Non-minimality of corners in subriemannian geometry

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.Comment: 11 pages, final versio

ERP evidence suggests executive dysfunction in ecstasy polydrug users

Background: Deficits in executive functions such as access to semantic/long-term memory have been shown in ecstasy users in previous research. Equally, there have been many reports of equivocal findings in this area. The current study sought to further investigate behavioural and electro-physiological measures of this executive function in ecstasy users. Method: Twenty ecstasy–polydrug users, 20 non-ecstasy–polydrug users and 20 drug-naïve controls were recruited. Participants completed background questionnaires about their drug use, sleep quality, fluid intelligence and mood state. Each individual also completed a semantic retrieval task whilst 64 channel Electroencephalography (EEG) measures were recorded. Results: Analysis of Variance (ANOVA) revealed no between-group differences in behavioural performance on the task. Mixed ANOVA on event-related potential (ERP) components P2, N2 and P3 revealed significant between-group differences in the N2 component. Subsequent exploratory univariate ANOVAs on the N2 component revealed marginally significant between-group differences, generally showing greater negativity at occipito-parietal electrodes in ecstasy users compared to drug-naïve controls. Despite absence of behavioural differences, differences in N2 magnitude are evidence of abnormal executive functioning in ecstasy–polydrug users

Prospective memory functioning among ecstasy/polydrug users: evidence from the Cambridge Prospective Memory Test (CAMPROMPT)

Rationale: Prospective memory (PM) deficits in recreational drug users have been documented in recent years. However, the assessment of PM has largely been restricted to self-reported measures that fail to capture the distinction between event-based and time-based PM. The aim of the present study is to address this limitation. Objectives: Extending our previous research, we augmented the range laboratory measures of PM by employing the CAMPROMPT test battery to investigate the impact of illicit drug use on prospective remembering in a sample of cannabis only, ecstasy/polydrug and non-users of illicit drugs, separating event and time-based PM performance. We also administered measures of executive function and retrospective memory in order to establish whether ecstasy/polydrug deficits in PM were mediated by group differences in these processes. Results: Ecstasy/polydrug users performed significantly worse on both event and time-based prospective memory tasks in comparison to both cannabis only and non-user groups. Furthermore, it was found that across the whole sample, better retrospective memory and executive functioning was associated with superior PM performance. Nevertheless, this association did not mediate the drug-related effects that were observed. Consistent with our previous study, recreational use of cocaine was linked to PM deficits. Conclusions: PM deficits have again been found among ecstasy/polydrug users, which appear to be unrelated to group differences in executive function and retrospective memory. However, the possibility that these are attributable to cocaine use cannot be excluded

Effect of temperature anisotropy on various modes and instabilities for a magnetized non-relativistic bi-Maxwellian plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those electromagnetic modes whose magnetic field perturbations are perpendicular to the ambient magneticeld, i.e.,B1 \perp B0, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them and the O-mode are affected by thermal anisotropies, since they satisfy the required condition B1\perpB0. By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfven waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations

The "Ram Effect": A "Non-Classical" Mechanism for Inducing LH Surges in Sheep

During spring sheep do not normally ovulate but exposure to a ram can induce ovulation. In some ewes an LH surge is induced immediately after exposure to a ram thus raising questions about the control of this precocious LH surge. Our first aim was to determine the plasma concentrations of oestradiol (E2) E2 in anoestrous ewes before and after the "ram effect" in ewes that had a "precocious" LH surge (starting within 6 hours), a "normal" surge (between 6 and 28h) and "late» surge (not detected by 56h). In another experiment we tested if a small increase in circulating E2 could induce an LH surge in anoestrus ewes. The concentration of E2 significantly was not different at the time of ram introduction among ewes with the three types of LH surge. "Precocious" LH surges were not preceded by a large increase in E2 unlike "normal" surges and small elevations of circulating E2 alone were unable to induce LH surges. These results show that the "precocious" LH surge was not the result of E2 positive feedback. Our second aim was to test if noradrenaline (NA) is involved in the LH response to the "ram effect". Using double labelling for Fos and tyrosine hydroxylase (TH) we showed that exposure of anoestrous ewes to a ram induced a higher density of cells positive for both in the A1 nucleus and the Locus Coeruleus complex compared to unstimulated controls. Finally, the administration by retrodialysis into the preoptic area, of NA increased the proportion of ewes with an LH response to ram odor whereas treatment with the α1 antagonist Prazosin decreased the LH pulse frequency and amplitude induced by a sexually active ram. Collectively these results suggest that in anoestrous ewes NA is involved in ram-induced LH secretion as observed in other induced ovulators

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

Chronic digital infection presenting with gross enlargement of the toes: two case reports and review of the literature

There are many conditions ranging from the benign to the malignant, which can present with enlargement of one or more digits. An understanding of the differential diagnosis is important such that the potentially serious aetiologies are not missed and patients can therefore be treated appropriately

Asteroseismology

Asteroseismology is the determination of the interior structures of stars by using their oscillations as seismic waves. Simple explanations of the astrophysical background and some basic theoretical considerations needed in this rapidly evolving field are followed by introductions to the most important concepts and methods on the basis of example. Previous and potential applications of asteroseismology are reviewed and future trends are attempted to be foreseen.Comment: 38 pages, 13 figures, to appear in: "Planets, Stars and Stellar Systems", eds. T. D. Oswalt et al., Springer Verla

Statistical modeling of ground motion relations for seismic hazard analysis

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp(epsilon_0) of Joyner and Boore 1993) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions. etc

SPECULOOS exoplanet search and its prototype on TRAPPIST

One of the most significant goals of modern science is establishing whether life exists around other suns. The most direct path towards its achievement is the detection and atmospheric characterization of terrestrial exoplanets with potentially habitable surface conditions. The nearest ultracool dwarfs (UCDs), i.e. very-low-mass stars and brown dwarfs with effective temperatures lower than 2700 K, represent a unique opportunity to reach this goal within the next decade. The potential of the transit method for detecting potentially habitable Earth-sized planets around these objects is drastically increased compared to Earth-Sun analogs. Furthermore, only a terrestrial planet transiting a nearby UCD would be amenable for a thorough atmospheric characterization, including the search for possible biosignatures, with near-future facilities such as the James Webb Space Telescope. In this chapter, we first describe the physical properties of UCDs as well as the unique potential they offer for the detection of potentially habitable Earth-sized planets suitable for atmospheric characterization. Then, we present the SPECULOOS ground-based transit survey, that will search for Earth-sized planets transiting the nearest UCDs, as well as its prototype survey on the TRAPPIST telescopes. We conclude by discussing the prospects offered by the recent detection by this prototype survey of a system of seven temperate Earth-sized planets transiting a nearby UCD, TRAPPIST-1.Comment: Submitted as a chapter in the "Handbook of Exoplanets" (editors: H. Deeg & J.A. Belmonte; Section Editor: N. Narita). 16 pages, 4 figure