The number of crossings in multigraphs with no empty lens

Let $G$ be a multigraph with $n$ vertices and $e>4n$ edges, drawn in the plane such that any two parallel edges form a simple closed curve with at least one vertex in its interior and at least one vertex in its exterior. Pach and T\'oth (2018) extended the Crossing Lemma of Ajtai et al. (1982) and Leighton (1983) by showing that if no two adjacent edges cross and every pair of nonadjacent edges cross at most once, then the number of edge crossings in $G$ is at least $\alpha e^3/n^2$, for a suitable constant $\alpha>0$. The situation turns out to be quite different if nonparallel edges are allowed to cross any number of times. It is proved that in this case the number of crossings in $G$ is at least $\alpha e^{2.5}/n^{1.5}$. The order of magnitude of this bound cannot be improved.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

The value of information in a multi-agent market model

We present an experimental and simulated model of a multi-agent stock market driven by a double auction order matching mechanism. Studying the effect of cumulative information on the performance of traders, we find a non monotonic relationship of net returns of traders as a function of information levels, both in the experiments and in the simulations. Particularly, averagely informed traders perform worse than the non informed and only traders with high levels of information (insiders) are able to beat the market. The simulations and the experiments reproduce many stylized facts of stock markets, such as fast decay of autocorrelation of returns, volatility clustering and fat-tailed distribution of returns. These results have an important message for everyday life. They can give a possible explanation why, on average, professional fund managers perform worse than the market index.Comment: 11 pages, 5 figures, published in EPJ

The value of information in a multi-agent market model

We present an experimental and simulated model of a multi-agent stock market driven by a double auction order matching mechanism. Studying the effect of cumulative information on the performance of traders, we find a non monotonic relationship of net returns of traders as a function of information levels, both in the experiments and in the simulations. Particularly, averagely informed traders perform worse than the non informed and only traders with high levels of information (insiders) are able to beat the market. The simulations and the experiments reproduce many stylized facts of stock markets, such as fast decay of autocorrelation of returns, volatility clustering and fat-tailed distribution of returns. These results have an important message for everyday life. They can give a possible explanation why, on average, professional fund managers perform worse than the market index.Economics; econophysics; financial markets; business and management; information theory and communication theory

Experimental Spinal Fusion With Recombinant Human Bone Morphogenetic Protein-2 Without Decortication of Osseous Elements

Study Design. L4-L5 intertransverse process fusions were produced with 58 μg, 230 μg, or 920 μg of recombinant human bone morphogenetic protein-2 in 20 dogs. Eleven had traditional decortication of posterior elements before insertion of the implant. Nine were left undecorticated. All animals were evaluated 3 months after surgery. Objectives. To determine whether decortication is a prerequisite for successful fusion in the presence of osteoinductive proteins such as bone morphogenetic protein-2. Summary of Background Data. Recombinant osteoinductive proteins can induce de novo bone in ectopic soft-tissue sites in the absence of bone marrow elements. Traditional methods for achieving spinal fusion rely on exposure of bone marrow through decortication to facilitate osteogenesis. It is hypothesized that the presence of an implanted osteoinductive protein obviates the need for exposure and release of host inductive factors. Methods. Recombinant human bone morphogenetic protein-2-induced intertransverse process fusions were performed with and without decortication. Fusion sites were evaluated by computed tomography imaging, high-resolution radiography, manual testing, mechanical testing, and histologic analysis. Results. One hundred percent of decorticated spines and 89% of undecorticated spines were clinically fused by 3 months. Ninety-one percent of decorticated spines and 78% of undecorticated specimens exhibited bilateral transverse process osseous bridging. The only spines that failed to achieve solid bilateral arthrodesis were in the lowest dose group. With the higher two doses, there was histologic evidence of osseous continuity between the fusion mass and undecorticated transverse processes. Conclusions. There were no statistical differences in clinical and radiographic fusion rates between decorticated and undecorticated sites. With higher doses of recombinant human bone morphogenetic protein-2, there was little histologic distinction between fusions in decorticated versus undecorticated spines

Effective Doses of Recombinant Human Bone Morphogenetic Protein-2 in Experimental Spinal Fusion

Study Design Nineteen dogs underwent L4-L5 intertransverse process fusions with either 58 μg, 115 μg, 230 μg, 460 μg, or 920 μg of recombinant human bone morphogenetic protein-2 carried by a polylactic acid polymer. A previous study (12 dogs) compared 2300 μg of recombinant human bone morphogenetic protein-2, autogenous iliac bone, and carrier alone in this model. All fusions subsequently were compared. Objectives To characterize the dose-response relationship of recombinant human bone morphogenetic protein-2 in a spinal fusion model. Summary of Background Data Recombinant osteoinductive morphogens, such as recombinant human bone morphogenetic protein-2, are effective in vertebrate diaphyseal defect and spinal fusion models. It is hypothesized that the quality of spinal fusion produced with recombinant human bone morphogenetic protein-2, above a threshold dose, does not change with increasing amounts of inductive protein. Methods After decortication of the posterior elements, the designated implants were placed along the intertransverse process space bilaterally. The fusion sites were evaluated after 3 months by computed tomography imaging, high-resolution radiography, manual testing, mechanical testing, and histologic analysis. Results As in the study using 2300 μg of recombinant human bone morphogenetic protein-2, implantation of 58–920 μg of recombinant human bone morphogenetic protein-2 successfully resulted in intertransverse process fusion in the dog by 3 months. This had not occurred in animals containing autograft or carrier alone. The cross-sectional area of the fusion mass and mechanical stiffness of the L4-L5 intersegment were not dose-dependent. Histologic findings varied but were not related to rhBMP-2 dose. Inflammatory reaction to the composite implant was proportional inversely to the volume of the fusion mass. Conclusions No mechanical, radiographic, or histologic differences in the quality of intertransverse process fusion resulted from a 40-fold variation in dose of recombinant human bone morphogenetic protein-2

MAGNETIC FLUX CONSERVATION IN THE HELIOSHEATH INCLUDING SOLAR CYCLE VARIATIONS OF MAGNETIC FIELD INTENSITY

In the heliosheath (HS), Voyager 2 has observed a flow with constant radial velocity and magnetic flux conservation. Voyager 1, however, has observed a decrease in the flow's radial velocity and an order of magnitude decrease in magnetic flux. We investigate the role of the 11 yr solar cycle variation of the magnetic field strength on the magnetic flux within the HS using a global 3D magnetohydrodynamic model of the heliosphere. We use time and latitude-dependent solar wind velocity and density inferred from Solar and Heliospheric Observatory/SWAN and interplanetary scintillations data and implemented solar cycle variations of the magnetic field derived from 27 day averages of the field magnitude average of the magnetic field at 1 AU from the OMNI database. With the inclusion of the solar cycle time-dependent magnetic field intensity, the model matches the observed intensity of the magnetic field in the HS along both Voyager 1 and 2. This is a significant improvement from the same model without magnetic field solar cycle variations, which was over a factor of two larger. The model accurately predicts the radial velocity observed by Voyager 2; however, the model predicts a flow speed ~100 km s[superscript −1] larger than that derived from LECP measurements at Voyager 1. In the model, magnetic flux is conserved along both Voyager trajectories, contrary to observations. This implies that the solar cycle variations in solar wind magnetic field observed at 1 AU does not cause the order of magnitude decrease in magnetic flux observed in the Voyager 1 data.United States. National Aeronautics and Space Administration (Earth and Space Science Fellowship Program Grant NNX14AO14H