S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case

A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S-matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c /T_F is approximately 0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3 approximately 1.3 where n is the density and lambda the thermal wavelength, which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure

On questions of Fatou and Eremenko

Let $f$ be a transcendental entire function and let $I(f)$ be the set of points whose iterates under $f$ tend to infinity. We show that $I(f)$ has at least one unbounded component. In the case that $f$ has a Baker wandering domain, we show that $I(f)$ is a connected unbounded set

Experimental Results of Concurrent Learning Adaptive Controllers

Commonly used Proportional-Integral-Derivative based UAV flight controllers are often seen to provide adequate trajectory-tracking performance only after extensive tuning. The gains of these controllers are tuned to particular platforms, which makes transferring controllers from one UAV to other time-intensive. This paper suggests the use of adaptive controllers in speeding up the process of extracting good control performance from new UAVs. In particular, it is shown that a concurrent learning adaptive controller improves the trajectory tracking performance of a quadrotor with baseline linear controller directly imported from another quadrotors whose inertial characteristics and throttle mapping are very di fferent. Concurrent learning adaptive control uses specifi cally selected and online recorded data concurrently with instantaneous data and is capable of guaranteeing tracking error and weight error convergence without requiring persistency of excitation. Flight-test results are presented on indoor quadrotor platforms operated in MIT's RAVEN environment. These results indicate the feasibility of rapidly developing high-performance UAV controllers by using adaptive control to augment a controller transferred from another UAV with similar control assignment structure.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N000141110688)National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 0645960)Boeing Scientific Research Laboratorie

Actuator Constrained Trajectory Generation and Control for Variable-Pitch Quadrotors

Control and trajectory generation algorithms for a quadrotor helicopter with variable-pitch propellers are presented. The control law is not based on near-hover assumptions, allowing for large attitude deviations from hover. The trajectory generation algorithm ts a time-parametrized polynomial through any number of way points in R3, with a closed-form solution if the corresponding way point arrival times are known a priori. When time is not specifi ed, an algorithm for fi nding minimum-time paths subject to hardware actuator saturation limitations is presented. Attitude-specifi c constraints are easily embedded in the polynomial path formulation, allowing for aerobatic maneuvers to be performed using a single controller and trajectory generation algorithm. Experimental results on a variable pitch quadrotor demonstrate the control design and example trajectories.National Science Foundation (U.S.) (Graduate Research Fellowship under Grant No. 0645960

NRAS Mutation Is the Sole Recurrent Somatic Mutation in Large Congenital Melanocytic Nevi

Congenital melanocytic nevus (CMN) is a particular melanocytic in utero proliferation characterized by an increased risk of melanoma transformation during infancy or adulthood. NRAS and BRAF mutations have consistently been reported in CMN samples, but until recently results have been contradictory. We therefore studied a series of large and giant CMNs and compared them with small and medium CMNs using Sanger sequencing, pyrosequencing, high-resolution melting analysis, and mutation enrichment by an enhanced version of ice-COLD-PCR. Large–giant CMNs displayed NRAS mutations in 94.7% of cases (18/19). At that point, the role of additional mutations in CMN pathogenesis had to be investigated. We therefore performed exome sequencing on five specimens of large–giant nevi. The results showed that NRAS mutation was the sole recurrent somatic event found in such melanocytic proliferations. The genetic profile of small–medium CMNs was significantly different, with 70% of cases bearing NRAS mutations and 30% showing BRAF mutations. These findings strongly suggest that NRAS mutations are sufficient to drive melanocytic benign proliferations in utero

Air-Combat Strategy Using Approximate Dynamic Programming

Unmanned Aircraft Systems (UAS) have the potential to perform many of the dangerous missions currently own by manned aircraft. Yet, the complexity of some tasks, such as air combat, have precluded UAS from successfully carrying out these missions autonomously. This paper presents a formulation of a level flight, fixed velocity, one-on-one air combat maneuvering problem and an approximate dynamic programming (ADP) approach for computing an efficient approximation of the optimal policy. In the version of the problem formulation considered, the aircraft learning the optimal policy is given a slight performance advantage. This ADP approach provides a fast response to a rapidly changing tactical situation, long planning horizons, and good performance without explicit coding of air combat tactics. The method's success is due to extensive feature development, reward shaping and trajectory sampling. An accompanying fast and e ffective rollout-based policy extraction method is used to accomplish on-line implementation. Simulation results are provided that demonstrate the robustness of the method against an opponent beginning from both off ensive and defensive situations. Flight results are also presented using micro-UAS own at MIT's Real-time indoor Autonomous Vehicle test ENvironment (RAVEN).Defense University Research Instrumentation Program (U.S.) (grant number FA9550-07-1-0321)United States. Air Force Office of Scientific Research (AFOSR # FA9550-08-1-0086)American Society for Engineering Education (National Defense Science and Engineering Graduate Fellowship