retention (m2 habitat); however, C. racemosa had the largest particle retention capacity per structure surface area. Hence, in terms of enhancing particle trapping and reducing hydrodynamic forces at the sediment surface, Caulerpa beds provided a similar or enhanced function compared to P.oceanica and C. nodosa. However, strong seasonality in the leaf area index of C. racemosa and C. taxifolia within the Mediterranean, combined with a weak rhizome structure, suggests that sediments maybe unprotected during winter storms, when most erosion occurs. Hence, replacement of seagrass beds with Caulerpa is likely to have a major influence on annual sediment dynamics at ecosystem scales.This research was funded by the European Network of Excellence ‘‘Marine Biodiversity and Ecosystem Function’’ (MarBEF); FP6, EC contract no. 505446 and a grant from the Fundacio ´n BBVA. EPM was supported by a European Union Marie Curie host fellowship for transfer of knowledge, MTKD-CT-2004-509254, the Spanish national project EVAMARIA (CTM2005-00395/MAR) and the regional government of Andalusia project FUNDIV(P07-RNM-2516)

Synchronisation of egg hatching of brown hairstreak (Thecla betulae) and budburst of blackthorn (Prunus spinosa) in a warmer future

Synchronisation of the phenology of insect herbivores and their larval food plant is essential for the herbivores’ fitness. The monophagous brown hairstreak (Thecla betulae) lays its eggs during summer, hibernates as an egg, and hatches in April or May in the Netherlands. Its main larval food plant blackthorn (Prunus spinosa) flowers in early spring, just before the leaves appear. As soon as the Blackthorn opens its buds, and this varies with spring temperatures, food becomes available for the brown hairstreak. However, the suitability of the leaves as food for the young caterpillars is expected to decrease rapidly. Therefore, the timing of egg hatch is an important factor for larval growth. This study evaluates food availability for brown hairstreak at different temperatures. Egg hatch and budburst were monitored from 2004 to 2008 at different sites in the Netherlands. Results showed ample food availability at all monitored temperatures and sites but the degree of synchrony varied strongly with spring temperatures. To further study the effect of temperature on synchronisation, an experiment using normal temperatures of a reference year (T) and temperatures of T + 5°C was carried out in climate chambers. At T + 5°C, both budburst and egg hatch took place about 20 days earlier and thus, on average, elevated temperature did not affect synchrony. However, the total period of budburst was 11 days longer, whereas the period of egg hatching was 3 days shorter. The implications for larval growth by the brown hairstreak under a warmer climate are considered.

ADC Nonlinearity Correction for the Majorana Demonstrator

Imperfections in analog-to-digital conversion (ADC) cannot be ignored when signal digitization requirements demand both wide dynamic range and high resolution, as is the case for the Majorana Demonstrator 76Ge neutrinoless double-beta decay search. Enabling the experiment's high-resolution spectral analysis and efficient pulse shape discrimination required careful measurement and correction of ADC nonlinearities. A simple measurement protocol was developed that did not require sophisticated equipment or lengthy data-taking campaigns. A slope-dependent hysteresis was observed and characterized. A correction applied to digitized waveforms prior to signal processing reduced the differential and integral nonlinearities by an order of magnitude, eliminating these as dominant contributions to the systematic energy uncertainty at the double-beta decay Q value

Divided attention selectively impairs memory for self-relevant information

Information that is relevant to oneself tends to be remembered more than information that relates to other people, but the role of attention in eliciting this "self-reference effect" is unclear. In the present study, we assessed the importance of attention in self-referential encoding using an ownership paradigm, which required participants to encode items under conditions of imagined ownership by themselves or by another person. Previous work has established that this paradigm elicits a robust self-reference effect, with more "self-owned" items being remembered than "other-owned" items. Access to attentional resources was manipulated using divided-attention tasks at encoding. A significant self-reference effect emerged under full-attention conditions and was related to an increase in episodic recollection for self-owned items, but dividing attention eliminated this memory advantage. These findings are discussed in relation to the nature of self-referential cognition and the importance of attentional resources at encoding in the manifestation of the self-reference effect in memory