The Coven-Meyerowitz tiling conditions for 3 odd prime factors

It is well known that if a finite set $A\subset\mathbb{Z}$ tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization $A\oplus B=\mathbb{Z}_M$ of a finite cyclic group. We are interested in characterizing all finite sets $A\subset\mathbb{Z}$ that have this property. Coven and Meyerowitz (1998) proposed conditions (T1), (T2) that are sufficient for $A$ to tile, and necessary when the cardinality of $A$ has at most two distinct prime factors. They also proved that (T1) holds for all finite tiles, regardless of size. It is not known whether (T2) must hold for all tilings with no restrictions on the number of prime factors of $|A|$. We prove that the Coven-Meyerowitz tiling condition (T2) holds for all integer tilings of period $M=(p_ip_jp_k)^2$, where $p_i,p_j,p_k$ are distinct odd primes. The proof also provides a classification of all such tilings.Comment: 77 pages. Various edits and corrections in response to the referee's repor

Ageing and endurance training effects on quantity and quality of pulmonary vascular bed in healthy men

International audienceIt has recently been demonstrated that in healthy individuals, peak oxygen consumption is associated with a greater pulmonary capillary blood volume and a more distensible pulmonary circulation. Our cross-sectional study suggests that, in healthy men aged 20 to 60 years (n = 63), endurance sport practice (vigorous-intensity domain of the International Physical Activity Questionnaire) is associated with better quantity (pulmonary capillary blood volume) and quality (slope of increase in lung diffusion for carbon monoxide on exercise) of the pulmonary vascular bed, partly counterbalancing the deleterious effects of ageing, which remains to be demonstrated in a prospective longitudinal design

Development of an immunochromatographic test for diagnosis of visceral leishmaniasis based on detection of a circulating antigen

Background Visceral leishmaniasis (VL) is a life-threatening disease caused by protozoan parasites of the Leishmania donovani complex. Early case detection followed by adequate treatment is essential to the control of VL. However, the available diagnostic tests are either invasive and require considerable expertise (parasitological demonstration of the parasite in tissue smears) or unable to distinguish between past and active infection (serological methods). Therefore, we aimed to develop a lateral flow assay in the form of an immunochromatographic test (ICT) device based on the detection of a circulating Leishmania antigen using monoclonal antibodies (mAbs). Methodology/Principal Findings mAbs were produced by fusion of murine myeloma cells with splenocytes isolated from a mouse immunized with L. donovani soluble crude antigen. Out of 12 cloned hybridoma cell lines, two secreted mAbs recognizing the same leishmanial protein. These mAbs were used to produce an ICT as a sandwich assay for the detection of circulating antigen in serum and blood samples. The ICT was evaluated with 213 serum samples from VL patients living in VL endemic areas in China, and with 156 serum samples from patients with other diseases as well as 78 serum samples from healthy donors. Sensitivity, specificity and diagnostic efficiency of the new ICT was 95.8%, 98.7% and 97.3%, respectively. Compared with a commercially available antibody detecting ICT, our antigen-based ICT performed slightly better. Conclusion/Significance The newly developed ICT is an easy to use and more accurate diagnostic tool which fulfils the performance and operational characteristics required for VL case detection under field and laboratory conditions. As our ICT detects a circulating antigen, it will also be useful in monitoring treatment success and diagnosing VL in immunocompromised patients

The use of an inertial measurement unit in the flight testing of a small, remote-piloted air vehicle

A 3 meter-span, unmanned air vehicle has been flight tested in order to find its dynamic modes of motion, in-flight Euler angles, and in-flight angles of attack and sideslip angles. Instrumentation included an inertial measurement unit, a GPS, and a 3-axis sonic anemometer. Before flight, the inertial measurement unit was calibrated for rotation rate, temperature, and acceleration. Each of these calibrations was linear. The dynamic modes were estimated based on aircraft geometry, mass, and moments of inertia. For the short period pitch, Dutch roll, and roll modes, the estimates were compared to results from flight and were found to match. The Phugoid and spiral modes were found to be impractical to flight test due to space constraints and atmospheric turbulence, respectively. The low wing loading of the UAV strengthened the influence of atmospheric turbulence on the rate gyro data. The Euler angles were calculated from rate gyro data and compared to other measurement or calculation methods, including a ground-based video camera and equations using GPS and sonic anemometer data. It was found that roll and pitch angle errors fluctuate around zero due to coupling between the Euler angle equations. Yaw angle, however, does not exhibit this behavior. It was established that Euler angle drift rates of less than 6°/s can be achieved through calculation from rate gyros and that better results may be obtained by updating the Euler angles with outside sources of information. The angles of attack and sideslip angles were calculated from rate gyro and GPS data and compared to sonic anemometer calculations. It was found that angle of attack calculated the former way did not match the sonic anemometer calculations due to error in pitch angle and possibly the GPS\u27 slow, 4 Hz update rate. Sideslip angle did match the sonic anemometer data after accounting for error in yaw angle and GPS lag. These results can be used as a foundation for the improvement of cheap, light flight testing equipment for small UAVs