Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. We find that a seven-parameter rational function of three variables with a numerator equal to one (reciprocal of a polynomial of degree two at most) can be expressed as a pullbacked 2F1 hypergeometric function. This result can be seen as the simplest non-trivial family of diagonals of rational functions. We focus on some subcases such that the diagonals of the corresponding rational functions can be written as a pullbacked 2F1 hypergeometric function with two possible rational functions pullbacks algebraically related by modular equations, thus showing explicitely that the diagonal is a modular form. We then generalise this result to eight, nine and ten parameters families adding some selected cubic terms at the denominator of the rational function defining the diagonal. We finally show that each of these previous rational functions yields an infinite number of rational functions whose diagonals are also pullbacked 2F1 hypergeometric functions and modular forms.Comment: 39 page

Towards a quantum Hall effect for atoms using electric fields

An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate

Can Emergency Physicians Perform Carotid Artery Point-of-Care Ultrasound to Detect Stenosis in Patients with TIA and Stroke? A Pilot Study

Introduction: Patients with severe, symptomatic carotid stenosis can have their subsequent stroke risk reduced by surgical intervention if performed soon after a transient ischemic attack (TIA) or stroke. Patients presenting to an emergency department (ED) without computed tomography angiography (CTA) with TIA/stroke, may require transfer to another hospital for imaging to rule out carotid artery stenosis. The objective of this study was to determine the test characteristics of carotid artery point-of-care ultrasound (POCUS) in detecting greater than 50% stenosis in patients presenting with TIA/stroke.Methods: We conducted a prospective cohort study on a convenience sample of adult patients presenting to a comprehensive stroke centre with TIA or stroke between June–October 2017. Carotid POCUS was performed. Primary outcome measure, stenosis ≥ 50%, was determined by the final radiology report of CTA. A blinded POCUS expert separately reviewed the archived carotid POCUS scans. We calculated sensitivity and specificity for stenosis ≥ 50%.Results: We conducted POCUS on 75 patients, of which 70 were included in our analyses. Of those 70, 14.3% were diagnosed with greater than 50% stenosis. Carotid POCUS performed as follows: sensitivity 70.0% (95% confidence interval [CI], 34.8%-93.3%); specificity 86.7% (95% CI, 75.4%-94.1%); positive likelihood ratio (LR +) 5.3 (95% CI, 1.2-9.3); negative likelihood ratio (LR -) 0.4 (95% CI, 0.0-0.7). The inter-rater reliability between POCUS performer interpretation and expert interpretation had moderate agreement (k = 0.68). Scans took a mean 6.2 ± 2.2 minutes to complete.Conclusion: Carotid POCUS has low to moderate association with CTA for detection of carotid artery stenosis ≥ 50%. Further research and investigation is needed prior to widespread use of carotid POCUS in patients with acute cerebral ischemia. Additionally, external validity is likely affected by availability of training, maintenance of competency, and experience in more rural centres

From brain to earth and climate systems: Small-world interaction networks or not?

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with commonly used time series analysis based approaches to network characterization

A linear Stark shift in dressed atoms as a signal to measure a nuclear anapole moment with a cold atom fountain or interferometer

We demonstrate theoretically the existence of a linear dc Stark shift of the individual substates of an alkali atom in its ground state, dressed by a circularly polarized laser field. It arises from the electroweak nuclear anapole moment violating P but not T. It is characterized by the pseudoscalar equal to the mixed product formed with the photon angular momentum and static electric and magnetic fields. We derive the relevant left-right asymmetry with its complete signature in a field configuration selected for a precision measurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transition frequency shift amounts to 7 $\mu$Hz for a laser power of about 1 kW at 877 nm, E=100 kV/cm and B larger than 0.5 G.Comment: Article, 4 pages, 2 figure

A comparison of soft and hard decision-directed feedforward phase estimators

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200

Suivi des variations spatio-temporelles du stock d'eau près d'une mare endoréique au Sahel par résonance magnétique des protons et par gravimétrie

L'infiltration profonde sous les mares temporaires est la principale source de recharge des aquifères libres au Sahel. Au Niger semi-aride, une tomographie et un suivi RMP (résonance magnétique protonique) ainsi que plusieurs campagnes de mesures de gravimétrie absolue et relative ont été réalisés entre 2008 et 2010 pour étudier la sensibilité des deux méthodes géophysiques aux variations spatio-temporelles du stock d'eau souterrain à proximité d'une mare. Les résultats montrent une bonne cohérence et une complémentarité des méthodes, les sondages RMP étant davantage précis pour caractériser les variations verticales et horizontales du stock d'eau et la gravimétrie étant plus performante pour l'estimation des variations temporelles et/ou superficielles. (Résumé d'auteur

WHOOPING CRANE NEST BUILDING IN SOUTHWEST INDIANA

The first documented case of whooping crane (Grus americana) nest building in Indiana is described. During spring 2015, a pair of whooping cranes did not leave their wintering grounds in Gibson County, Indiana, to return to their summering area in Wisconsin. Three nest platforms were discovered after the death of the female crane. To date, this is the only documented example of a whooping crane pair in the reintroduced Eastern Migratory Population (EMP) building nest platforms outside of Wisconsin. Although fidelity to the core nesting areas in Wisconsin is strong, and natal dispersal is usually \u3c30 km, this example from Indiana shows that whooping cranes in the EMP may have the potential to pioneer nesting areas far outside of core reintroduction areas

Are short-term variations in solar oscillation frequencies the signature of a second solar dynamo?

In addition to the well-known 11-year solar cycle, the Sun's magnetic activity also shows significant variation on shorter time scales, e.g. between one and two years. We observe a quasi-biennial (2-year) signal in the solar p-mode oscillation frequencies, which are sensitive probes of the solar interior. The signal is visible in Sun-as-a-star data observed by different instruments and here we describe the results obtained using BiSON, GOLF, and VIRGO data. Our results imply that the 2-year signal is susceptible to the influence of the main 11-year solar cycle. However, the source of the signal appears to be separate from that of the 11-year cycle. We speculate as to whether it might be the signature of a second dynamo, located in the region of near-surface rotational shear.Comment: 6 pages, 2 figures, proceedings for SOHO-24/GONG 2010 conference, to be published in JPC