GEODESIC BEHAVIOR FOR FINSLER METRICS OF CONSTANT POSITIVE FLAG CURVATURE ON S 2

International audienceWe study non-reversible Finsler metrics with constant flag curvature 1 on S 2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metric with constant positive flag curvature is completely integrable. Finally, we give an example of a Finsler metric on S 2 with positive flag curvature such that no two closed geodesics intersect and show that this is not possible when the metric is reversible or has constant flag curvature

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio

Deep Variational Lesion-Deficit Mapping

Causal mapping of the functional organisation of the human brain requires evidence of \textit{necessity} available at adequate scale only from pathological lesions of natural origin. This demands inferential models with sufficient flexibility to capture both the observable distribution of pathological damage and the unobserved distribution of the neural substrate. Current model frameworks -- both mass-univariate and multivariate -- either ignore distributed lesion-deficit relations or do not model them explicitly, relying on featurization incidental to a predictive task. Here we initiate the application of deep generative neural network architectures to the task of lesion-deficit inference, formulating it as the estimation of an expressive hierarchical model of the joint lesion and deficit distributions conditioned on a latent neural substrate. We implement such deep lesion deficit inference with variational convolutional volumetric auto-encoders. We introduce a comprehensive framework for lesion-deficit model comparison, incorporating diverse candidate substrates, forms of substrate interactions, sample sizes, noise corruption, and population heterogeneity. Drawing on 5500 volume images of ischaemic stroke, we show that our model outperforms established methods by a substantial margin across all simulation scenarios, including comparatively small-scale and noisy data regimes. Our analysis justifies the widespread adoption of this approach, for which we provide an open source implementation: https://github.com/guilherme-pombo/vae_lesion_defici

Density of a gas of spin polarized fermions in a magnetic field

For a fermion gas with equally spaced energy levels that is subjected to a magnetic field, the particle density is calculated. The derivation is based on the path integral approach for identical particles, in combination with the inversion techniques for the generating function of the static response functions. Explicit results are presented for the ground state density as a function of the magnetic field with a number of particles ranging from 1 to 45.Comment: 9 pages, 8 figures; To appear in Phys. Rev. E on December 1, 2000; e-mail addresses: [email protected], [email protected], [email protected], [email protected]

Association between congenital toxoplasmosis and preterm birth, low birthweight and small for gestational age birth.

OBJECTIVE: To determine the association between congenital toxoplasmosis and preterm birth, low birthweight and small for gestational age birth. DESIGN: Multicentre prospective cohort study. SETTING: Ten European centres offering prenatal screening for toxoplasmosis. POPULATION: Deliveries after 23 weeks of gestation in 386 women with singleton pregnancies who seroconverted to toxoplasma infection before 20 weeks of gestation. Deliveries after 36 weeks in 234 women who seroconverted at 20 weeks or later, and tested positive before 37 weeks. METHODS: Comparison of infected and uninfected births, adjusted for parity and country of birth. MAIN OUTCOME MEASURES: Differences in gestational age at birth, birthweight and birthweight centile. RESULTS: Infected babies were born or delivered earlier than uninfected babies: the mean difference for seroconverters before 20 weeks was -5.4 days (95% CI: -1.4, -9.4), and at 20 weeks or more, -2.6 days (95% CI: -0.5, -4.7). Congenital infection was associated with an increased risk of preterm delivery when seroconversion occurred before 20 weeks (OR 4.71; 95% CI: 2.03, 10.9). No significant differences were detected for birthweight or birthweight centile. CONCLUSION: Babies with congenital toxoplasmosis were born earlier than uninfected babies but the mechanism leading to shorter length of gestation is unknown. Congenital infection could precipitate early delivery or prompt caesarean section or induction of delivery. We found no evidence for a significant association between congenital toxoplasmosis and reduced birthweight or small for gestational age birth

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page

Barriers to medication counselling for people with mental health disorders : A six country study

