Non-linear conformally invariant generalization of the Poisson equation to D>2 dimensions

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that is second order, and in which the scalar $phi$ couples to the sources $\rho$ via a $\phi\rho$ contact term. The symmetry is used to generate solutions for the field for some non-trivial configurations (e.g. for two oppositely charged points). Systems comprising N point charges afford further application of the symmetry. For these I derive e.g. exact expressions for the following quantities: the general two-point-charge force; the energy function and the forces in any three-body configuration with zero total charge; the few-body force for some special configurations; the virial theorem for an arbitrary, bound, many-particle system relating the time-average kinetic energy to the particle charges. Possible connections with an underlying conformal quantum field theory are mentioned.Comment: Revtex, 16 pages. To be published in Phys. Rev.

Dark matter and non-Newtonian gravity from General Relativity coupled to a fluid of strings

An exact solution of Einstein's field equations for a point mass surrounded by a static, spherically symmetric fluid of strings is presented. The solution is singular at the origin. Near the string cloud limit there is a $1/r$ correction to Newton's force law. It is noted that at large distances and small accelerations, this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. When interpreted in the context of a cosmological model with a string fluid, the new solution naturally explains why the critical acceleration of Milgrom is of the same order of magnitude as the Hubble parameter.Comment: 12 pages, REVTeX, no figure

Distant star clusters of the Milky Way in MOND

We determine the mean velocity dispersion of six Galactic outer halo globular clusters, AM 1, Eridanus, Pal 3, Pal 4, Pal 15, and Arp 2 in the weak acceleration regime to test classical vs. modified Newtonian dynamics (MOND). Owing to the non-linearity of MOND's Poisson equation, beyond tidal effects, the internal dynamics of clusters is affected by the external field in which they are immersed. For the studied clusters, particle accelerations are much lower than the critical acceleration a_0 of MOND, but the motion of stars is neither dominated by internal accelerations (a_i >> a_e) nor external accelerations (a_e >> a_i). We use the N-body code N-MODY in our analysis, which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo, and Nipoti (2006) to derive the line-of-sight velocity dispersion by adding the external field effect. We show that Newtonian dynamics predicts a low-velocity dispersion for each cluster, while in modified Newtonian dynamics the velocity dispersion is much higher. We calculate the minimum number of measured stars necessary to distinguish between Newtonian gravity and MOND with the Kolmogorov-Smirnov test. We also show that for most clusters it is necessary to measure the velocities of between 30 to 80 stars to distinguish between both cases. Therefore the observational measurement of the line-of-sight velocity dispersion of these clusters will provide a test for MOND.Comment: A&A, accepted, LaTeX, 8 pages, 4 figure

Near-optimal asymmetric binary matrix partitions

We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an $n \times m$ binary matrix $A$ and a probability distribution over its columns. A partition scheme $B=(B_1,...,B_n)$ consists of a partition $B_i$ for each row $i$ of $A$. The partition $B_i$ acts as a smoothing operator on row $i$ that distributes the expected value of each partition subset proportionally to all its entries. Given a scheme $B$ that induces a smooth matrix $A^B$, the partition value is the expected maximum column entry of $A^B$. The objective is to find a partition scheme such that the resulting partition value is maximized. We present a $9/10$-approximation algorithm for the case where the probability distribution is uniform and a $(1-1/e)$-approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization.Comment: 17 page

Exact gravitational lensing and rotation curve

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation and corrections to it.Comment: 12 pages, 1 figur

N-body simulations in modified Newtonian dynamics

We describe some results obtained with N-MODY, a code for N-body simulations of collisionless stellar systems in modified Newtonian dynamics (MOND). We found that a few fundamental dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter. In particular, violent relaxation, phase mixing and galaxy merging take significantly longer in MOND than in Newtonian gravity, while dynamical friction is more effective in a MOND system than in an equivalent Newtonian system with dark matter.Comment: 4 pages, no figures. To appear in EAS Publication Series (Proceedings of Symposium 7 of the JENAM 2008, Vienna

Role for targeted resection in the multidisciplinary treatment of metastatic gastrointestinal stromal tumor

