On the maximum size of an anti-chain of linearly separable sets and convex pseudo-discs

We show that the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes is close to quadratic in n. We approach this problem by establishing the equivalence with the problem of the maximum monotone path in an arrangement of n lines. For a related problem on antichains in families of convex pseudo-discs we can establish the precise asymptotic bound: it is quadratic in n. The sets in such a family are characterized as intersections of a given set of n points with convex sets, such that the difference between the convex hulls of any two sets is nonempty and connected.Comment: 10 pages, 3 figures. revised version correctly attributes the idea of Section 3 to Tverberg; and replaced k-sets by "linearly separable sets" in the paper and the title. Accepted for publication in Israel Journal of Mathematic

Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent \gamma= 2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power-laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution figures is available at http://www.pks.mpg.de/~edugal

Symmetry breaking perturbations and strange attractors

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system, e.g. transitions from two sided to one sided strange attractors as the other parameters are varied. Moreover, slight asymmetries may cause substantial asymmetries in the relative size of the basins of attraction of the unforced nearly symmetric attracting regions. These changes seems to be associated with homoclinic bifurcations. Numerical evidence indicates that \textit{strange attractors} appear near curves corresponding to specific secondary homoclinic bifurcations. These curves are found using analytical perturbational tools

Plasma level of mannose-binding lectin is associated with the risk of recurrent pregnancy loss but not pregnancy outcome after the diagnosis

STUDY QUESTION: Are low or high plasma mannose-binding lectin (p-MBL) levels associated with recurrent pregnancy loss (RPL) and the reproductive and perinatal outcomes before and after RPL? SUMMARY ANSWER: The prevalence of low p-MBL levels was significantly higher in RPL patients, while high levels were significantly less prevalent. No association was found between p-MBL level and reproductive and perinatal outcomes before and after RPL. WHAT IS KNOWN ALREADY: Mannose-binding lectin (MBL) is an important component in the innate immune system. Low p-MBL levels have been associated with RPL, while the correlation with high levels has been poorly studied. Adverse perinatal outcomes are generally more frequent among RPL patients, but reports concerning the association between maternal p-MBL levels and perinatal outcomes, including birth weight (BW) and gestational age (GA), are conflicting. STUDY DESIGN, SIZE, DURATION: This study was a combined cross-sectional and cohort study of 267 RPL patients admitted to the RPL Center of Western Denmark between January 2016 and March 2020. RPL patients were followed until birth of a liveborn child or until end of follow-up, March 2021. A sample of 185 healthy female blood donors of reproductive age was used as a MBL reference group. PARTICIPANTS/MATERIALS, SETTING, METHODS: All RPL patients had ≥3 consecutive pregnancy losses, a regular menstrual cycle and no known significant chromosomal or uterine malformations. At the first consultation, routine blood samples including p-MBL measurement and detailed obstetrical and perinatal information were collected. p-MBL levels in RPL patients were compared to the MBL reference group. A logistic regression analysis adjusted for relevant confounders assessed the association between low p-MBL levels and an unsuccessful reproductive outcome in RPL patients in first pregnancy after admission. Perinatal outcomes before and after RPL were compared between RPL subgroups according to low (≤500 µg/l), intermediate (501–3000 µg/l) and high (>3000 µg/l) p-MBL levels. MAIN RESULTS AND THE ROLE OF CHANCE: Significantly more RPL patients had low p-MBL levels (prevalence proportion ratio (PPR): 1.79, 95% CI: 1.34–2.38) and fewer had high p-MBL levels (PPR: 0.56, 95% CI: 0.40–0.79) compared to the reference group, while the prevalence of intermediate p-MBL level was not different between the groups (PPR: 0.86, 95% CI: 0.69–1.08). In the prospective study, low p-MBL level was not a significant risk factor for a pregnancy loss in the first pregnancy after admission after adjustment for age, BMI and smoking. Neither before nor after the RPL diagnosis were maternal p-MBL levels significantly associated with BW or GA. LIMITATIONS, REASONS FOR CAUTION: Only 161 (60.3%) patients had given birth after RPL during the follow-up period, which limited the possibility to detect clear associations between p-MBL levels and perinatal outcomes after RPL. WIDER IMPLICATIONS OF THE FINDINGS: In agreement with several previous studies, low p-MBL levels are strongly associated with RPL, while this study for the first time documents that high levels may play a protective role, which suggests a causal relationship. We suggest that larger prospective studies evaluate the association between p-MBL levels and RPL prognosis. STUDY FUNDING/COMPETING INTEREST(S): No external funding was received. We acknowledge the Department of Obstetrics and Gynaecology at Aalborg University Hospital for financial support. U.S.K. has reported personal fees from Merck, consulting fees from IBSA Nordic, and a grant from Gedeon Richter, Merck and IBSA Nordic outside of the submitted work. TRIAL REGISTRATION NUMBER: ID from clinicaltrials.gov is NCT04017754

