The central configurations of four masses x, -x, y, -y

The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, -x, y, -y with x different from y (a parallelogram and two trapezoids) and two planar non-collinear central configurations for masses x, -x, x, -x (two diamonds). Except the case studied here, the only known case where the four-body central configurations with non-vanishing masses can be listed is the case with equal masses (Albouy, 1996), which requires the use of a symbolic computation program. Thanks to a lemma used in the proof of our result, we also show that a co-circular four-body central configuration has non-vanishing total mass or vanishing multiplier

Computational Results for Extensive-Form Adversarial Team Games

We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary. We define three different scenarios according to the communication capabilities of the team. In the first, the teammates can communicate and correlate their actions both before and during the play. In the second, they can only communicate before the play. In the third, no communication is possible at all. We define the most suitable solution concepts, and we study the inefficiency caused by partial or null communication, showing that the inefficiency can be arbitrarily large in the size of the game tree. Furthermore, we study the computational complexity of the equilibrium-finding problem in the three scenarios mentioned above, and we provide, for each of the three scenarios, an exact algorithm. Finally, we empirically evaluate the scalability of the algorithms in random games and the inefficiency caused by partial or null communication

On the potential of Cherenkov Telescope Arrays and KM3 Neutrino Telescopes for the detection of extended sources

We discuss the discovery potential of extended very-high-energy (VHE) neutrino sources by the future KM3 Neutrino Telescope (KM3NeT) in the context of the constraining power of the Cherenkov Telescope Array (CTA), designed for deep surveys of the sky in VHE gamma rays. The study is based on a comparative analysis of sensitivities of KM3NeT and CTA. We show that a minimum gamma-ray energy flux of E^2{\phi}_{\gamma}(10 TeV) > 1x10^{-12} TeV cm^{-2} s^{-1} is required to identify a possible neutrino counterpart with a 3{\sigma} significance and 10 years of KM3NeT observations with upgoing muons, if the source has an angular size of R_{src} = 0.1 deg and emits gamma rays with an E^{-2} energy spectrum through a full hadronic mechanism. This minimum gamma-ray flux is increased to the level of E^2{\phi}_{\gamma}(10 TeV) > 2x10^{-11} TeV cm^{-2} s^{-1} in case of sources with radial extension of R_{src} = 2.0 deg. The analysis methods are applied to the supernova remnant RX J1713.7-3946 and the Galactic Center Ridge, as well as to the recent HAWC catalog of multi-TeV gamma-ray sources.Comment: 15 pages, 7 figure

Clinical and biochemical response to neridronate treatment in a patient with osteoporosis-pseudoglioma syndrome (OPPG)

Osteoporosis-pseudoglioma syndrome (OPPG) is a rare autosomal recessive syndrome characterized by juvenile-onset osteoporosis and ocular abnormalities due to a low-density lipoprotein receptor-related protein 5 (LRP5) gene mutation. Treatment with bisphosphonates, particularly with pamidronate and risedronate, has been reported to be of some efficacy in this condition. We report on a patient with OPPG due to an LRP5 gene mutation, who showed an encouraging response after a 36-month period of neridronate therapy. We report a case of a patient treated with bisphosphonates. Bisphosphonates should be administered in OPPG patients as a first-line therapy during early childhood

Serum creatine kinase isoenzymes in children with osteogenesis imperfecta

This study evaluates serum creatine kinase isoenzyme activity in children with osteogenesis imperfecta to determine its usefulness as a biochemical marker during treatment with bisphosphonate. The changes of creatine kinase (CK) isoenzyme activity during and after discontinuation therapy were observed. These results could be useful in addressing over-treatment risk prevention. Introduction The brain isoenzyme of creatine kinase (CKbb) is highly expressed in mature osteoclasts during osteoclastogenesis, thus plays an important role in bone resorption. We previously identified high serum CKbb levels in 18 children with osteogenesis imperfect (OI) type 1 treated for 1 year with bisphosphonate (neridronate). In the present study, serum CK isoenzymes were evaluated in the same children with continuous versus discontinued neridronate treatment over a further 2-year follow-up period. Methods This study included 18 children with OI type 1, 12 with continued (group A) and 6 with ceased (group B) neridronate treatment. Auxological data, serum biochemical markers of bone metabolism, bone mineral density z-score, and serum total CK and isoenzyme activities were determined in both groups. Results Serum CKbb was progressively and significantly increased in group A (p < 0.004) but rapidly decreased to undetectable levels in group B. In both groups, the cardiac muscle creatine kinase isoenzyme (CKmb) showed a marked decrease, while serum C-terminal telopeptide (CTx) levels were almost unchanged. Conclusions This study provides evidence of the cumulative effect of neridronate administration in increasing serum CKbb levels and the reversible effect after its discontinuation. This approach could be employed for verifying the usefulness of serum CKbb as a biochemical marker in patients receiving prolonged bisphosphonate treatment. Moreover, the decreased serum CKmb levels suggest a systemic effect of these drugs