Provision of medication information may improve adherence and prevent medication related problems. People with mental health disorders commonly receive less medication counselling from pharmacists than people with other common long term and persistent disorders. Objective: The objective of this study was to compare and contrast barriers pharmacy students perceive toward providing medication counselling for people with mental health disorders in Australia, Belgium, Estonia, Finland, India and Latvia. Methods: Barriers identified by third-year pharmacy students as part of the International Pharmacy Students' Health Survey were content analysed using a directed approach. Students' responses were categorised as pharmacist related, patient related, health-system related, or social or cultural related. Quantitative data were analysed using SPSS version 14.0. Results: Survey instruments were returned by 649 students. Of the respondents, 480 identified one or more barriers to medication counselling for people with mental health disorders. Patient related factors accounted for between 25.3% and 36.2% of barriers identified by the pharmacy students. Pharmacist related factors accounted for between 17.6% and 45.1% of the barriers identified by the pharmacy students. Students in India were more likely to attribute barriers to pharmacist and social and cultural related factors, and less likely to healthsystem related factors, than students studying in other countries. Conclusion: The nature of barriers identified by pharmacy students differed according to the country in which they studied. Undergraduate and postgraduate pharmacy education programs may need to be amended to address common misconceptions among pharmacy students.publishersversionPeer reviewe

A Mission to Explore the Pioneer Anomaly

The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of $\sim 20-70$ astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of $\sim(5.99 \pm 0.01)\times 10^{-9}$ Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of $a_P = (8.74 \pm 1.33)\times 10^{-10} {\rm m/s^2}$. This signal has become known as the Pioneer anomaly. The inability to explain the anomalous behavior of the Pioneers with conventional physics has contributed to growing discussion about its origin. There is now an increasing number of proposals that attempt to explain the anomaly outside conventional physics. This progress emphasizes the need for a new experiment to explore the detected signal. Furthermore, the recent extensive efforts led to the conclusion that only a dedicated experiment could ultimately determine the nature of the found signal. We discuss the Pioneer anomaly and present the next steps towards an understanding of its origin. We specifically focus on the development of a mission to explore the Pioneer Anomaly in a dedicated experiment conducted in deep space.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020", 19-21 April 2005, ESTEC, Noordwijk, The Netherland

Fundamental Physics with the Laser Astrometric Test Of Relativity

The Laser Astrometric Test Of Relativity (LATOR) is a joint European-U.S. Michelson-Morley-type experiment designed to test the pure tensor metric nature of gravitation - a fundamental postulate of Einstein's theory of general relativity. By using a combination of independent time-series of highly accurate gravitational deflection of light in the immediate proximity to the Sun, along with measurements of the Shapiro time delay on interplanetary scales (to a precision respectively better than 0.1 picoradians and 1 cm), LATOR will significantly improve our knowledge of relativistic gravity. The primary mission objective is to i) measure the key post-Newtonian Eddington parameter \gamma with accuracy of a part in 10^9. (1-\gamma) is a direct measure for presence of a new interaction in gravitational theory, and, in its search, LATOR goes a factor 30,000 beyond the present best result, Cassini's 2003 test. The mission will also provide: ii) first measurement of gravity's non-linear effects on light to ~0.01% accuracy; including both the Eddington \beta parameter and also the spatial metric's 2nd order potential contribution (never measured before); iii) direct measurement of the solar quadrupole moment J2 (currently unavailable) to accuracy of a part in 200 of its expected size; iv) direct measurement of the "frame-dragging" effect on light by the Sun's gravitomagnetic field, to 1% accuracy. LATOR's primary measurement pushes to unprecedented accuracy the search for cosmologically relevant scalar-tensor theories of gravity by looking for a remnant scalar field in today's solar system. We discuss the mission design of this proposed experiment.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020," 19-21 April 2005, ESTEC, Noodrwijk, The Netherland