The management of advanced gastrointestinal stromal tumors (GISTs) has evolved in the modern era due to the discovery of c-kit mutations and the development of tyrosine kinase inhibitors (TKIs). Until the advent of TKIs such as imatinib, the median survival reported for patients with advanced GIST was 19 months. Although surgery is the treatment of choice for resectable primary GIST, its role in cases of recurrence and metastasis remains to be unclear. This review outlines the potential beneficial role of repeat surgical resection in the multidisciplinary treatment of advanced GIST in the era of TKIs

Children's tooth decay in a public health program to encourage low-income pregnant women to utilize dental care

<p>Abstract</p> <p>Background</p> <p>A community-based public health program to provide a dental home for women covered by the Oregon Health Plan (Medicaid) in Klamath County, Oregon USA was instituted with the long-term goal to promote preventive oral care for both mothers and their new infants provided by dental managed care companies.</p> <p>Methods</p> <p>As part of the evaluation of the program, children in Klamath and comparable non-program counties were examined in their 2^ndyear of life to begin to determine if benefits accrued to the offspring of the mothers in Klamath County.</p> <p>Results</p> <p>Eighty-five and 58.9% of the children were caries free in the Klamath and comparison county samples, respectively (RR = 1.48, 95% CI 1.13, 1.93). The mean (SD) number of teeth with any decay was .75 (2.5) in the test population and 1.6 (2.5) in the comparison population (t = 2.08, p = .04).</p> <p>Conclusions</p> <p>The assessment showed that children of mothers in the Klamath County program were about one and a half times more likely to be caries free than children in the comparison counties. Additional controlled studies are being undertaken.</p

Tidal dwarf galaxies as a test of fundamental physics

Within the cold dark matter (CDM) framework tidal dwarf galaxies (TDGs) cannot contain dark matter, so the recent results by Bournaud et al. (2007) that 3 rotating TDGs do show significant evidence for being dark matter dominated is inconsistent with the current concordance cosmological theory unless yet another dark matter component is postulated. We confirm that the TDG rotation curves are consistent with Newtonian dynamics only if either an additional dark matter component is postulated, or if all 3 TDGs happen to be viewed nearly edge-on, which is unlikely given the geometry of the tidal debris. We also find that the observed rotation curves are very naturally explained without any free parameters within the modified Newtonian dynamics (MOND) framework if inclinations are adopted as derived by Bournaud et al. We explore different inclination angles and two different assumptions about the external field effect. The results do not change significantly, and we conclude therefore that Newtonian dynamics has severe problems while MOND does exceedingly well in explaining the observed rotation curves of the 3 TDGs studied by Bournaud et al.Comment: Accepted for publication in A&A Letters, 5 pages, 3 figure

An Assessment of the Academic Impact of Shock Society Members

Professional society membership enhances career development and productivity by offering opportunities for networking and learning about recent advances in the field. The quality and contribution of such societies can be measured in part through the academic productivity, career status, and funding success rates of their members. Here, using Scopus, NIH RePORTER, and departmental websites, we compare characteristics of the Shock Society membership to those of the top 55 NIH-funded American university and hospital-based departments of surgery. Shock Society members' mean number of publications, citations and H-indices were all significantly higher than those of non-members in surgery departments (P < 0.001). A higher percentage of members also have received funding from the NIH (42.5% vs. 18.5%, P < 0.001). Regression analysis indicated that members were more likely to have NIH funding compared with non-members (OR 1.46, 95% CI 1.12-1.916). Trauma surgeons belonging to the Shock Society had a higher number of publications and greater NIH funding than those who did not (130.4 vs. 42.7, P < 0.001; 40.4% vs. 8.5%, P < 0.001). Aggregate academic metrics from the Shock Society were superior to those of the Association for Academic Surgery and generally for the Society of University Surgeons as well. These data indicate that the Shock Society represents a highly academic and productive group of investigators. For surgery faculty, membership is associated with greater academic productivity and career advancement. While it is difficult to ascribe causation, certainly the Shock Society might positively influence careers for its members