Crossovers in Unitary Fermi Systems

Universality and crossover is described for attractive and repulsive interactions where, respectively, the BCS-BEC crossover takes place and a ferromagnetic phase transition is claimed. Crossovers are also described for optical lattices and multicomponent systems. The crossovers, universal parameters and phase transitions are described within the Leggett and NSR models and calculated in detail within the Jastrow-Slater approximation. The physics of ultracold Fermi atoms is applied to neutron, nuclear and quark matter, nuclei and electrons in solids whenever possible. Specifically, the differences between optical lattices and cuprates is discussed w.r.t. antiferromagnetic, d-wave superfluid phases and phase separation.Comment: 50 pages, 15 figures. Contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge

High field level crossing studies on spin dimers in the low dimensional quantum spin system Na2_2T2_2(C2_2O4_4)3_3(H2_2O)2_2 with T=Ni,Co,Fe,Mn

In this paper we demonstrate the application of high magnetic fields to study the magnetic properties of low dimensional spin systems. We present a case study on the series of 2-leg spin-ladder compounds Na$_2$T$_2$(C$_2$O$_4$)$_3$(H$_2$O)$_2$ with T = Ni, Co, Fe and Mn. In all compounds the transition metal is in the $T^{2+}$ high spin configuation. The localized spin varies from S=1 to 3/2, 2 and 5/2 within this series. The magnetic properties were examined experimentally by magnetic susceptibility, pulsed high field magnetization and specific heat measurements. The data are analysed using a spin hamiltonian description. Although the transition metal ions form structurally a 2-leg ladder, an isolated dimer model consistently describes the observations very well. This behaviour can be understood in terms of the different coordination and superexchange angles of the oxalate ligands along the rungs and legs of the 2-leg spin ladder. All compounds exhibit magnetic field driven ground state changes which at very low temperatures lead to a multistep behaviour in the magnetization curves. In the Co and Fe compounds a strong axial anisotropy induced by the orbital magnetism leads to a nearly degenerate ground state and a strongly reduced critical field. We find a monotonous decrease of the intradimer magnetic exchange if the spin quantum number is increased

Jets, Stickiness and Anomalous Transport

Dynamical and statistical properties of the vortex and passive particle advection in chaotic flows generated by four and sixteen point vortices are investigated. General transport properties of these flows are found anomalous and exhibit a superdiffusive behavior with typical second moment exponent (\mu \sim 1.75). The origin of this anomaly is traced back to the presence of coherent structures within the flow, the vortex cores and the region far from where vortices are located. In the vicinity of these regions stickiness is observed and the motion of tracers is quasi-ballistic. The chaotic nature of the underlying flow dictates the choice for thorough analysis of transport properties. Passive tracer motion is analyzed by measuring the mutual relative evolution of two nearby tracers. Some tracers travel in each other vicinity for relatively large times. This is related to an hidden order for the tracers which we call jets. Jets are localized and found in sticky regions. Their structure is analyzed and found to be formed of a nested sets of jets within jets. The analysis of the jet trapping time statistics shows a quantitative agreement with the observed transport exponent.Comment: 17 pages, 17 figure

Infrastructure and Trade

This paper explores the role that quality of infrastructure has on a country's trade performance, estimating a gravity model that incorporates bilateral tariffs and a number of indicators for the quality of infrastructure. The paper looks at the impact of the quality of infrastructure (road, airport, port and telecommunication, and the time required for customs clearance) on total bilateral trade and on trade in the automotive, clothing and textile sectors. In order to obtain unbiased estimators, multilateral resistances for tariffs and remoteness are introduced in the gravity equation. Moreover, the robustness of the results is tested by estimating a fixed-effect model, where bilateral indexes of the quality of infrastructure are included. The results can be summarised in four main findings: (i) bilateral tariffs, generally neglected in gravity regression of bilateral flows, have a significant negative impact on trade; (ii) quality of infrastructure is an important determinant of trade performance; (iii) port efficiency appears to have the largest impact on trade among all indicators of infrastructure; (iv) timeliness and access to telecommunication are relatively more important for export competitiveness in the clothing and automotive sector respectively

Density correlations and dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates

We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the dynamical Casimir emission of pairs of Bogoliubov phonons when the atom-atom scattering length is modulated in time. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical calculations of Hawking radiation from analog black holes

Foliations of Isonergy Surfaces and Singularities of Curves

It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the bifurcation set has singularities at the corresponding energy level. We formulate certain genericity assumptions for two degrees of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure